Ted Hoffman

bd-from-kg
moral statements are not propositions

Moral statements are declarations that express moral ideas.

A proposition, by definition is that which is expressed by a statement.

A moral statement makes a moral proposition.

Is it therefore correct to state that moral statements are not propositions but are statements that make moral propositions?

longbow: I don't understand how you can say that moral statements aren't true or false but then turn around and say that they are a part of reality.

Any statement is part of reality. That does not entail that they are true.

bd-from-kg If by “a priori proposition” you mean a proposition that can be known to be true independently of any evidence, then yes, all such propositions are analytic.

I don't agree with this. How can a proposition be arrived at without consideration of facts and then the same proposition be analytic?

First you will have to provide an example of an "a priori proposition" then:
(1) demonstrate that whatever ideas it expresses were gained independently of experience (ie through innate ideas or mental faculties)

(2) That it is analytic (ie based on Reasoning or acting from a perception of the parts and interrelations of a subject)

From the above, it should be clear that a priori propositions can not be analytic.

Because there are no moral propositions.

Yes there are dear bd, and here is one:

"Rape is bad."

The following is a moral statement that makes the above moral proposition.

"Mike don't rape your girlfriend because rape is bad."

Note that the existence of moral propositions does not preclude the existence of moral principles.

Longbow

Is this only true about math? Or, are most philosophical subjects this way as well? Obviously, philosophical subjects generally aren't *formal* like math is, but is it true that they are conceptualizations of something that is not tied to the physical world and nonetheless objective? Or perhaps I should back up and ask do you think that mathematics is "objective"?

I know. I'm not talking about that -- that you uttered a sentence -- unless I specifically say so (usually). I am referring to the meaning of the sentence,

I see. So when you say that moral principles are part of reality, you just mean that the statements of them are made. But could moral states constitute an objective conceptualization of something that is not realted to the physical world?

Well "2+3=5" can be applied to the physical world and that is usually our motivation for discussing it. "The Absolute is glissential," is apparently not an attempt to communicate anything, so you could only say that it is or is not about the physical world once meaning is put to it.

I would agree that what "2+3=5" really says is not a statement about the physical world. But, I think the same is true about moral statements even if the statements often include aspects of the physical world. In other words, the reference to the physical world is accidental to moral statements, not essential.

I thought that their being emergent phenomena means that they are caused by events in the physical world. Saying that mental events "exist", sounds more like radical idealism than along the lines of emergent phenomena of physical states of nature. In other words, I don't think that their being the quality of physical objects or the nature of events in the physical world makes them "exist". And, I think that physical objects might exist that correspond to, say, "love" or "hate", but those terms simply do not refer to a certain kind of physical object (even if one does exist that corresponds precisely to that emotion).

Well, for one thing, I think that moral statements are propositions or more precisely that they contain assertions. As for the definition of "reality", just take it for granted for the sake of argument. As to whether that actually is the definition of reality is a matter of looking at how the term is used. Most people would count mathematical truths as "real". When you say that something is "real" or "part of reality" you are usually talking merely about the way things are regardless of whether or not they could be different.

Why do you say this? A sentence about morality is usually a declarative sentence. They are communicative. So, there must be a reason why we must interpret them in a novel way from any other such sentence. Otherwise, we must assume they contain propositions.

Is it not an *assertion* (that is a true or false proposition abotu something) that applying Ockham's Razor is an essential aspect to being rational? If we take this same approach to morality, then we end up saying things like "To be moral is (among other things) to ...." These things are assertions -- they are the moral propositions that you say do not exist.

You cannot possibly be saying that not applying Ockham's Razor could be rational. Would you say that we can define "rational" any way we want to? That would equivocate in practice. I would say "You're not being rational!" And, they would reply with "I AM being rational (according to MY definition)." This would be basically equivalent to the point of contention being "true for them but false for me".

Surely there is a common definition of "rational" that we all must be referring to when we use the term and it either includes Ockhams Razor or it doesn't. But, if that is the case, then the statement you are making above is an assertion. And if this is the model for morality, then moral statements are assertions as well.

I basically agree with all of this, but I fail to see how this implies that these questions aren't normal questions about reality. Of course, one comeback is to say that "reality" is limited to the physical world, but that is arbitrary. And, if it starts turning entire classes of propositions into non-propositions, then we have to abandon such a definition. Regardless of how precise or knowable something like whether or not Ockham's Razor is rational, such a thing is an assertion that is either true or false, and so, I would contend, "real" (or "not real" if it is false).

bd-from-kg

Agnos1:

Sorry for the long delay. A don’t have the time I had earlier for this stuff.

First, let’s get a couple of side issues out of the way.

1. The nature of consciousness

What difference does it make (wrt the subject of this thread) why it’s controversial, or for that matter whether it’s true? One thing at a time.

2. “Hardwired” behavior

None to speak of.

First, I object to your rephrasing my “keeping women in an inferior status” as “dominating women” and “giving preference to members of our own race” as “racism”. Both “dominating women” and “racism” have ugly overtones. It is very easy to interpret “dominating women” as “beating women (or worse) forcing them into abject submission” and “racism” as referring to the Ku Klux Klan, whites-only facilities, lynch mobs, and the like. I certainly don’t think that that sort of behavior is hard-wired.

Second, your comments about not trusting authority is rather ironic here. The reason that you find the claim that such behaviors are more or less hard-wired is that you have heard the contrary from people (such as professors) who have presented themselves as authorities on such matters. In reality I think that you’d have a hard time finding serious scientific research purporting to show that such behavior is not “hard-wired” in the sense that humans (or in the first case men) have a genetic predisposition to behave in these ways.

Actually it doesn’t take a lot of scientific research to verify that these are innate predispositions. One needs only to look at the behavior of actual human beings. These tendencies are so strong in every society that it requires a willful blindness to fail to recognize them. In what civilization have men not kept women in an inferior status? Where has it not been the nearly universal practice to give preference to members of one’s own race? In fact, the only society that has ever even regarded these things as undesirable and taken some steps to combat them is modern western society.

If you say that these behaviors have everywhere been the result of social conditioning, then how did it come to happen that every society has conditioned its members in the same way? History is replete with examples of societies that have differed radically in their organization and prevailing attitudes. It seems inconceivable that they would all have been alike in some important respect by sheer chance. Nor is it reasonable to suppose that some primordial “proto-civilization” was able to influence all of the civilizations that came after it to retain customs and attitudes that do not reflect deep, innate human propensities. Again, when we look at the variety among historical civilizations in so many respects, we are compelled to conclude that any such proto-civilization had very little ability to influence future ones beyond a millennium or two at most.

And of course we have the experience of our own civilization, where the cultural elite has been battling both of these tendencies determinedly for some time. But although their more egregious manifestations have been eliminated in some cases, the attitudes themselves have stubbornly resisted these efforts.

But before leaving this subject, I want to emphasize two things:

A) The fact that a predisposition is “hard-wired” in this sense does not mean that we are all doomed to act accordingly. Upbringing and social conditioning can overcome these tendencies. What’s hard-wired is only a predisposition to act in certain ways.

B) The fact that a predisposition is hard-wired certainly does not imply that it
is morally right. It implies only that in the past it tended to produce success in making new copies of the genes of the individuals who had it.

Now let’s get to the meat.

3. The nature of moral principles.

I do commit to its rationality. I just see no point in simply stating it. This kind of dogmatic declaration rubs me the wrong way. What I was saying was “Enough with the speechmaking. Show me an argument.”

Nonsense. “1 + 1 = 2” is a tautology. “I believe that 1 + 1 = 2” is descriptive. “One should believe that 1 + 1 = 2” is prescriptive.

This isn’t rocket science. Blurring such fundamental distinctions is not conducive to clear thinking.

First, moral principles are not “truths”. Second, tautologies are not a “higher” kind of truth. “1 + 1 = 2” is a statement about the meaning of “1”, “2”, “+”, and “=”. In the final analysis, this is true of all tautologies. “1 + 1 = 2” says nothing about the “real world” any more than “There are no married bachelors” does.

Because it’s not a proposition. For example, “Act and think rationally” isn’t true. Of course, it isn’t false either. Compare this to “Close the door”. Is this true or false?

This is not a trick or a verbal quibble. Morality deals with questions like “How shall I live” and “How shall I treat other people?” Answers to questions of this kind are necessarily of the form “Act in such-and-such a manner”. When one says “You ‘should’ act in such-and-such a manner” one is merely using a different grammatical form to answer the same kind of question. The use of this grammatical form is rather unfortunate, because it is often used to express propositions. And this has misled a great many people into thinking that moral statements of this kind also express propositions, when in fact they are recommending, advising, or approving the course of action in question.

That doesn’t mean that the recommendation or advice embodied in a moral statement cannot be objectively valid. It makes perfectly good sense to say that a piece of advice or a recommendation can be objectively valid. For example, suppose you’re in Chicago and someone says, “I want to get to Texarkana. What shall I do?” The advice “Head south” is objectively valid (though incomplete), whereas the advice “Head north” is objectively invalid. (Of course, moral statement aren’t valid in this simple sense either.)

4. Morality and emotion

Not quite. If “Jonny” is consistent, he doesn’t blame people for having feelings like guilt and remorse; he is dismissing them as irrational. My point is that there is no objective basis for declaring any emotion to be irrational. The fact that certain emotions, which have no rational basis, tend to accompany certain kinds of moral judgments doesn’t mean that the moral judgments themselves have no rational basis. One might as well say that the fact that the triumphant emotions which typically accompany a belief that one’s team has won the big game have no rational basis shows that the belief that one’s team has won the big game has no rational basis.

Certainly they’re a part of it in the sense that whether an act is right or wrong depends (at least in part) on the emotional effect it has on those affected. The emotional effect it has on you is irrelevant. Unless, of course, you consider the feeling of approval that automatically accompanies a belief that an action is morally right an “emotion”. But that’s not very helpful; since this “emotion” is an inevitable result of a belief that an act is right, it cannot also be a guide to or criterion of “rightness” – i.e., it cannot be used to help determine whether an action is “right”.

