owleye

Walrus...

What does subjective truth mean?

owleye

Kim o' the Concrete Jungle

The debate between idealism and rationalism lies at the heart of questions like this.

On the one hand, the idealist holds that all knowledge is subjective -- derived from the senses. So no knowledge can exist independently from human beings, and reality is created by the mind. On the other hand, you have the rationalists who say that there are some objective axioms -- statements that are necessarily and universally true, which can be understood by human beings, but which are independent of them. There are considerable difficulties with both of these positions.

While it is true to say that all knowledge is human knowledge, it does not follow that the outside world does not exist, or that you can change reality by changing your thoughts about it. Similarly, the rationalist thesis begs the question, where does our knowledge of an a priori axiom come from, and what possible basis can you have for saying that an axiom is universally and objectively true? Both of these philosophies have been used to argue for the existence of God.

I hold to a position that differs from both of these.

I admit the idealist argument that no knowledge is absolutely objective. It cannot be perfectly objective, because "knowledge" is a function of the human brain. To know something is to hold it in the mind. If you do not or cannot hold it in the mind, then you don't know it.

I, however, reject the idea that the lack of pure objectivity necessarily means that the world outside the mind does not exist. I reject it because, even though there is no pure objectivity, we still have access to the outside world via our human senses. We can see, hear, touch, taste, and smell things. And we can note that certain things within our sensory experience possess continuity. I can note that my coffee cup is blue, and that -- barring some strange occurrence -- it will probably remain blue. Furthermore, I can tell you that it is blue, and you will have a rough idea of what I mean by that. I share the idea of "blue" with other people, so I can conclude that there is continuity of knowledge between human beings.

I conclude that the world outside the mind does indeed exist, and that it can be revealed through the existence of such continuities. Reality, therefore, is the experience of continuity.

While I share the rationalist's conviction that the universe is real, I do not buy the rationalist argument that there are some fundamental axioms that are universally, necessarily, and absolutely true, at every time, in every context, and independent of the human mind. That conviction, in my opinion, goes way beyond what can be empirically tested, or what can be known by human beings whilever we remain human beings.

At best, you could reasonably say that the fundamental axioms of logic are necessary to the way human beings interpret information about the world. But I wouldn't even go that far. The most I am prepared to say is that the axioms of logic are necessary to logic and logical arguments. I say this because there are ways of thinking about things apart from logic, which do not necessarily share the same set of axioms.

The question then remains, how can you know anything if logic is not absolutely and universally true? What possible basis could there be for saying anything about the world outside the mind, or acting within that world?

First of all, we acknowledge that no human knowledge is ever perfect or absolute. Everything we know about the world is filtered through our senses, and distorted by our emotions, memories, and values. So that in any given circumstance, there is always the possibility that we might be wrong. But we also know that we can identify continuities in the outside world. So we can test any statement that we make, to see if it is continuous with our experience of the outside world. So, through testing, we have a basis for judgement, and we can say that some ideas of the world are better and truer than others (even though we can never hold any idea to be perfect).

We can proceed by constructing abstract metaphysical models concerning various aspects of "reality". We admit, upfront, that the axioms we choose for our models are not based on anything more than our human suspicions. But that is not a problem, because once we have built our model we can test it against our experience of reality, or we can test it scientifically (which is better, because science has certain procedures for ensuring the maximum possible objectivy of an experimental observation). We do not judge a model according to the supposed "truth" of its axioms, but by the accuracy of the results it produces.

An abstract metaphysical model is useful. All of its axioms are known and comprehensible to human beings. And though we cannot say that these axioms are absolutely "true" in relation to the material world, we can say that they are true of the model, and insist upon them. We can apply logic within the context of a model, to draw inferences, or to determine whether a statement is true or false in relation to the model.

The conclusions that we can draw from our metaphysical model can then be related back to the real world. And we can reasonably expect that the accuracy of the conclusion (properly determined) is equal to the accuracy of the model. If the model has already proven a certain degree of accuracy, then we can be reasonably confident in the conclusion that we draw. And if one model proves more accurate at answering certain kinds of questions than another model, then it's no big deal to switch to that model, if you understand it is just one of many possible models. (Compare this to the destructive effect of a conflict between two metaphysical models who's adherents believe that their model is "absolutely true".)

So WJ, to answer your original question. 1/3 + 2/3 = 1 is true according to the abstract metaphysical model that we call mathematics. And the confidence you have in that mathematical equation is based upon the extent to which mathematics has proven itself accurate when compared to reality. There are other models besides mathematics. There is the scientific method, there is logic, there is English grammar. All such abstract models contribute to our abstract knowledge, and collectively this abstract knowledge can relate back to material reality with a degree of accuracy that is impressive, but always less than absolute,
because not even mathematics is perfect.

...And I draw that conclusion, not from some position of absolute truth, but from my own particular philosophical model.

sotzo

MaxMain/Devil:

Hi! And I join you as a non-mathematician myself, but I still beg to differ on your understanding of this semantic/mathematic comparison, to wit:

By no strech of the imagination am I a mathematician, but my understanding is that you have defined your abstract mathematical inference system as one in which a+b = b+a and then what is follows is an series of statements (one of which is 1/3 + 2/3 = 1) are demonstrated to be consistent within your axiomatic system. This does not imply any "truth" value to these statements. Only that they are consistent with your axioms.

