LinuxPup

The fundamental principles of logic, for example, the law of non-contradiction, law of identify (A = A), law of excluded middle, law of causality, etc.

jpbrooks

Sorry I missed your post, LinuxPup.

I'm not so sure that the two issues are unrelated. It is true that we can demonstrate the existence of "absolute truths" (plural; not singular). However, this doesn't mean that it is possible, in principle, for us to demonstrate the existence of "Absolute Truth" (singular). Demonstrating that would require omniscience, which I doubt any of us in this forum possesses.
We infer its existence on the basis of what we already know (absolutely) about truth.

I didn't mean to imply that logical principles are not absolute truths. My point is that our "models" of the world are based on a set of assumptions that are derived from and tested by our perceptions of the world. This means that we can never be 100% certain that our "models" (which may even include the existence of "absolute truth[s]" as one of the assumptions) coincide with the real world that we are "modelling". The fact that all of the assumptions in our "models" are interrelated has implications for our knowledge of "absolute truth", and thus what we are able to say about it.

Kim appears to be talking about our ability to "affirm" (i.e., to state as a confirmed truth or fact) "absolute truth(s)". Since everything that we learn by observation, measurement and experimentation about the world is "filtered" through our perceptions, and since our "models" of the world are based on a set of interrelated assumptions (one of which may be that absolute truth exists) we cannot "affirm" with 100% certainty that "absolute truth" exists. We are "fenced in" by our epistemological situation because we are not omniscient.

In other words, we can demonstrate the existence of "absolute truths", but we can't
be completely certain about anything that we believe we know about them that we learned from observing the world (which includes the "belief" that they are absolute).

[ April 03, 2002: Message edited by: jpbrooks ]</p>

Kim o' the Concrete Jungle

What makes you think this is merely an assumption?

There is no "mere" about it. If you want to formulate any kind of philosophical system, you have to make assumptions, otherwise, where would you start? Wouldn't any possible starting point have to be proved, if you didn't allow for it to be an arbitrary assumption? When I say that the founding assumptions of a philosophical system are arbitrary, I do not mean this in a perjorative way. In fact, I think it is a very admirable method, because it avoids circularity.

Is this definition borne of the continuity of perception you ascribe to?

I don't know what it's born of. I wasn't around when Aristotle and co. were inventing logic. I don't need to know either, because I have the definitions to work from. I can just assume the definitions of logic within the context of logic -- that's no skin off my nose.

I'd like to ask in what context a normal human being could pass through a foot thick stone wall..

You know, it took me all of five seconds to think of one. I'm a big fan of 3d shooters. My particular favorites are the old build engine games -- Duke Nukem 3d, Blood, Redneck Rampage. In build engine games, there's usually a cheat code, DNCLIP or something, that switches off the wall blocking, so you can walk through walls. If you were passing, and you overheard me saying, "Just walk through that wall there," you might think that strange. But if I was talking to someone playing Duke Nukem 3d with the wall blocking off, I wouldn't think it strange at all.

Seriously though, language is part of the context. The specific meanings that you give to words like stone and marble is part of the context. It is also clear you are talking about the real world, as opposed to the world of a computer game, or a Harry Potter book, and that too is part of the context. Within the limits of a context, I am perfectly happy to allow a statement to be true, even true now and all times. All I say, is that if the context changes, the truth changes. If you can't imagine a different context, that doesn't really reflect on my philosophical system, only on your imagination. I'm surprised that you don't know what context means when you even used the magic phrase: "under these conditions". What about under other conditions? In Chinese, "you can't walk through walls," isn't true, it's gibberish.

Now you might counter this by saying that you were referring to the truth behind the statement, rather than just the wording of it. But that would lead us down the path to Platonic ideal forms, and that's not at all where I want to go. I want to stay with what is knowable and definable to human beings, so idealism is no part of my philosophical model.

I'm concerned here that something can only exist simply because we see, perceive or know it. I didn't realise the universe only came into being as we perceived it.

I'm not saying that the universe comes into being as we perceive it. I'm saying, how can you know something really exists if you can't know it at all? And I'm referring here to those Platonic ideal forms, not to the universe -- which we can see and perceive and know, with suitable allowances for uncertainty.

Which brings up points made earlier in the thread, about the round earth etc. Was the earth round before we perceived it was round? Was the sun the centre of our solar system before we realised it was?

I was quite fond of my flat earth example, so I'm sorry you missed the point. I'll try to make it again, with a little bit less rhetorical excess. I posed a definition of flat that ignored gravity and employed a spirit level. It's the definition of flat that a builder would use, and in that context it's still as valid today as it ever was. If you measured something with a spirit level and the air bubble was dead center, wouldn't you say it was flat? It's right that this definition of flat should ignore gravity, because using gravity to explain the behavior of a spirit level would be disfunctional in the context in which we generally use a spirit level.