Absolutely. We could claim that the act was immoral because of the emotional effect on the victims even if it had no such effect on us. For that matter, some things are crimes even if those affected are pleased by it. For example, allowing a child to avoid learning to read and write, etc. might make the child very happy, but it’s immoral just the same. In my opinion it would be immoral to keep him ignorant all his life even if he were also happy through his entire life.

5. Deriving moral principles

Sorry. People recommend books for me to read all the time on this forum alone. I don’t have time to read them all. The reviews at Amazon are not detailed enough to give me a clear idea of what Waals is claiming, or what research his opinions are based on.

Anyway, this is a side issue. The fact that certain kinds of behavior have evolved through natural selection tells us nothing about what moral principles are valid; it tells us only what behaviors promote the propagation of genes. Unless one starts with the premise that the propagation of one’s genes is the highest value, this tells us nothing about what behaviors are morally right.

Such a structure might result in behavior that most people would call “moral”, but how could it “result in morality/ethics”? Morality does not consist of moral behavior, any more than arithmetic consists of people writing things like “1 + 1 = 2”. Arithmetic is how we evaluate whether arithmetical statements are true or false; morality is how we evaluate whether actions are right or wrong.

Also, you cannot at the same time maintain that morality has a rational basis and that animals “display morality” by engaging in behavior based on “structures” that produce predispositions to that kind of behavior. For any kind of behavior to be meaningfully described both as “moral” and “rational”, it must not only be in accordance with valid moral principles, but must be done (at least partly) because it conforms to such principles. Behavior that springs from “building-block structures” that are connected with emotions doesn’t cut it.

OK, one more time: evolutionary theory may be able to tell us why we behave the way we do, but what bearing can it possibly have on whether we ought to behave that way? How do you get from “A genetic predisposition to behave in this way tends to result in reproductive success” to “Behaving in this way is moral”?

I more or less agree, although on reflection I think that it might be better to call a morality based on principles that are (in a sense) universally accepted a “universal” morality rather than an objective one.

What does “detrimental” mean in this context? Obviously this term contains a moral premise. A little later you become ,ore explicit about this:

In the first place, humans have a high degree of empathy only in the sense that they are capable of a great deal of empathy. But this in itself doesn’t imply that they should use this capability to the utmost, any more than the fact that they have the capability to inflict pain implies that they should use that capability to the utmost.

Second, if all that empathy tells us is that other people basically feel as I do, how does that imply that I should try to get them what they want? Perhaps it implies that I should use the similarity of other people’s mental processes to mine to manipulate them into helping me as much as possible. You don’t seem to have grasped the gap between “is” and “ought”.

Let me put the problem in yet another way. Empathy tells me that other people desire that they have a happy life, just as I desire that I have one. This is not really “feeling the same about many things”. What it would mean for someone else to feel the same as I do with respect to my desire to have a happy life would be that he would also desire that I lead a happy life. While such a desire does exist in many people, it is normally very weak compared to their desire to have a happy life themselves. To show that a happy life for me is intrinsically (i.e., objectively) good, and not merely good from my biased point of view, you need to show that other people have a rational reason to desire that I have a happy life.

You’re reifying “good” here. That is, you call anything that has the property of being good from someone’s point of view as part of “the good”. This implicitly assumes that being “good” is an objective property – i.e., that what’s good for one is good for all. This is the very point at issue.

If you mean that certain moral principles will someday be shown to be valid by a sound logical argument, I disagree.

Or at least we may reasonably hope that this will someday come to pass. On this point we are in agreement.

As I’m sure you realize by now, I disagree. Morality cannot be driven by “evolutionary imperatives”. The only real evolutionary imperative is the imperative to multiply one’s genes as much as possible, and this is hardly a moral principle. And by “necessary” I gather than you mean “logically necessary”. But the only things that are logically necessary are tautologies, and moral principles are clearly not tautologies.

Aside from the “like 1+1=2” part I agree with this in a sense. But this is clearly not the sense in which you mean it.

At this point you might want to read the exposition of my own ideas on the foundations of morality which start around the bottom of page 7 of this thread. The essence of my position is that people really do have the same basic goals and purposes at bottom, but this fact is obscured by a radical lack of knowledge and understanding. I believe (and give reasons for believing) that if everyone had enough knowledge and understanding they would regard my welfare as being equally as desirable as their own and act accordingly (and conversely, of course). This is a real foundation for morality. It implies that altruistic behavior is rational in the sense that it is how we would behave if we had enough K&U. And as I also argue, it is rational to pursue the goals that one would have if one had enough K&U (insofar as it is possible to know what they would be) and irrational not to.

bd-from-kg

Not so. Here are several statements that actually express something. None of them expresses a proposition.

1. Close the door.
2. Which way is Winchester?
3. A triangle is a polygon with three sides.
4. Let’s go to the movies tonight.
5. We’ve got to win this game.
6. Oh my gosh!

It’s also possible, of course, for a statement to express nothing at all.

No. Obviously I meant that moral statements do not express propositions.

OK, maybe you’ll believe the Britannica.

On the contrary, only a priori propositions can be analytic.

I deny that this is a proposition.

bd-from-kg

Longbow:

Is any of this really relevant to moral foundations? Unless you can show me where there’s a connection, I suggest that we move on.

But the meaning of a sentence is not part of reality.

Please clarify.

True in a sense. But this is itself a statement about the physical world. It’s not true a priori.

Please clarify.

That was not my understanding. But after checking a few articles, it appears that the term can refer either to phenomena that are not themselves physical but arise from complex physical phenomena, or “higher-level” physical phenomena that arise from lower-level ones. (For example my computer’s “playing” a pretty strong game of chess is an emergent phenomenon in this sense.) I had the latter meaning in mind.

Not at all. Saying that ideas exist would be “radical idealism”. To say (for example) that emotions exist is just stating an obvious, straightforward fact. Of course, saying that anything (like the chair I’m sitting on) exists is an interpretation of reality, and thus in a sense isn’t perfectly straightforward.

Come again?

Please clarify. But first, are you going somewhere relevant with this?

(1) What do you mean by saying that they contain assertions? How is this different from saying that they express propositions?

(2) Assuming that you do not consider moral statements to be tautologies, what would constitute falsifying evidence?

You don’t get to specify how I define terms. I find my definition far more useful than yours.

Used by whom? “Ordinary” usage is often confused and inconsistent. That’s why the definition of “reality”, like that of a lot of other terms, is the subject of a lot of debate among philosophers. After due reflection, philosophers often decide on a clear, consistent meaning that agrees with ordinary usage in many respects. but it can’t agree in all particulars because of the confusion and inconsistency of ordinary usage.

I often talk that way myself when I’m doing mathematics. Anyway, "what most people think" is irrelevant for the reasons mentioned above. Philosophers are divided. Some say that mathematical “objects” (such as numbers) are “real”, others say they aren’t. I’m not sure what it would mean to say that a truth is “real” as opposed to “true”.

Not so. Of course, I can’t speak for others.

True enough. And I would love to learn of a reasonable interpretation of moral statements as expressing propositions (whose meaning is independent of who utters them). Feel free to offer one.

What would count as falsifying evidence for the statement “Applying Ockham's Razor is an essential aspect to being rational”? So far as I can see, nothing whatsoever. So it is not a synthetic proposition. And it is obviously not an analytic proposition. So if it is a proposition, what kind of proposition is it?

On the contrary. But the statement that rejecting Occam’s Razor is irrational does not express a proposition.

Not so. For example, have you heard of presuppositionalism? There are also some insane people in the world. And even if we did all agree on a definition of “rational”, that wouldn’t make it objectively correct.

If it’s impossible even to say what Occam’s Razor and the Principle of Induction assert, how can they be propositions? If one cannot imagine any evidence that would falsify them, how can they be statements about reality?

I don’t say that reality is limited to the physical world, but what does that have to do with it? What part of “reality” are Occam’s Razor and the Principle of Induction about?

Why? More precisely, what’s wrong with deciding that a number of statements that appear at first sight to express propositions really don’t? Isn’t that exactly what Hume, Ayer, and a number of more modern philosophers have done?

Fine. I ask for the last time, what is the criterion for judging its truth or falsehood? What would constitute falsifying evidence? What is it, operationally speaking, that it asserts?

My own position is that things like the Principle of Induction and Occam’s Razor are metaphysical axioms, and that metaphysical axioms are not propositions. (Actually calling them “axioms” is a bit misleading since, as explained earlier, I think they are properly formulated as principles of action.) For a more detailed explanation of this idea see the old thread <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=21&t=000384" target="_blank">On the nature of metaphysical axioms</a>.

[ September 25, 2002: Message edited by: bd-from-kg ]</p>

Longbow

Yes. You sound as though you are something of an Empiricist. It sounds like moral philosophy (and for that matter all of philosophy), according to you, is not going to really be a legitimate pursuit of knowledge. I, on the other hand, am a conceptualist. I think that math an philosophy are both a priori pursuits of knowledge. In particular, moral statements do actually contain propositions that when true are part of reality. Because of your view of what reality is, I think you are incorrectly characterizing moral philosophy.

And if you want to know where this discussion is likely to end up, then, I think that the root of this view lies in the fact that philosophy is informal while math is formal. It will likely become my contention that you are basically reacting to this fact by doubting the legitimacy of philosophy as it is traditionally practiced. I will say that it is really just how big a role “philosophical vagueness” plays in the subject matter as to whether or not something is formal and that really does not affect its nature as being an analysis of propositions.

I don’t know for sure that any of this will come to pass because it is hard to figure out where you stand exactly. But basically if you are a positivist or empiricist, then this is the likely direction the discussion will go in. (I’m trying to figure out how much of one you are…)

Of course, by this you mean not part of the physical world. I agree that it is not part of the physical world. If you are using my definition of “reality”, then I do think that you can have propositions about propositions.