A I pointed out in my last post, we could, for the purposes of our discussion, replace the word "water" with "ret" and then carry on a discussion about how good "ret" feels after a long day of lawn work. As long as we defined the word "ret" with the same semantic content as the word "water" we would not have a problem understanding each other. Now if we attempted to enact this change on a grander scale, say to get a whole city of people to begin using the word "ret" as another term for "water", it would be much more difficult. But it could still theoretically be done as the history of linguistics shows us (ie, the word "pop" used in place of "soda" or "soft drink", etc.).

In the same way if a+b=b+a is just a conventional system used by man to do mathematics, then it follows that we should be able to change that convention to a+b<>b+a or a+b=a-b or anything that we wish. I'm not saying that it wouldn't be difficult to change such an ingrained convention. What I am saying is that a convention is just that..a convention. And conventions, such as language, change over time.

But I am arguing that mathematical axioms are not conventions as Devil holds (if I understand him correctly). If changed, the result is nonsense. I agree with you and Devil that they convey truth only insofar as they work within the system they're a part of. But because a change, for instance in the associative property, results in nonsense, this is a strong suggestion for the existence of objective truth.

In other words, to argue against the proposition that a+b=b+a one must sustain that such axioms are merely conventions subject to change - the result of this position is a reductio ad absurdum.

cheers,
jkb

[ May 30, 2002: Message edited by: sotzo ]</p>

sotzo

It's tautalogical, neither objective nor subjective. It's true because we *define* it to be true, not because it was found to be true after investigation.

1. I challenge you to show, then , how a+b=b+a could be redefined to make sense any other way than in the form of the construct above. If we merely define it as such then it should be no problem to redefine as one would the word "cool" in order to describe the latest Rush album as opposed to a block of ice

2. Investigation presupposes axioms in the first place such as sense perception, logic and all sorts of background knowledge that didn't come through personal observation. You cannot approach an investigation "axiomless", else you would never begin the investigation.

cheers,

jkb

WJ

All!


First, thank you all so much for the fabulous input thus far! I have to say, that one main reason I came here was because I saw a good breadth or cross-section of experience and thought, that would be a good contrast in my skepticism for rational, logical thinking particularly relative to the epistemology behind the arguments about the non-existence of God. Now this mathematical metaphor is not a mere hidden aggenda for such personal analogy(axe's to grind), but I can't help but to bring forward cosmological and/or metaphysical 'concepts' that, (which I'll touch on later) as I've grown older, have somehow subconsciously effected me and how I think. It is a part of my Being and I can't shake it. Nor do I necessarily want to. Ok, enough of the personal commentary junk. I just want to say I appreciate all the learn-ed mind's on this board.

In the forgoing, I'm going to take a slightly different slant or detour but welcome any other continued thought on this issue of mathematical metaphor viz. objective existence. The detour may encroach on a bit of ontology.

Now, to answer some of the questions relative to why I'm approaching axiomatic logic viz. subjectivsm/objectivism is probably obvious (which I'll respond to below). Kim, of course, zero'd in on part of it [truth] right away. However, Max's point is well taken, and Nailscorva poses an interesting question or statement that suggests mathematics just happens to work, but it only works because to some degree we can empirically verify it [truth] via our physical world(?). But, the question remains, why does math work so well in describing the laws of our physical natural world? Is it simply because there are objects that we can count? Is existence all about physical objects? And, does mathematics have an independent transendent existence (Platonism) in our minds that is absolute or does our own sense of logic only create these axioms out of our finitude? The answer seems to be both, because our perfect forms of logic and ideas (mathmatical essences) still have not solved the deep questions of cosmological existence, yet, come close to such an accuracy.

What's more, philosphically, we see that the rationalist errs towards such objectivity to explain certain truths to his/her existence. Where I was in fact going with the question to Devil, was that the decimal equivalent = .9999 ad infinitum, is not an 'absolute metaphor'. What kind of 'metaphorical' problem does that pose to science viz. human conscious existence? While I'm not a physicist nor a mathematician, it has become obvious to me that mathematics is in fact a metaphor for certain physical truth's. Or I should say 'finite' physical truth's. Physic's has not solved the deepest questions of why, and to some degree how, there exists mind and matter [consciousness]ex-nihilo or otherwise (Big Bang).

So it seems to me that pure mathematical objectivity (ie, Formal Logic-deduction) cannot do that which the rationalist thinks it can do. For example, a conclusion that says God doesn't exist or that a Deity can't explain the origins of the universe cannot be refuted/solved thru objective axioms alone. If it can, please tell me how or if at some future point there is such a method of exclusive hope? Where should one put their faith and hope? In pure objective reason? Is that all we have until 'further notice', if you will?