However, when we changed the context, from measuring a building site to measuring the entire planet, we were now working on a scale in which gravity does have a significant effect. In this new context, the builder's definition of flat -- based on the spirit level -- doesn't work. The builder's definition of flat is an example of a "truth" that works in one context but not another.

In relation to Bill's point about the law of non contradiction, you make this your very beginning assumption, and so in making it you are unequivocally not asserting the contradictory statement to this. In doing this you have assumed the law of non contradiction must hold, or else you would have to say, 'I am....perceptual, or not'. In making this assertion as a foundation of your position, you must not be making the contradictory assertion simultaneously.

I suppose it serves me right for trying to add bits on the fly. Very well, I will change my first statement to:

(0) I will assume perception.

In relation to Bill's point about the law of non contradiction...

Blah blah blah. What do you want from me? You seem to be suggesting I should be out here trying to disprove the law of non contradiction. That would be a pretty bloody stupid thing for me to do since it's part of my own philosophical system. But it's not the first part. Before you can have the law of non contradiction, you must have the "experience of continuity" in the "perception of your sensory data". And to have that, you must first have "perception". The law of non-contradiction comes later because it is an abstraction derived from the experience of continuity.

John Page

Let's start with the law of identity, which you represent as A = A. Here's what I posted earlier in this thread:

Therefore, the form of representation you used above, which is repeated throughout propositional logic is at odds with the Law of Identity itself. The Law of Identity is a comprehensible tautology in words - hence my use of A and A' above. Hence, a truth is a subjective, abstract, value in your mind. You can go touch physical reality but you can't (literally) show me truth because its an abstract concept. A truth can be made intersubjectively true by the social convention of proof but thats as far as it goes.

Is algebra logical? It uses expressions like a = 2b + x. A contradiction of both the law of identity and law of non-contradiction in my book if taken literally - but algebra does seem to work!!

There are a number of other instances when logic seems to fail due to misrepresentation or some other flaw. Certain of the paradoxes result in contradictions if propositional logic is applied to them. Given self-contradiction, propositional logic is hoisted on its own petard and absolute truth goes out the window with the bathwater.

Cheers!

[ April 03, 2002: Message edited by: John Page ]</p>

Bill Snedden

Kim -

I read your last post with interest, but I am still unconvinced.

I wonder if perhaps we are operating under different understandings of what it means for a truth to be absolute.

So that we're clear, as a non-theist my definition of "absolute truth" has nothing to do with transcendence. In order for a truth to be known, it must be capable of being perceived. That which is imperceptible to human sense or cognition has an existential quality equivalent to non-existence (for all practical purposes).

To my mind, "absolute truth" refers to something that is necessarily always true within the limits of human cognition. I admit, as do you, that human knowledge is necessarily limited, but even so, there are some things that we must accept as true and always true if we want to avoid solipsism.

In addition, while I admit the limits of human knowledge, I also must deny that the assumptions of LnC and I are "arbitrary." The term implies that it would be possible for these foundational assumptions to be other than as they are. However, this is clearly impossible. If experience is in any way intelligible, LnC and I must be true. Solipsism is the only alternative.

I attempted to demonstrate this in my previous post, but apparently you missed it. There is simply no way to argue that LnC or I are not true: any attempt to do so assumes their truth and is therefore self-contradictory. LnC and I are therefore necessarily always true within the limits of human knowledge.

Therefore, I would still argue that your claim to base your epistemology on "perceptual continuity" without necessarily assuming the laws of non-contradiction or identity is false.

Without the assumption of the LnC, you have no way of knowing that your perception is continuous. Without LnC, there is no way to distinguish one moment in time from another; it would be entirely possible for 12:30 to be exactly the same as 12:31.

The only thing that your perceptions "prove" is your own existence (as Descartes demonstrated). In order to get from those perceptions to infer or state anything about the outside world, you must make further assumptions about what those perceptions mean; doing so necessarily involves LnC and I.

But, as a thought experiment on "absolute truth" or "the impossibility of the contrary", let's assume for the moment that your claim is true, and that the only foundation necessary for epistemology is "perceptual continuity". Given this foundation, is it "absolutely true" that you exist?

Is there any context in which you might not exist? If so, can you demonstrate by constructing an argument in that context in which you "prove" your non-existence?

Regards,

Bill Snedden

P.S. I love your screen name! Is there a story behind it?

[ April 03, 2002: Message edited by: Bill Snedden ]</p>

Bill Snedden

John -

I'm not sure what you're getting at here, but the expression a = 2b + x doesn't violate the law of identity or non-contradiction. The mathematical symbology indicates the operations to be performed that will ensure that a = a.

If by "taken literally" you mean "disregarding the context of mathematical operations", then it wouldn't be a statement at all, it would merely be an incoherent grouping of symbols much like "dhdkslei8". As such, it could no more violate the LnC or I than "dhdkslei8" does.

Regards,

Bill Snedden

John Page

Agreed, but is said if taken literally.

I take this as agreement that the expression is a representation. In math this abstraction is OK because quantities are defined as homogenous (a set of two is a set of two whether its cows dogs, pigs etc.)