As you will see, my view is that there is a physical world of things that “exist”. But, “reality” is not limited only to that which “exists”. Reality is also not only that which is the case as opposed to some other counterfactual possibility but also that which is the case because it must be the case. In other words, reality is simply that which is the case whether it is a logical necessity or not. And furthermore, almost all declarative sentences state assertions or in other words have propositional content. What makes certain of them meaningless are deliberate attempts to make such sentences up. What makes some of them “subjective” has to do with an implicit reference to the author of the statement. (For instance, “Jazz is good music,” is “subjective” because it really means “I, the author of the statement, like jazz.” When it doesn’t mean something like that, it ceases to be “subjective” and becomes an objective aesthetic statement about some technical aspect of the music.)

I exist. My chair exists. That I am sitting in my chair does not “exist”. Instead it is “the way things are”. Now it is entirely about things that exist (me and the chair), but the fact that I am in the chair is not, itself, a physical object. Only physical objects “exist”. (And, for that matter, that which exists is called a “physical object” according to me.) This is one reason I say that “reality” is more like “that which is represented by all true propositions” rather than “that which exists”. It is part of reality that I am sitting in a chair, but that I am sitting in a chair does not “exist”.

The only real difference between an assertion and a proposition is that someone actually claimed the assertion to be true as I am using the terms. I use them interchangeably for the most part. I do not think that what I believe to be moral propositions are tautologies. And I do think they are a priori, so evidence is irrelevant. So I guess I am saying that they are ultimately derived from synthetic a priori propositions.
Right. The main thing is that it is usually not a convention. They have to use the relevant definition to the discussion that gave rise to the issue. It is usually an outgrowth of common usage because typically the problem and the discussion surrounding the problem that the term comes up in is all based on informally posed questions that most people ask themselves.

Well you can figure out what it would mean to people that don’t define things as you have. Like I say, what most people think of as being “reality” is “that which is”. Perhaps this is where you get the identification to the physical world by interpreting “that which is” as “that which exists”. Actually, I think to get all of reality, you have to be able to interpret it more broadly than that as meaning more like “that which is the case”.

“Truth” as in a true proposition is not a physical object. It is part of “reality” in that one can formulate assertions about it. The whole subject of numbers being real is really the problem of universals. I am a conceptualist. I am not a nominalist who believes that numbers are names for classes of objects (e.g. 7 refers to the collection of all collections of 7 things, “blue refers to the collection of all blue things, and so on). I am not a realist who thinks that numbers “exist” like physical objects. However, I do think that statements about numbers can be true or false in the ordinary sense of the words which (I say) means that they are “real” and that statements about them express some aspect of “reality”.

Well, first of all, of course I have my own view of what morality is. But before I launch into that, the lack of such an interpretation should not imply that none is possible. In other words, if you agree with what I said, then you must either furnish an argument that actually shows that moral statements do not express propositions or you must assume they do, even if you don’t know what those propositions really are.

Furthermore, I will say that my moral philosophy is certainly disputable. Perhaps I have not really captured the relevant “definition” of “morality” in some cases. That doesn’t mean there isn’t one, and we must generally assume there is.

But, without further adieu, I have a deontological moral world view that is not too different from the Kantian idea of respect. It is my contention that the principle of universalizability alone gives us an objective notion of “justice”. (When I speak of the principle of universalizability, I am referring to what is often called a “thin” concept of morality with it as opposed to some of the thicker notions that Kant, for instance, might suggest.) Perhaps a general way of characterizing my views as to say that morality is basically about impartiality. It’s not that different from a Kantian view, but I would hate to besmirch his name with my views.

It is an a priori proposition. And I guess I would say that it is “synthetic” in that it is derived from other synthetic a priori propositions. The reason these propositions are “synthetically” true is because it is impossible for them to be false rather than that their predicates are contained in their subjects. It is actually entailed in the meanings of terms and the subsequent ideas that are being considered, but no one of the statements, themselves, is necessarily “analytic”. Perhaps this should be considered analytic, but I think that Kant thought of this as being synthetic.

For instance, in the classic example of a synthetic a priori proposition: “I think”, I used to say that it is really analytic because “think” is actually contained in “I”. But then, it is often retorted, things like “Will you be thinking when you’re dead,” or “Do you cease to exist when you stop thinking,” that sort of thing. Then, perhaps that I am thinking is not contained in the “I”, but is instead a necessary fact if I am considering the proposition “I think”. Perhaps you will say that you observe that you are thinking when you are thinking about “I think”. Whether that is true or not, I think you can know that you must be a priori, so I do think that “I think” is a priori true.

Anyway, this sort of thing could digress into a huge discussion that is actually probably not that relevant to my view but maybe more central to yours. What is more important is that morality is a priori. I think that the reason the whole synthetic/analytic dichotomy can become important is if you actually make the criticism that moral statements cannot be analytic and so cannot be a priori.

I didn’t say that our agreeing on it makes it correct. I am saying something more like that it being correct makes it “the definition” that we must be using when we talk about it.

If reality is not limited to the physical world, then what else is there, according to you? Ockham’s razor is about epistemology and informal logic – what constitutes knowledge and what constitutes justification. Like you said, they are bout being rational. You can always ask, “But, what’s that about,” but I don’t think the lack of definition is that meaningful. It is enough that you have some idea of what it is about, and we certainly do. The simple fact that we can talk about it means that we do.

This probably goes back to the lack of formality, I think. Is it the lack of a precise definition that you have a problem with? Is that why you are saying that these topics have no propositional content?

Well, that’s what they have done, but not very convincingly. In general, there is nothing wrong with it if you recognize where your burden of proof lies. And specifically, with regard to Ayer, for instance, you have to be able to square your interpretation of language with common usage. I am not saying that it has to be the same as common usage, but in some sense, it has to remain faithful to it. In other words, you are rendering yourself irrelevant if you are not coming up with the “correct” (as we were talking about it above) definitions of terms.

For instance, the whole discussion about what “reality” is presumably has some relation to common issues about reality. You cannot just be speaking your own private language to yourself. Otherwise, nothing you say is relevant to what I say and unbeknownst to me, everything I am saying is non sequitur to what you are saying. Ultimately it comes down to what you really mean and how that relates to what other people mean when they talk about the same subjects. So, using your own terminology is one thing, but on some level we have to be talking about the same thing.

So, much like applying Ockham’s Razor, you must come up with the most faithful interpretation of the topic. It is similar to interpreting the law. Often the law is inconsistent, so the idea is to come up with the most consistent interpretation of the law that is as faithful as possible to the legislators’ intent. It is the same with all of these: interpreting language, interpreting the law, interpreting evidence. If you start to add gratuitous propositions, then you are begging the question on those extra assertions. There is no particular reason to believe them. If our interpretation of everything results in a bigger violation of the relevant usage than mine does, we must reject yours in favor of mine.

Especially with your mentioning Ayer, this sounds like logical positivism. Do you adhere to the principle of verification? Are you aware of the criticisms of logical positivism? And with regard to moral philosophy, I believe even the logical positivists believed they had the burden of proof to show a different interpretation of ethical terms that results in moral statements having no propositional content.

[ September 25, 2002: Message edited by: Longbow ]

[ September 25, 2002: Message edited by: Longbow ]</p>

bd-from-kg

Longbow:

I’m afraid that this post is a bit on the long side. The issues that you raised are pretty fundamental and I haven’t discussed some of them before. Hopefully after this we’ll be able to zero in on the important issues that we actually disagree about.

1. What are we talking about?

Ultimately what we’re talking about here is the meaning of moral language – e.g., what it means to say “X should do Y”. But we immediately come up against the problem that there is no such thing as an “objectively correct” meaning of a word or phrase; there is only “how it is used”. Anyone can define “should” to mean whatever he likes, but if we want to use words to communicate it is advisable to try to use them in ways that correspond to the way other people use them. Thus if we want to discuss something that most people would recognize as “morality” we are not free to simply make up any definitions we please; we must pay attention to common usage. As you say:

Unfortunately, in the case of philosophical issues, taking “common usage” as a guide is not terribly helpful in many cases because most people have confused, inconsistent, or mistaken notions about the subject. (That’s why it became a philosophical issue in the first place.) Thus it is often more helpful to look at the internal logic of ordinary usage than it is to look at typical “definitions” offered by ordinary people.

An example of the kind of problem that can arise in trying to use language in ways that correspond to ordinary usage can be seen in common statements about the sun’s relationship to the earth. Thus it is often said (in fact we’ve all said it lots of times) that the sun is going to “rise” or “set” at such-and-such a time, or that the sun “rises” in the east. Today we know that this language is technically incorrect, but let’s imagine that we are living around 5000 B.C. and happen to know the true state of affairs, but that the vast majority of people believe that the sun really goes around the earth. We might therefore propose to interpret statements to the effect that the sun will “rise” at a certain time as meaning that it will be below the horizon shortly before that time and above it shortly afterward. But at this point Smith might object that this will not do, because this interpretation clearly does not “square with common usage”. We might then explain to him the true state of affairs. At this point Smith might argue that, given that the sun does not go around the earth, the ordinary way of speaking is simply meaningless, and that it is pointless to try to “interpret” it at all. At this point we might reasonably say that, although this language is based on a mistaken conception of “the way things are” it is nevertheless meaningful; it refers to a reality about the world. Thus if someone says that the sun is going to rise tomorrow at such-and-such a time, it is more sensible to interpret this as a statement about when the sun will be above the horizon rather than to dismiss it out of hand as meaningless.

In the kind of issues dealt with by philosophy, ordinary usage is often meaningless in a similar way, except that the meaninglessness arises from conceptual confusion rather than erroneous beliefs about the “real world”. For example, people often say that someone acted “of his own free will”. If they are asked what they mean by this they will generally give an account that is clearly incompatible with determinism – i.e., they are referring to what is often called “libertarian” or “metaphysical” free will. But careful analysis shows that this concept is logically incoherent. Yet when people say that a person acted “freely” they are clearly referring to something significant. It matters whether a person acted freely or not; it is morally significant whether the circumstances were such that an agent would generally be said to have acted of his own free will. The task of the philosopher is to discover just what this difference really consists of and explain why it matters – why it is a morally significant difference.