In my mind, that question perhaps leads us to the virtues and vices of objective and subjective ways of thinking:


Ideas are timeless or "eternal." They go beyond particulars to the whole. They are not about this or that merely, but include each and every. They do not refer merely to now or then, but soar beyond to the always or eternal. One's thinking can run far ahead and soar above one's particular existence. This is the difficulty of existence -- that one can think the infinite and the eternal (one runs ahead to the ideal and universal in the mind) but one has to live the finite and the temporal (one's existence lags far behind the projections of the mind). The precise achievement of existence is to hold together the concrete particular lived moment and the vision of the universal ideal. The tension between the two diametrically opposed and irreconcilable polarities of the right now and the forever ideal produces subjective passion, a longing for the eternity that the mind anticipates but cannot have. The ethical thinker stretches his existence between earth and heaven, between real and ideal. He feels and lives this simultaneity, this contradiction, bringing together in one life the detachment of thought and the attachment to (and interest in) his concrete existence.

The abstract or objective thinker has no such problem. He simply makes his home in the ideal or eternal -- or thinks he does. He forgets his time-bound existence and lives in his mind, -sub specie aeterni- (from the eternal point of view). Like the subjective thinker, his mind runs freely ahead of existence and soars objectively above existence; but he makes no attempt to "remember" his existence.

The subjective thinker finds great difficulty in living a single idea. The objective thinker roams indifferently from idea to idea. The subjective thinker attempts to put together the particular (his own reality) and the universal (the ideal norm). The objective thinker, on the other hand, considers universals in their relation to one another, but not in relation to himself. For the subjective thinker, contradiction is real; the either/or of ethical choice is ever-present. For the objective thinker, contradiction is overcome in "pure being"; the either/or gives way to the both/and. Subjective existence implies interest, passion, partiality, striving, and decision. Objective existence indicates disinterest, dispassion, impartiality, and suspension of striving and decision. The objective thinker lives a postponement and a parenthesis. The subjective thinker lives each moment in the light of universal principle. For the objective thinker, eternity is already here. For the subjective thinker, eternity is hereafter, in the future. [end quote]

<a href="http://www.fred.net/tzaka/kierkega.html" target="_blank">http://www.fred.net/tzaka/kierkega.html</a>

I conclude, for one, that any notion or virtue of 'pure Being' or a 'dispassionate interest' [via mathematical explainations/objectivism/rationalism] are stumbling blocks to the epistemic rationalist when asserting an absolute truth about his own existence. And if that has any merit, how is it then possible to rely on such methodology to conclude with absolute certainty that Deity doesn't exist as an explaination of existential truth-Being?

In this context of ontology, should subjectivism take primacy over objective ways of thinking? Which is more germain to the psychology of Being and/or ontological existence? Both, or more or less a formula of 2/3 +1/3 respectively? And is it still fallible, this formula that is?

Walrus

[ May 30, 2002: Message edited by: WJ ]</p>

Bookman

Not so fast, sotzo.

There are actually useful mathematics that are noncommutative (the associative property is the one that goes a+(b+c)=(a+b)+c)) -- the commutative property is a useful construct, but there exist equally "valid" (by which I mean useful and descriptive) mathematics which don't require it as an axiom.

Bookman

James Still

And therein lies the rub. Science answers the "how" of things rather than the "why" of things and to expect it to answer the so-called ultimate questions is asking too much. Niascorva gave you what I consider to be the best answer. That one-third and two-third equal a whole is tautological and says nothing about the world. But as William James said, and I'm paraphrasing from memory, we can't seem to help going beyond what is warranted to reach conclusions that are not supported by reason or evidence.

WJ

James!

"Niascorva gave you what I consider to be the best answer. That one-third and two-third equal a whole is tautological and says nothing about the world. But as William James said, and I'm paraphrasing from memory, we can't seem to help going beyond what is warranted to reach conclusions that are not supported by reason or evidence."

In that regard, some physicist might conclude that god is a mathematician. Aside from such issues as James' will to believe, and getting back to the so-called tautological arguments, do you believe that since mathematics does such a remarkable job in/of discovering the laws of nature itself, that the world is nothing but tautologies?

Also, if the fact that math works viz. the physical world, does it not directly imply aposteriori methods of truth/discovery? In that regard, I'm not sure I understand Nailscorva's statement.

Walrus

[ May 30, 2002: Message edited by: WJ ]</p>

Bookman

You appear to be concluding something that is not only not obviously true, it is demonstrably false. Mathematics does nothing to discover the laws of nature for there are infinitely many mathematics and only one universe. Dicovering laws of nature has always been a triumph of empiricism, not pure thought.

The world is the world. It is mathematics which is nothing but tautologies.

Bookman

WJ

Book!

But if mathematics, in its essence, is an axiom like I think you mentioned earlier, then it follows that a synthetic apriori assumption/proposition about the world is the exact method/formula that combines your idea of empiricism-testing in physics. No?

In the interim, generally speaking, why/how does the world exist is the type of question that results from the success of math itself, in describing/explaining such laws of existence(?)

So we're using a particular method of truth to discover that which we seek answers for; it's just that some are verifiable and some are not...like you would not know if the water I gave you was in a state of boiling an hour ago.

Walrus