But mathematical relations and logical identity relations are different! Math does not require the Law of Identity. If anything it requires a "Law of Homogeniety" as a founding assumption. Maybe this is equivalent to Peano's second axiom "For each x there exists exactly one natural number, called the successor of x, which will be denoted by ƒx"

Here's a practical example at what I'm driving at. You perceive two cows. Are the cows identical. No. In what ways are the cows similar? Check the attributes that define them as cows (legs, shape etc.). In what way are they different? (maybe color, size, location). So no two cows are ever the same. This is consistent with the Law of Identity. If you symbolize both cows as A this contravenes the Law of Identity - you have merged their abstract instances into one but the cows are clearly different. All you have established is a 1:n relationship between your concept of a cow and the cows themselves.

Maybe there should be a Law of Similarity that allows the transformation of sets of instances of objects into quantities.

I hope this makes my point about the interface between external reality and representational systems clearer. Let me know if I'm still communicating poorly.

Cheers!

Bill Snedden

Of course, but as I demonstrated, if taken literally it's just gibberish. Gibberish doesn't violate any laws, but neither does it purport to obey them.

Actually, Peano's axioms do depend upon basic logic. That's actually what Peano (well, really it was Dedekind, from whom Peano got the ideas) was attempting to prove: that mathematic principles could be derived from the principles of logic and some postulates about numbers.

In addition, while the principle you state is the second of Peano's axioms regarding numbers, they are preceded in his treatise (The Principles of Arithmetic) by four axioms regarding equality. The second of which is, "Every number is equal to itself."

That sure sounds like a description of the law of identity to me...

Well yes, that's true. But what have you just demonstrated, that similar things are not always the same? I don't see how this affects the truth status of the law of identity...

I guess not, and I apologize if I seem overly dense.

Regards,

Bill Snedden

[ April 03, 2002: Message edited by: Bill Snedden ]</p>

Adrian Selby

"All I say, is that if the context changes, the truth changes. If you can't imagine a different context, that doesn't really reflect on my philosophical system, only on your imagination. "

You didn't describe a different context where a normal human being walked through a wall, you described a computer game where a simulation of a human being walks through a simulated wall. Is there any alternative context to 'real human being walking through real marble wall' that involves real human beings and real walls and that the human walks through the wall? Only if we're talking about reality, my point remains that I didn't understand how truth could be contextual when we talked about epistemological truths, or more precisely, truths about reality, specifically, truths about people and marble walls.

I'm sorry you don't wish to go down a platonic road, I've never studied Plato, but not wishing to talk about the truth behind statements instead of the wording of them isn't a sufficient reason to doubt there is truth behind statements.

With regard to Aristotle, I'm sure he formulated logical laws, but was the fact that something is itself and not another thing invented by him, or just some language that described that fact. My point being that the law of non contradiction is a description of facts of the world, as well as our perceptions. You are right that it is through our perceptions we experience continuity in certain things, and ascribe truth on that basis, but the continuity is in the world, in order that we experience it. To this end, I wonder whether before you can say you perceive (premise 0), you have to put in a more basic premise that there is something that exists that is the subject of your perception, and by definition whatever that something is, is going to be what it is and not something else, which happens to be an example of something that is put into words as 'the law of non contradiction'. A possible counter to this is hallucination, but if you never experienced something while not hallucinating you could have no content for the hallucination. I am reluctant to assert only that the law of non contradiction applies to our perceptions and not to that which we perceive. I see no good reason to stop short of asserting that the things we perceive are 'continous', or they aren't, and our perception allows us to deduce this more, or less, effectively. Our perception I would argue does not determine the continuity, for we could be wrong in perceiving, and examples linuxpup outlined are useful here.

Finally, I'm not trying to get you do to anything, other than to point out things I'm not sure work in your theory. Surely that's the reason for posting this here, to accept critical scrutiny (good or bad ) in order to ascertain the stability and internal coherence of your theory? Bill again is pursuing the Lnc thing more cogently than I could, I leave it there because he's outlining problems he has that I would want to raise too. John, I need more time, I have a young baby, so this becomes an intermittent pleasure these days.

Adrian

John Page

Bill:

Thanks, I honestly didn't know about the equality thing in number being an axiom - I'm not a mathematician and I thought it was a conclusion!

First, I'm not trying to disprove the Law of Identity. All I'm saying is that the representation A = A misrepresents the Law of Identity and, indeed, contravenes it.

Let me suggest that instead of the cows in my earlier example we substitute letter A's. Not the (axiomatic) letter A, but two real instances of the letter A. Here they are:

A = A

They are the same in form but in different locations. To say that they are the same contravenes the LOI. Cows, symbols, the rules are the same and this is why I insist on using A and A'.

In any event, I believe that there is sufficient evidence here to point to a flaw in the representation of logic that LinuxPup puts forward as evidence of the existence of absolute truths. Some A's are more equal than others!

Am I making more sense now?

Cheers!