So yes, if one wants to be “relevant”, one must “square” one’s interpretation with common usage. But as these examples illustrate, what it means to square an interpretation with common usage is not entirely straightforward. It certainly does not consist of asking people what they “mean” and accepting that as the correct interpretation. It means analyzing how the relevant language is actually used and finding a consistent, meaningful interpretation that is as consistent as possible with this usage. If common usage is based (as it often is) on misconceptions and logical confusions, no interpretation can be completely consistent with common usage. Sometimes it’s not clear which of two or more interpretations are “most consistent”, or at any rate it’s a pretty close call. In such cases it is legitimate to consider factors such as simplicity, usefulness, and fecundity.

2. On the burden of proof

In response to my question of what’s wrong with deciding that some statements that appear to express propositions really don’t, you said:

This may or may not be reasonable, depending on what you mean by “burden of proof”. If you’re demanding a positive demonstration that there is no possible interpretation of a statement as expressing a proposition which bears any reasonable relationship to common usage, it’s absurd. Obviously it is never possible to demonstrate anything of the sort. But in philosophy we are not dealing with such questions for the very first time; they have been discussed for hundreds if not thousands of years. In most cases of interest, a number of interpretations of such statements as expressing propositions have been proposed. A reasonable requirement is that it should be shown that each of these proposed interpretations fails for one reason or another. As I put it on another thread (with respect to the meaning of “X should do Y” (when “should” is used in a moral sense):

If this is what you mean by the “burden of proof”, I have no quarrel with it.

3. On what “exists” and what is “real”.

Applying the “common usage” criterion to the question of what “exists” is straightforward in cases like snails, trees, yeti, aliens from Arcturus, or unicorns; we all understand what it means to say that such things exist. Beyond that, things get murkier. Some people apparently deny that emotions exist. Some question whether the past can properly be said to exist. So it’s not surprising that there is disagreement about whether the natural numbers can be said to exist. In all of these cases the problem with taking common usage as a guide is that we are taking the term beyond its original domain where the meaning is clear and straightforward, and trying to apply it to more “fuzzy” areas where there is no clear consensus. At this point considerations of consistency and utility come into play.

The same kind of problem appears in trying to interpret what it means to say that something is real, or “part of reality”. Some people take the position that saying that something is “real” or “part of reality” means the same thing as saying that it “exists”. You prefer to make a distinction. And on this point I agree with you. Thus, the relationship between me and the chair I’m sitting on does not “exist”, but it is “real” or “part of reality”. This corresponds much better to the way such words are normally used.

As you may recall, I accepted your definition of “reality” with one modification. Instead of saying that “reality” is "that which is represented by all true propositions" I suggested defining it as “that which is represented by all propositions which are true in this world, but not in all possible worlds.” This easily includes things such as the relationship between me and my chair; in other words it admits a great number of things as “real” which cannot properly be said to “exist”.

In fact, on reflection I’m not at all sure that there is any substantive difference between your definition and mine. The only difference in the definitions themselves is that mine excludes tautologies. But tautologies cannot properly be said to “represent” anything, so excluding them does not exclude anything from “reality” that would be included by your definition.

But I gather that you don’t agree that analytic statements don’t “refer” to anything. Specifically, you point out that they refer to numbers. Thus:

Certainly statements about numbers can be true or false. But I fail to see how this implies that numbers themselves are “real”. Your reasoning seems to be that “1 + 1 = 2” is a true analytic statement about the numbers 1 and 2, therefore it refers to “1” and “2”; therefore “1” and “2” are real. But the same reasoning can be applied to unicorns. Thus “Unicorns have a single horn” is a true analytic statement about unicorns; therefore it refers to unicorns; therefore unicorns are “real”. Now if your answer is “This is perfectly correct; unicorns are real – they just don’t exist”, we don’t have a serious problem; you just use “real” in a nonstandard way. But if you say that there’s something wrong with the latter argument, you’ll need to explain what the difference is between these arguments that makes the former sound while the latter is not.

4. On “synthetic a priori” propositions

It seems that you are determined to say that moral statements express propositions. but since (unlike many of the people in this forum) you recognize that they cannot be expressing either analytic or empirical propositions, you are forced to say that they express some other kind of proposition.

But it’s hard to see what other kind of proposition there could be, because analytic and empirical propositions between them seem to cover all of the logical possibilities. To see this, suppose that a proposition is not analytic (or self-contradictory). Thus there are logically possible worlds in which it is true and other logically possible worlds in which it is false. So in order to determine whether this world is in the first category or the second we need information about it. In other words, we need evidence. But to say that it cannot be determined whether a proposition is true or false without looking at evidence is to say that it is empirical.

In spite of this seemingly airtight argument you say that there is another category of propositions, which (following Kant) you call “synthetic a priori” propositions. By an “a priori” proposition you mean one whose truth can be determined independent of any evidence. but a synthetic proposition is one that entails actual information about the world – i.e., that something is true which is not a tautology. You explain this idea as follows:

Now the notion of analytic statements as statements whose predicates are “contained” in their subjects has a respectable philosophical pedigree, but it seems to me to be basically meaningless. For example, consider “Either (A and B), or not-A, or not-B” This is clearly an analytic statement. But what exactly are the “subject” and the “predicate”? In what sense is the predicate “contained” in the subject?

It seems to me that a much better definition is the one used in formal logic: a statement is analytic if it is logically impossible for it to be false. Or equivalently, it is analytic if there is no model in which it is false. (The equivalence of these definitions is guaranteed by Godel’s completeness theorem.) But this is exactly your definition of “a priori” propositions.

Another perfectly good definition of an analytic proposition is that it is one whose truth is entailed by the meanings of the terms involved. But you seem to consider this as well to be a defining characteristic of “synthetic a priori” propositions:

However, I have no idea what you mean by “the subsequent ideas that are being considered” or what statements you’re referring to when you say that they are not necessarily analytic, so I’m not really sure what to make of this.

These comments seem to get us nowhere in terms of understanding how there could be a proposition which entails real information about the world but which can be known to be true without evidence. So let’s turn to your alleged examples: Occam’s Razor and “I exist”.

A) Occam’s Razor

As I pointed out earlier, it is impossible to say what it is that Occam’s Razor supposedly asserts. This isn’t just a matter of being “fuzzy”: it’s impossible to specify any statement about the real world that it entails. For example, it does not say that a simpler hypothesis is more likely to be true than a more complicated one. In fact, it’s impossible to say what it means say that one scientific hypothesis is “more likely to be true” than another. (In fact, it’s impossible even to say what it means to say that a scientific hypothesis is true.) What is says is that the simpler hypothesis is to be preferred to the more complicated one. But this is not a statement of fact; it is more in the nature of a recommendation

It’s also impossible to say what it means to say that it’s “true”. In other words, it seems to me that Occam’s Razor would be equally valid in any possible world, which means that it says nothing about the nature of the world.

I gather that your answer to this would be that the mere fact that Occam’s Razor is a valid principle in all possible worlds doesn’t mean that it says nothing about the nature of the world. But try as I might, I can’t make any sense out of this notion. If an alleged proposition does not “divide” possible worlds into two nonempty classes - those in which it is true and those in which it is false - it is empty: it has no informational content. But the only true empty propositions are analytic ones - i.e., tautologies. And tautologies are true merely by virtue of the meaning of the terms that appear in them, so they say nothing about the nature of the world.

B) “I think”

Unlike Occam’s Razor, it’s clear enough what “I think” means, even though its meaning is basically impossible to define. (It’s inevitable that the process of defining concepts in terms of simpler ones must eventually terminate in concepts that are absolutely basic – they cannot be defined in terms of anything simpler still. But that doesn’t mean that such concepts are meaningless; otherwise we would have to conclude that all concepts are meaningless. In the case of “I think” we seem to be dealing with two absolutely basic concepts: “I” and “think”.) It’s also clear that it’s possible for it to be false in the sense that there are logically possible worlds in which it is false. Finally, it’s clear (or at least it seems to be) that I don’t have to look around for evidence that i exist; I “just know”. So have we arrived at last at a “synthetic a priori” proposition?

Not really. It just seems that way because it’s a conclusion I reached so long ago that I can’t remember doing so, or the process by which I reached the conclusion. Indeed, my mind was in such a primitive state at the time that it’s something of a stretch even to say that I “concluded” that I exist, and the process involved had nothing to do with “reason” as it is normally understood. But this is true of many other “conclusions” that I reached around that time. The most important and relevant of these was that there is an “external world” or external reality. Now the process by which I “concluded” that I exist and the one by which I “concluded” that there is an external world were actually the same process. The realization slowly dawned that some of the things perceived could be manipulated or controlled by an “act of will”, while others couldn’t. (Later it was learned that these things were parts of what was called my “body”.) Much later it was found to be a productive explanatory hypothesis that the things that could not be controlled directly included objects that appeared to “control” their own movements. And still later the realization dawned that some experiences (such as seeing trees, chairs, etc.) were shared by these “self-controlled” objects, while others (like pain, anger, likes and dislikes, memories) were not – or at least, not with any consistency. Eventually the things that could be controlled directly and the aspects of experiences that were not shared by self-controlled objects came to be thought of as “me”; the former constituted my “physical” self and the latter my “mental” self or consciousness. At a very early stage this became such a fundamental, essential part of the conceptual framework that was developed to make sense of experiences that it came to seem “self-evident”. No conceivable evidence, it seemed, could shake the conviction that there is an “I” – a “self” – who is having these experiences, distinct from the experiences themselves. But in fact this belief is based on evidence: the evidence of my earliest experiences.

But that’s not the end of the story. One of the most striking conclusions that seems to be arising from the rapidly developing science of consciousness is that there really is no “I” – that the “self” is an illusion. I don’t want to get into this in detail here. The point is that the fact that this question can even be asked shows that “I exist” is indeed an empirical hypothesis, and that it might conceivably be false. Whether it’s true will ultimately be decided by the evidence. So this is very far from being an a priori proposition.

This shouldn’t be too surprising. Many of the things that Kant proposed as “synthetic a priori” truths have turned out to be either ordinary empirical propositions which in fact are false, or analytic propositions. The theorems of Euclidian geometry are a good case in point. Kant thought that these were clearly “synthetic a priori truths”. But it is now clear that this was a mistake. Taken in one way, Euclid’s theorems are analytic truths: his system can be rigorously axiomatized, and the theorems can be shown to follow logically from the axioms. But the axioms can also be interpreted as assertions about physical reality, and when taken in this way they are false. Either way they are not “synthetic a priori” truths.

5. Your moral theory

So far you haven’t said much about your own moral theory. What you have said is this:

Some comments:

i) Certainly any “reasonable” theory of morality has to involve impartiality. But as has often been noted, this concept can hardly be “all there is to it”. One can impartially consign everyone (including oneself) to eternal torment, or make everyone incredibly happy but stark raving mad, or ... but you get the idea. In addition to impartiality there has to be at least one positive principle. This seems to lead unavoidably to the idea of an “intrinsically good” state of affairs. And as soon as actions are judged “right” or “wrong” at least partly on the basis of whether they tend to lead to or produce such a state of affairs, one no longer has a purely deontological theory; it is at least partly consequentialist or teleological.

ii) This is all rather vague at this point. you haven’t offered an actual statement which supposedly expresses one of those “synthetic a priori” moral propositions that you’ve talked so much about. And this gets you off the hook (for the moment) in terms of explaining just how we can know without evidence of any kind that such a proposition is true.

iii) Finally, there is a problem inherent in all moral theories that try to interpret moral statements as expressing propositions. How do you get from “You should do X” to “Do X”? The first (in your interpretation) is simply a declarative sentence, like “Grass is green”, while the second is an imperative or injunction. To put it another way, the question “Why be good?” is unanswerable in terms of your theory. It yields no motive or purpose for “doing the right thing”; all that it does (at best) is to identify what “the right thing” is.

6. My moral theory

I think that you have some basic misconceptions about my theory. For example, you say:

That depends on what you mean by “knowledge”. But I emphatically do not agree with Ayer that moral statements are fundamentally nonsensical. That was the point I was trying to make in my discussion of Occam’s Razor. This principle (in my opinion) does not express a proposition, but it is certainly not nonsensical. It expresses a universally valid fundamental principle: that one should always prefer the simplest explanation consistent with the facts. What exactly is the sense of the “should” here? That’s impossible to define. One can say that it means that it is irrational to prefer a more complicated explanation to a simpler one, or that Occam’s Razor describes what rational people do. But these are just different ways of saying the same thing; they just substitute the undefined term “rational” for the undefined term “should”. I prefer to say that Occam’s Razor is a valid principle of action, but once again we have an undefined term: “valid”. It seems that we have reached a very fundamental level here where it is impossible to go “deeper”; the terms “should”, “rational”, and “valid” are all pointing to the same indefinable concept. Yet everyone who is not insane recognizes the validity (or rationality if you prefer) of Occam’s Razor even though no one can define just what it means to say that it is valid, or that it is irrational to reject it.

My position is that some moral statements are like Occam’s Razor in that they can be derived from principles of action that a sufficiently rational person with enough knowledge and understanding will recognize as valid. When people say that a moral statement is “true” they really mean that it is in this category. (but only in the same sense in which, when someone who believes that the sun goes around the earth says that the sun is going to rise tomorrow morning, he “really” means that it will appear above the horizon for the first time in several hours.) But ordinarily when we say that a declarative statement is “true” we mean something quite different, namely that it expresses a true proposition. And as we have seen, true propositions come in only two flavors: analytic and empirical. Analytic propositions are tautologies, while empirical ones say something about the “real world” – that is, there are logically possible worlds in which they are false. It seems clear that moral statements are neither analytic nor empirical, so they cannot be properly said to express propositions. This has led some, like the logical positivists, to dismiss them as meaningless or as merely expressions of emotions or attitudes. But this is as wrongheaded as saying that Occam’s Razor is meaningless or merely an expression of an emotion or attitude.

This kind of misunderstanding arises from trying to analyze moral statements as expressing propositions. Once we recognize that they actually express of principles of action (or things that can be derived from such principles) this difficulty vanishes and the way is open for interpreting them as meaningful and (in some cases) universally valid.

7. The relationship between our theories

Actually we are not as far apart in our views of morality as might at first appear. You say that valid moral principles are synthetic a priori propositions; I prefer, for technical reasons, to say that they are not propositions at all but valid principles of action that any sufficiently rational person with enough knowledge and understanding will recognize as such. The similarities here are obvious. In both cases we say that moral principles cannot be derived or proved from facts about the world, but that nevertheless a sufficiently rational person with enough understanding should be able to “just see” that they are valid.

[ September 28, 2002: Message edited by: bd-from-kg ]</p>

Longbow

Agreed. That is part of the philosophical problem. You must identify the problem as well as solve it. It is common to come up with novel interpretations of what moral statements "really" mean. If this plays a significant role in one's view, then the relevance of their conclusions based on such an interpretation is going to play a significant role. In the case of what moral statements mean, the first thing we must do if we are not interpreting them like we would normally interpret similar statements (i.e. declarative sentences) is explain why.

I am not sure. I think this is going to be one of the issues that will have to be handled on a case by case basis. What you are saying is generally about right by my estimation. But, I am not sure that you can always just assume a new interpretation when you have disproved the others. Your interpretation might be just as faulty or nonintuitive. You might have to just not know what the statements really mean.

Also, if you have a precise interpretation while others are informal and imprecise, then I do not think that gives your interpretation any more credibility (necessarily). Ultimately, a big part of the problem of understanding morality is to correctly identify the concepts. As part and parcel with understanding the true nature of moral concepts, you will always have to quarrel over the relevance of the concepts you imagine to those that most people are alluding to when they make moral statements. All-in-all, it's a big philosophical issue that cannot be easily averted.

Okay, well, I don't think that "unicorns are real" which I think means "physically exist". I think that they exist as concepts but perhaps not "in reality" (which again means "physicallt exist"). I do think "that unicorns have one horn" is part of reality. If you are talking about a unicorn then you are talking about something with one horn. You cannot be talking about what everyone understands as being a "unicorn" and somehow end up showing that it has two horns or no horns.

I also think that the term "unicorn" refers to a concept and that it is more than just an arbitrary part of the definition of the term that such a concept includes the aspect of having one horn. Even if you went to a land where everyone used the term "unicorn" to refer to some other thing, there would still exist the concept of essentially a one horned horse. And, you could say to yourself and others that such a thing does not exist

Actually, it is more like that you refuse to allow the possibility of another kind of proposition that you must come up with the itnerpretations of morality that you do. I am not actually saying that there is another kind of proposition. It just seems like there are because of the existence of subjects like mathematics, morality, epistemology, logic, etc. These subjects seem to be completely a priori. But, they are not obviously a matter of just semantically deriving results either. Especially in the case of mathematics, it would seem that assuming that mathematics is analytic would suggest that one would have some set of precise definitions that covers all the areas of mathematics from which one could formally derive all that follows in mathematics.

Strictly speaking, the statement is "'Either (A and B), or not-A, or not-B' is true". And actually, I think that the predicate is actually what appears to be the subject, namely 'Either (A and B), or not-A, or not-B'. The definition, then, of "true" or of "truth" would entail the standard rules of logic. Now, that may sound like I'm reaching, but it actually is a pretty straightforward response. Sometimes the entire area of semantics is characterized as aimed at answering the question "What is 'truth'," and otherwise defining the term 'truth'. And, in fact, the kind of formal statement you are using is very intimately connected with such discussions of semantics.

In any case, the sentence you are coming up with is either true "by definition" or it isn't. If you are going to say that there is more to its truth than just the definition of "truth", then you are, in a very profound way, endorsing the possibility of what philosophers often characterize as "the synthetic a priori". And for that matter, if you think the definition of "truth" is not arbitrary, I would argue that you have to accept such a possibility. So, the question back to you, then is how would you prove that such a statement as you give is true? Would you go back to the three formal laws fo logic and leave it at that? Suppose that someone questions the veracity of those laws? What then?

Would you argue a case beyond that or would you just stop talking to them? If you just stop talking, then perhaps you can accept that the statement is true by the definition of "true". If you think that you can say things like "it wouldn't make sense of being meaningful to say otherwise," then it seems to me that you are implicitly accepting what Kant would say is the synthetic a priori. What you are doing is sort of "backing into" the truth of some proposition informally by determining that it is essential to the enterprise you are already engaging in. That makes it not just a derivative of some arbitrary definition you have come up with but a much more profound statement about "the way things are."

That's why I use an alternative definition of "analytic". The term is meant (especially by Kant) to distinguish it from "a priori". If you merely define the distinction away, then there is a problem with that in terms of its relevance to other philosophical issues. But, if you are willing to accept the possibility of what Kant calls a "synthetic a priori" proposition, then it is really a moot point.

The main reason I asked you if you thought math was analytic was not to ask you if you thought it was a priori. What I am driving at might be almost characterized as asking you if you are a Logical Positivist. There is a distinction, I think, among logical positivists between the terms or otherwise saying something like that their position is characterized by the rejection of the possibility of a synthetic a priori proposition wouldn't really be all that meaningful. And this is exactly the sort of thing I think one of them said, for instance. (I am too lazy to get the quote, but I think it was Carnap that said it.)

In any case, the real issue lies in "how true", for instance, you think the laws of logic, say, are. If you think that they are just an arbitrary construct, then I think you are much more in line with the outlook of positivism and empiricism. If you think that there is more to it than that -- that it is nonsense to question them -- then I think you are starting to digress from such a view.

That has been a problem for quite sometime in the history of philosophy. Empiricism is so intuitively appealing, but it has this problem of philosophical skepticism that plagues it. Hume was certainly plagued by it and, I think, that everyone runs into a variation of the "skeptics paradox". The positivists have the criticism of verifying the principle of verification. Wittgenstein talks about his philosophy in the Tractatus as being a ladder that you use to climb out of such considerations with and then discard. The approach has always been to bootstrap your way into it, and I don't think you can do that in philosophy. Instead you need to create a foundation that everything rests on, so if there is a point where things are coming out of thin air, then that is your foundation: thin air.

I don't see why. The discussion of whether or not something is true is a conceptual discussion. You are looking at concepts and saying something about them. This is true even when you are talking about the physical world. You are saying that the notion that there is a chair under your butt is "true". You are not saying that the sentence "There is a chair under my butt," is considered "true" but that the proposition it represents is true.

The direction you are headed is to do away with propositions and replace them with sentences. You are not going to say anymore that: 2+2=4. Instead you will say: "2+2=4" is "true". Of course that statement, itself, is conceptual, so we are back to the issue of philosophical skepticism. (I am fairly certain you will contest this paragraph, but I am not sure in what way.)

That is what is meant by "the subject is contained in the predicate" -- that if follows from the definitions of the terms within it. It seems like it is even possible, actually, to get a statement that is true sort of "by definition" but not just by the definitions of the terms it contains. I don't know if this would be considered "analytic" so much as just "semantically true". And in any case, I am not sure if there isn't something that could be more conceptually true on a priori grounds. It certainly seems to me that something like the rules of logic aren't really negotiable, for instance. Sure you can formally play with the three laws, but that isn't philosophically meaningful, I don't think. In other words, it isn't as though we really could reject the laws fo logic. But on the same token, if I say this, then I am saying something about the world -- not the physical world, but about the way things are in any case. It is much more substantial than what follows from an arbitrary set of definitions.

And, incidentally, I think it sounds like you wuold say a similar thing since you say that these analytic truths are so because they are true in all possible worlds. It sounds like you are saying they are universally true. Perhaps, you just mean that you find it expedient to assume them independently of the world you happen to be in.

Okay, here you are making a pretty straightforward error in confusing the proposition "I exist" with "I know that I exist". You are telling me how you came to have the belief that you exist. That would be relevant if we were trying to figure out whether you know that you exist or just believe it, but it doesn't help us know if you actually do exist or not. And, furthermore, you seem to be saying that you don't know that you exist since you came to have that belief a long time ago before you could formulate rational arguments or "know" anything.

That should indicate that such a discussion is irrelevant to the proposition "I exist." Perhaps you had the belief before you even knew what a "belief" was, but that doesn't mean that know that you do know what a belief is, you cannot go back and figure out how you know that you exist. Now, we certainly are well-developed minds that can know that "I exist". This proposition seems true -- why? Not why does it seem true or why do we believe it to be true -- why is it true?

I don't think that is quite right. I am nto saying that you cannto have other geometries, I am just not sure that Kant thought you couldn't either. And, in any case, there is a limit to what is possibly a "geometry", anyway. Do the axioms of logic form "a geometry"? Probably not (unless you force such a definition of "geometry"). I think this is more like how one should interpret the idea that Euclidean Geometry is synthetic. And, more generally, I think the contention was more along the lines that the physical world is Euclidean. Of course it si common place now to say otherwise, but again, I am not sure how meaningful that is to Kant's contention. I don't think he is saying that it isn't possible to create abstract models of things far removed from your own experience. I also don't think it is fair to construe his statements as being specific statements about physics.

You are already making some objective statements about what is or isn't possibly "moral". It is now possible to say somethings are immoral. You can know that this true because they are not consistent with a doctrine of impartiality. So, there are true moral propositions out there.

That would not be treating everyone impartially. This is a common mistake that is really just a more sophisticated version of interpreting the Golden Rule to imply that masochists should go around hurting people. In this case you are assuming that since the law that you are considering is universal then it must be impartial. Suppose I was suicidal. Then I could command everyoen to commit suicide. That would be treating myself preferentially to everyone else since I don't mind (indeed would like it) if I die, but everyone else wants to live. Creating universal laws that treat soemone preferrentially is not impartial.

The idea of negatively determining something is not an easy one. It is much like using a reductio ad absurdum to prove the existence of something. But, it can be done (in principle at any rate). And, there is a positive principle to the concept of "virtue" which is actually at least partially subjective. That is the real reason that there must be a positive principle -- because otherwise it does not adequately correspond to everything one can say usingmoral statements. However, it is not true that the "negative" aspect of it is underdetermined in that it it does not adequately solve the moral dilemmas it is supposed to.

Well, all of morality is "synthetic a priori", I guess. Like I say, it doesn't really matter which one is the synthetic statement or how we want to call the statements (as being "sythetic" or "analytic"). Perhaps a candidate might be that we have wills. Or, perhaps the identification of morality (actually "justice") with impartiality.

In any case, you have said that impartiality is essential to morality. Is that a "recommendation"? It sounds like an assertion about the nature of morality. And it doesn't sound like you are saying that everyone is creatign impartial moralities (which isn't even the case).

That is true. I have even gone so far as to say that morality does not and, indeed, should not be its own motivation. In fact, I will claim that sometimes immorality will be in your rational self-interest such that a rational agent will act immorally.

Identifying what the "right thing" is is all a moral philosophy has to do. What I think you are refering to is the question of obligation: "Why should I be moral?" It is easy to construe this "should" as not in a specific moral sense but in a more general sense. The truth is that it only means that morality must apply to everyone equally. The other question of why I should (rationally speaking) find that it is the moral thing to do be a persuasive argument for doing it is actually not essential to moral dilemmas. (Again, this about squaring up our metaethical views to common usage of ethical terms.)

Is that Ayer's view? The classic paper is by CL Stevenson: "The Emotive Meaning of Ethical Terms". I guess it is not Ayers paper so they could have disparate views, but If we take this as the exposition of the Logical Positivist view of Morality, then it is nto saying that moral statements are literally nonsense. What it is saying is precisely what you are sayig -- that they simply have no propositional content. Instead, it is contended, they are phrased as propositions to convey an additional emotive meaning that is not carried by the simple imperative statement that they actually are.

You actually see this sort of thing. I might change word order to emphasize something or I might add honorifics to convey respect. The couching of an imperative statement in the form of a declarative sentence is just an extreme version of that sort of thing, so Stevenson seems to suggest. Of course, I disagree with this characterization of moral statements, arguing that it doesn't adequately capture the usage. And, I claim to have a better interpretation anyway.

I don't think that is really true. And besides that, it is beside the point. The issue is that Ockhams Razor must be used as a principle of rational thought. So, if for instance you claim to know something but have contradicted Okham's Razor, then you do not really "know" it. That's the issue. Now, you can either say that what it means to "know" something is independent of Okham's Razor or you could say that consistency with Ockham's Razor is required to have knowledge. If you say the latter (or for that matter even the former) it seems like you are making an assertion. Actually, you are making an assertion. Maybe it is true by the definition of "knowlege" or maybe it is true by some other means, but you are not recommending something. This cannot all go back to a recommendation to "see things your way". It is more "real" than that. It is about how things are even if the person doesn't see things your way.

If you believe something in a way that is inconsistent with Ockham's Razor then you don't really know what you claim to.

This is what I am referring to when I say that it is your rejection of the possibility of the "synthetic a priori" that leads to a rather unusual interpretation of philosophical subjects. I am not hell bent on having such propositions. I do think they probably exist based on the nature of philosophical considerations, especially if saying they don't implies that metaphysics, epistemology, morality, and so on are no longer about propositions.

Sometimes I get the impression that you just say that as a matter of definition -- that there is no real difference between such subjects and any other subject of inquiry, but that strictly speaking they are not subjects involving propositions. Other times it sounds like there might be a more profound aspect of them not being about propositions than just semantics. What is the real difference between a subject like epistemology and functional analysis? Of course there are some differences, but I wonder what you consider to be the real meanignful ones.

Well, first of all, the major contention is simply that they do not have propositional content -- just as you are contending. The emotive interpretation I don't think is supposed to characterize them as being quite as flakey as you might think. Stevenson, I believe, thinks that it is still very much an important subject for us all to consider. In fact, so does Wittgenstein who says very similar things about morality. And they both, I think, would have an awful lot to say about a subject that they think has no propositional content. (That is the main problem with this kind fo approach -- one that I thik your approach shares.)

Beyond that, the Logical Positiists are certainly very vocal about moral and political philosophy. Basically, they were Marxist, I think, as any good philosopher was at the turn of the Century. And, there were several papers on things like how Marxism was a paradigm of scientificly approaching ethics and how this is how ethics should be handled and so on. So, it isn't what it may sound like: a dismissal of all moral discourse. I think that is the problem -- it should be, but it isn't.

And I think that your view should be, too, but somehow isn't. You have trouble wrapping your hands aroudn the possibility of a syntehtic a priori proposition. I have trouble wrapping my hands around how your views on any philosophical matter could possibly be compelling or persuasive. What does it mean that Ockham's razor is "a recommendation"? Then its not true? What are the consequences for rejecting it? Why does it matter at all, intellectually speaking?

And more generally, are you saying that science isn't "true"? You can't be, right -- you are saying that it consists of propositions. But is that statement -- that science consists of propositions -- "true"? We're back to the "skeptics paradox". That statement seems to me to be a metaphysical or perhaps epistemological one. Okay, that philosophy does not consist of propositions -- is that a proposition? It has to be. But it is a philosophical statement. Perhaps some philosophical statements are propositions and others aren't since after all you haven't really said that all of philosophy lacks propositional content. Then what's the difference between things like saying that Ockham's Razor is essential to proper justification (which is essential to knowledge) and other philosophical statements? They are all informal, if that's the problem. They are all extremely foundational, if that's the problem.

I'm just saying that "principles of action" are propositions and you are saying that they aren't. How are they universally valid if they aren't propositions? How do you account for the fact that someone can be "wrong" but not "mistaken"? Or maybe they are mistaken, but I don't see how if it is not over a proposition.

The problem with your view is that it lacks veracity. (Of course!) What I mean by that is that the statements in it are not compelling. They do not have the veracity of a "true statement". Yet, you seem to think they are as compelling without being "true".

Well of course! No rational person could disagree with me! Seriously, though, it sounds like that might be the case -- it is hard to tell at times, even with yuor first posts that weren't even to me. My criticism of your view, then, would be much like my criticism to Logical Positivisms view of science. Who would question their ideas about how science is done? A lot of them are scientists. Similarly, who would question Bertrand Russell's mathematical savy? But I think they both have fatal flaws on their ultimate conclusions about the foundations. In particular, they seem to have cleverly boot-strapped their way into conclusions that seem suspended in mid air with nothing holding them up. Whenever that happens, you get into this real paradoxical pinch of having solved all these profound problems but not being able to know anything about them at the same time.

Perhaps my views are the same...

bd-from-kg

Longbow:

Since your last post was so long and my time lately has been short, I still haven’t been able to put together a full reply to it. But here’s a response to the first part - i.e., the part before you get around to discussing morality proper. I hope to get the rest done sometime tomorrow.

It’s not clear that we have any real disagreements on the first two points, so let’s proceed directly to the third.

3. On what “exists” and what is “real”.

But numbers such as “1” and “2” also also “exist” as concepts but not physically. Ordinarily something (like a unicorn) that “exists” only in the sense that the concept of it “exists” is not said to be “real”.

Yes, and I’m perfectly willing to say that “that 1 + 1 = 2” is part of reality. But in both cases they are “part of reality” only in the sense that it is a fact about this world that most people who use the terms involved at all use them in such a way that these statements express analytic propositions.

4. On “synthetic a priori” propositions
You’re mixing apples and oranges here. Mathematics and logic are analytic, so their truths can be known a priori. But morality and epistemology are not analytic, and in each case the fundamental principles are not propositions.

Yes. That’s exactly what Russell and Whitehead did in Principia Mathematica. IN fact, their intent was to go even further and demonstrate that mathematics is a branch of logic itself – that is, that all mathematical theorems can be derived formally from the axioms of logic once the appropriate definitions have been given. Whether they succeeded in the latter aim is of course still a matter of some controversy, but they left no room for intelligent doubt that all of mathematics is analytic – that is, that the theorems are logically entailed by the meanings of the terms involved.

Oh, please.

First, you’re analyzing a different statement than the one I proposed. “X is true” may mean the same thing as “X” in the sense that the one is true if and only if the other is, but they aren’t the same statement. If you want to show that it makes sense to say that an analytic statement is one whose predicate is contained in its subject, you have to show that the predicate of the original statement is contained in its subject, not that the predicate of some other statement is.

Second, you can’t just redefine the subject as the predicate and the predicate as the subject. If I asked you what were the subject and predicate of the sentence “Grass is green”, you wouldn’t say (contrary to all the rules of grammar) that the subject is “green” and the predicate is “grass”. “Grass” is a noun; “green” is an adjective. “Greenness” is the property being predicated of grass; “grassness” is not being predicated of green. In the same way, the sentence “‘Either (A and B), or not-A, or not-B' is true" is predicating the property of truth to the sentence ‘Either (A and B), or not-A, or not-B'; it is not predicating the property of ‘Either (A and B), or not-A, or not-B'-ness to “true”.

Finally, if this is the correct analysis of my sentence, it’s the correct analysis of any sentence. Thus, if I were to ask what are the subject and predicate of the sentence “This beach ball is big”, according to your analysis the correct answer is: “Strictly speaking the statement is “ ‘This beach ball is big’ is true.’ And the predicate is actually what appears to be the subject. Thus the subject is “true” and the predicate is “This beach ball is big”. I can assure you that this answer would earn you an “F” in any English class in the country.

Well, of course it’s true by definition.

Huh? The statement is not true by virtue of the definition of “truth” (which seems to me to be a meaningless statement anyway), but by virtue of the definitions of “either”, “or”, “and”, and “not”.

How true is a definition? Well, the “laws of logic” are definitions, so they are just as “true” as any definition.

For example, why is it “true” that “If A implies B and A, then B” ? Because that’s what “implies means. Why is it true that “If A and B, then A”? Because that’s what “and” means. (Or rather, it’s half of what it means, the other half being “If A and B, then B”.)

Well, in one sense it’s nonsense to question them, but in another sense it’s not. As for any definitions, it is always possible to argue that other definitions would be more useful, at least for a specific purpose one has in mind. That’s the motivation behind “nonstandard” logics. There’s nothing wrong with nonstandard logics, just as there’s nothing wrong with defining a nautical mile to be either 1852 meters or the length of one minute of arc on a great circle on the earth’s surface. (The two definitions are significantly different because the earth is not a sphere, so that the length of one minute of arc is not the same everywhere. Both definitions are in regular use; which is chosen in a given situation depends on which is most useful in that context.)

Obviously there’s a difference in the meaning of “a priori” and “analytic”. The term “analytic” applies to propositions, whereas the term “a priori” applies to knowledge. The question is whether there are any a priori propositions that are not analytic – i.e., any propositions other than ones that are true simply by virtue of the meanings of the terms they contain which can be known to be true without evidence. My position is that there are not. This is not “defining away” the distinction; it is a substantive claim for which I have presented an argument.

Apparently I didn’t make myself clear. Mathematical theorems are true by virtue of the meaning the terms they contain, which is to say that they are analytic.

No, I’m not a logical positivist. (Or at least I don’t agree with the major ones in all respects.) But as you have already figured out, I’m strongly influenced by their ideas.

Sorry, I can’t make head nor tail of this. Please rephrase.

Skepticism is certainly a problem, but it is not “solved” by simply postulating that various things are “synthetic a priori truths”. What if your supposed synthetic a priori truths aren’t true?

The “principle of verification” or falsification, or what have you) is not a proposition; it is not being asserted. It is a definition of what it means to be a proposition about the “real world”. (By the way, I don’t agree with this definition, at least as I understand it. I think, for example, that the statement “There is another universe similar to ours but which does not interact with ours in any way” expresses a perfectly meaningful proposition even though it is in principle completely unverifiable. To say that it is meaningless is to say that it is impossible in principle even to speculate about such a possibility, which seems to me to be plainly false.)

This is the solution to some “skeptic’s paradox” problems – to note that some things that appear at first sight to be assertions about the “real world” for which there cannot, even in principle, be any evidence, are really disguised definitions. The other main strategy is the one you’re already familiar with – by saying that things like the Principle of Induction, Occam’s Razor are properly formulated as principles of rational action.

Perhaps my problem here will be clarified by explaining Godel’s Completeness Theorem (not to be confused with his more famous Incompleteness Theorem). The Completeness Theorem says that, for any set of axioms A which includes the axioms of logic, any proposition P entailed by them can be proved. Here “prove” means just what it normally does, but the meaning of “entail” needs to be defined carefully in order to illuminate the theorem’s real import. P is entailed by A if and only if any model of A is also a model of P. In other words, P is entailed by A if it is logically impossible for P to be false if all of the axioms in A are true. (If you’ve had a course in formal model theory all of this will be perfectly clear; otherwise it may be confusing.)

In particular, let A consist only of the axioms of logic, and suppose that Occam’s Razor actually expresses a proposition – call it OR. If OR is true in all models of A (i.e., if it is true in all possible worlds) by the Completeness Theorem it can be proved from A. But the only things that can be proved from A are tautologies – i.e., analytic statements. This follows directly from the fact that A consists entirely of definitions. Or if you want to quarrel with this, at any rate it consists entirely of propositions which are true by virtue of the meaning of the terms that occur in them. But clearly the only sorts of things that can be proved from such propositions are other propositions that are true by virtue of the meaning of the terms in them – i.e., analytic propositions. And it is clear that OR is not an analytic proposition. Therefore it is not true in all models of A – i.e., it is not a valid principle in all possible worlds.

Huh? From what you said earlier about ‘Either (A and B), or not-A, or not-B', that seems to be what you want to do. I want no part of such nonsense.

That isn’t what’s meant by "the subject is contained in the predicate", but it’s a perfectly good definition of an analytic statement. (As you can see, the Completeness Theorem implies that pretty much all reasonable definitions of “analytic” are logically equivalent.)

This is unclear to put it mildly, but it appears that what you’re trying to get at is that maybe the Completeness Theorem is false. I assure you that it has been proved rigorously.

No, You’re saying something about your unwillingness to accept new definitions of logical terms like “implies”, “and”, “or”, “not”, etc.

No. They’re true in all possible worlds because they’re analytic, not the other way around.

Not so. When you call “I exist” an a priori proposition you are claiming that it can be known independently of any evidence. By showing that my knowledge that I exist is based on evidence I have shown that it is not a priori.

The account of how I came to believe that I exist would indeed be pointless in terms of explaining why this belief is rationally justified if it were not for the fact that it shows how this process can be rationally reconstructed as a series of justified inferences that “track” it reasonably accurately. In the same way, when I swerve onto the shoulder to avoid colliding with a truck that has just crossed the center line, I canrationally reconstruct the process by which I came to believe that this action was the best way to avoid being killed and thereby show that this belief was justified, even though what actually went through my mind at that moment can hardly be considered a series of rational inferences from the evidence.

The reason for this “historical” approach was to explain how it can seem that my knowledge that I exist is a priori even thought it’s actually based on evidence.

Actually we have a great many justified beliefs about the “real world” that were not the product of a series of rational inferences from the evidence. The human mind doesn’t typically work that was. What matters is that the processes leading to these beliefs can be rationally reconstructed in this form. If all of the beliefs that we formed this way, including all of the beliefs about the “real world” formed in childhood, were considered “unjustified” because they were not the product of rational inferences, we would have virtually no justified true beliefs at all.

Note: You may prefer to say that the kinds of beliefs that I’m talking about really were the product of a series of rational inferences, but that they just weren’t conscious inferences. I have no problem with that. One can argue that even a baby is thinking “rationally”, but is just unable to put this rational thought in the form of words.

Once again you’ve lost me.

It’s notorious that Kant did indeed believe this. For example, here’s an excerpt from an <a href="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html" target="_blank">article on non-Euclidean geometry</a> by J J O'Connor and E F Robertson:

In other words, not only did Kant believe that no other geometries were possible, but this opinion was so influential that even the great Gauss didn’t dare to question it.

What constitutes a geometry is a matter of definition. That the axioms of logic (and lots of other things) are not geometries is an analytic truth, since it follows from the definition of “geometry”.

As we can see from the passage above, he did indeed believe that when it came to geometry. But more to the point, Riemannian geometry is not an “abstract model” “far removed from experience”. It describe the actual structure of physical space. And the curvature of space is significant enough, even locally, that it has to be taken into account in “correcting” (or more accurately correctly interpreting) the signals from the GPS satellites.

It’s pretty hard to construe them any other way. According to the <a href="http://www.utm.edu/research/iep/k/kantmeta.htm#Kant's%20Transcendental%20Idealism" target="_blank">Internet Encyclopedia of Philosophy article on Kant</a>:

I quoted the whole paragraph because it sheds some light on Kant’s concept of “synthetic a priori claims”. The last sentence sets out my difference with him very clearly: I say that it is not possible to “add to what is contained analytically in a concept without appealing to experience”. That is to say, you cannot call the result knowledge or even justified belief.

At any rate, when Kant says that "the quantity of matter is always preserved" is a synthetic a priori claim, he is clearly saying that scientific hypotheses – things that are obviously not true in all possible worlds – can be known independently of evidence. I say that this is crapola.

[ October 03, 2002: Message edited by: bd-from-kg ]</p>

Longbow

In some cases that is true. I am not sure the concept of addition is analytic, though. I am not sure that a lot of concepts in math that could be construed as "true by definition" really is. I think that the definitions aren't arbitrary, for instance.

Obviously that is the point of contention. I am sayign that moral philosophy, like all of philosophy and mathematics as well, is a priori. I dispute the identification of analytic as meaning the same thing as a priori. And, I think that there is probably more to your identifying these two with each other than just a different definition of "analytic".

What?!? I don't think so. Judging from your apparent exposure to Godel, perhaps this is just a case of not recognizing the philosophical events unfolding between Russell and Godel. There is a whole website on the history of mathematics at the University of St. Andrews in Scotland. In particular, here is their entry on Godel:

<a href="http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html" target="_blank">http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html</a>

In particular:

"He is best known for his proof of Gödel's Incompleteness Theorems. In 1931 he published these results in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme . He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved.

This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis. One major attempt had been by Bertrand Russell with Principia Mathematica (1910-13). Another was Hilbert's formalism which was dealt a severe blow by Gödel's results. The theorem did not destroy the fundamental idea of formalism, but it did demonstrate that any system would have to be more comprehensive than that envisaged by Hilbert's. "

So, the point, then, is that I think the common view is that Godel not only completely refuted Logicism, but practically did as much to Formalism. I think that the idea that one could formally derive all that is true in math from formal axioms is generally rejected. And, certainly, the Principia is not an example of the formalization of mathematics.

Then, your sentence is meaningless. Perhaps you are confusing what I am saying slightly, here, with "'X' is true." I am not saying that the sentence is saying something about another sentence. I am saying that the sentence is an assertion that says that whatever proposition it refers to is true. If you do not interpret it this way, then the sentence is meaningless. In fact, it isn't even a complete sentence, but rather merely a sentence fragment.

I agree that what is the subject or the predicate in a sentence is not up for grabs. What I am saying is that the sense in which "the subject is contained in the predicate" of a sentence such as you present is that such a formal logical fact follows from the definition of "truth". The examination of this question "What is truth" is often called Semantics by philosophers. And, it is, in fact, usually based on such a subject that rules of logic are proposed and defended. As for this same argument applying to any assertion, it certainly doesn't. Usually the very idea of what it means for something to be true is not what the truth of an assertion is based on. In the case of logic, though, it probably is (if it is held to be analytic).

Also, you cannot just present formal symbols arbitrarily as if they were always meaningful. There is an informal sentence -- a complete sentence -- that your string of symbols corresponds to whcih is clearly what the characterization "the subject contains the predicate" refers to. In other words, rewrite the formal expression of symbols you presented as a complete sentence using no symbols. Furthermore, you must take such a complex sentence and reduce it to a form where you can easily get the atomic propositions out of it. Then, if you can prove that there is still no sense in which "the subject is contained in the predicate" you will have shown that such a characterization is meaningless (at least in that case).

How do you do that without bringing up the issue of truth (or "truth value" if we are trying to stick to a formal development)? I guess, formally speaking, it must seem as though what it means to have a truth value of "True" is being defined by the logic. But, informally it really goes in the other direction. For instance, you might define "not" as meaning something more like "it is absurd that". And then you might reject the idea that p is equivalent to its double negation as well as developing a great many other results for this new logic.

It might seem like "truth value" is derived from the character of the logic. And I suppose it is in the sense that "truth value" just refers to whatever can be derived with that logic. But, if we are trying to contend that this is actually relevant to the way we think, then the issue is whether or not that notion of what it means to make an assertion corresponds to what people are trying to do when they make assertions. In other words, it boils down to what it means to claim something is true.

Okay, I hate to be pedantic, but we are really going to have to be more precise in how we are saying these things. First of all, "a priori" doesn't have to refer to "knowledge". "Knowledge" consists of a proposition that you (if it is your knowledge) happen to assert, are warranted in asserting and that happens to also be true. "A priori" just refers to propositions, in general, whether anyone would assert them or not or whether or not they are even true. "Analytic", strictly speaking, refers to the sentences that represent the propositions.

That is not the same as saying that the propositions are a priori. This really is saying that you can derive the truth of the theorem based on the definitions of the terms in the sentence that states the theorem. This may seem like what you are doing when you prove a theorem, but I doubt it. And I think, I'll leave that discussion for discussions about the foundations of mathematics and Godel's Incompleteness Theorems.

"One of the main principles of the logical empiricism is the disintegration of the synthetic a priori. All statements can be divided into two classes: analytic a priori statements and synthetic a posteriori statements. Thus synthetic a priori statements do not exist. Now I shall briefly trace the history of Carnap's efforts to give a precise definition of the distinction between analytic and synthetic statements."

-- The Internet Encyclopedia of Philosophy (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html)

Actually, there is a quote by Carnap, I think, to this effect. I just don't know where it is right now.

But stating a definition rests on the assertion that you are correctly defining whatever you are giving the definition of. Basically, I don't think yu can get out of making an assertion that easily. How is what you are saying meaningful, then, if it is not asserting that the other slightly different but very similar proposed definitions are not appropriate?

It sounds like you are construing "proposition" to mean a statement in formal logic or perhaps analyzable by formal logic. In general, perhaps you are saying that only that which is formal can be knowledge. In any case, my response to this is just that OR is a principle of informal logic. So you wouldn't even discuss it at all in symbolic logic.

Of course I am not saying that the Completeness Theorem is false. What I am saying is that there is more to a priori knowledge than either predicate calculus or all of mathematics for that matter.

Really? It is possible for something to be true in all possible worlds but not be analytic? That woudl be the synthetic a priori proposition.

Well, for one thing, just because a belief was formed before you were rational, that certainly does not make it justified. And, if that means that we don't have very many justified beliefs, then so be it. You must have an argument for your beliefs for them to be justified. What you have presented doesn't give us the argument for "I exist." If you reconstructed the events leading to your swerving, then presumably you would eventually get at just what you could have known at the moment you swerved and produced the argument you could have had to justify such a belief. If not, then the belief wasn't justifiable.

In any case, I don't think this development of how we came to believe that we exist -- basically because we were created with it -- is an explanation of how such a belief is a posteriori.

What Kant clearly thought was that mathematics was synthetic, including geometry. What Kant definitely did not do (as far as I know) was launch into a long discussion about precisely what all that entailed. Did he specifically endorse the parallel postulate? Perhaps he even claimed it was provable from the other axioms of geometry. In that case, we was wrong about that particular mathematical claim that he made. It really should nto be used to judge the rest of his contentions. And certainly, describing Euclidean geometry informally and claiming that such a thing is synthetic a priori should not be construed as making specific technical claims about the axiomatic system.

But, I think that the definition of "geometry" refers to something conceivable independently of the physical world. In that case, what is or isn't part of this concept and how other concepts relate to it is not simply a matter of definition.

That is far removed from personal experience. You do not personally experience the curvature of space. You cannot even directly perceive it. That it applies to our science and technology is not realy relevant to the philosophical question that Kant is discussing.

First of all, lets be clear here that he is not being too serious about a particular contention in science or geometry. In other words, if he did specifically claim that the parallel postulate was essential to geometry, then it was not essential to his philosophy by any means. (And, by the way, if what you say is true about geometry being what it is by definition, then saying something like that must be construed as just defining "geometry" as meaning "Euclidean Geometry". In other words, he actually wouldn't be mistaken.) The contention is not so much that this or that is always true but that whatever it is that is always true is true a priori. While he does make plenty of claims about what is or isn't true, refuting him on these things doesn't really speak much to the main contention of such contentions in general being a priori.

Secondly, I agree with Kant that some amount of our contentions about the physical world are a priori. I do not believe that there are possible worlds in which they are false if they are indeed synthetic a priori. Right now, our current scientific models seem to have plenty of a priori assumptions underpinning them. These assumptions are what makes science a legitimate pursuit of knowledge. Without them, it would be really difficult to interpret what a theory might mean. And I am quite certain these assumptions about how to properly handle the physical world, what constitutes experimentally establishing an empirical fact, and so on does not follow formally from first order propositional logic.

The extent to which Kant really defended the falsified assertions that are attributed to him is at least somewhat debatable. They are little more than passing remarks, and I don't think they are really crucial, personally, to the points he is usually trying to make in the Critique of Pure Reason. They certainly are at best only marginally related to the problem he is trying to solve. So, for instance, even if he is wrong about the parallel postulate, it is not clear that he is wrong about the epistemological nature of geometry in general. In fact, I don't think he is.