ZOMBIE FORUMS

Eh? I take it that's Icy's real name?

Say- you aren't the IcyBrian, are you?

And nice analogy, MiB. Gives me a rather amusing mental picture ^^
Still, if we ever find out that we've been living in a fake VR world created by evil machines, Icy'll probably handle it better than most.

I decided to revive this thread in order to respond to what some people have said in the Whys and Hows thread, so as not to bring that particular thread too far off-topic. So, er, here goes.



No. You're still relying on the idea that the subject exists. As I've said before, I deny the existence of the subject just as I deny the existence of the object. There is just experience - the pre-processed, pre-judgment, pre-conceptual bedrock that underlies absolutely everything. It could be just as accurately called objective as subjective, because both terms are equally inadequate, presuming as they do some sort of pre-organized, unified entity (the universe in the case of objectivity, and the subject/self in the case of subjectivity).

(Actually, to be honest, I don't even believe that pre-conceptual experience itself exists as a pure, foundational metaphysical entity. That's where we'd be getting into the Derridean notion of the fictionality of the moment and such. However, to simplify things, and for the sake of argument, I'm pretending that experience can be treated as a foundational semi-metaphysical entity.)

I have a question for you, however: how does the idea that there is an "objective reality" behind our perceptions explain our world any better than the idea that we are living in a collectively-created reality? I don't quite ascribe to either position, but it seems that, if anything, the "collective-reality" explanation is more logical(*), if only in the fact that it eliminates one entity (the objective world underlying humanity's perceptions) from our model. Assuming both ideas describe our observation equally well (and if someone disagrees with this assumption, please give me a reason for it), Occam's razor would imply that we should choose the latter option.

Reality is a bit hard to flesh out conceptually, as concepts are basically always going to be at least one step away from that reality, being essentially generalizations.



How am I playing word games simply by stating that truth is a fictional concept?



Ah, but even the medieval Christian model of the universe explained the observed reality perfectly. (Well, having observed certain things since then, we'd have to make a few alterations (just attribute any contrary observation to mass hallucination!), but still.) I could just say that everything happens totally at random, and that would explain everything that happens as well. Any regularities I see might just be coincidences.

The reason we don't do this is that we have things like Occam's razor telling us that we should use the least number of entities possible in our explanation. This is a totally arbitrary rule that we really have no reason to believe in, unless we just admit to ourselves that we are not pursuing the truth at all in any form, but are actually just pursuing explanations that will be more convenient and effective than other explanations. Science assumes that all reality can be reduced to a unified set of simple rules. In other words, when given two explanations, one that is very complicated and involves several rule sets governing different aspects of reality, and one that uses relatively few rules in a single rule set to govern every aspect of reality, we should choose the latter. There is absolutely no reason for us to do this, other than the fact that it is convenient for us. Thus, science may be a more convenient way to explain reality, but there is absolutely no reason we should assume that it is any more accurate than any other explanation.

If anyone can actually tell me why we should assume reality is as simple as possible, and is governed by a single rule-set, then please do so. Keep in mind that saying "well, things happen in a regular way, and unified laws can quite easily be made to explain our observations" is not a valid argument, as it still assumes that we should choose the explanation that involves unified laws. I realize that not doing so would seem patently ridiculous, but is there any real reason it should seem that way aside from the fact that we, as human beings, have a strong prejudice against such an idea?



But see, that's a tautology. We define 2 as "1+1", and we define 4 as "1+1+1+1". Thus, "2+2=4" is "(1+1)+(1+1)=1+1+1+1 ---> 1+1+1+1 = 1+1+1+1", which is essentially the same as saying "A is A".



A better question is: has it given me any reason to believe the above? The answer is no. The only reason I'd believe it is because my intuition tells me to, or society tells me to. All the books I have read have taught me nothing that I could not realize if I had enough time and spent enough effort analyzing my own assumptions, and the validity of those assumptions.





(*) In this case, when I say "logical," I'm talking about what I'll call "effectiveness-based" logic, the same logic whose validity I attack later on in the post.

Did you just say that experience exists independent of anything to be experienced or anyone to experience it?Yeah, you did. Why don't we start by throwing out the assumptions you can't even bring yourself to believe?Besides being a step further from falling over the brink into Solipsism, it's not. But you denied objective reality, and i mistook your claim that experience exists to mean that you accepted a subject who experiences. Therefore, given the assumptions that A: I exist to experience this debate, B: the debate exists to be experienced, and C: you exist to refute my assumptions, i posit that there must be a consentual reality which includes, at a minimum, myself, you, and the debate. I support this proposition by my experience of the debate, and my experience of your participation in the debate. When i assume your existance and participation, i then must assume a medium through which we can debate. A consensual reality where we agree on certain things. Primarily, the existance of the debate. (If we both exist, and we are both participating the the debate, we both implicitly agree that the debate exists, even if one of us explicitly denies it in the course of the debate.)

If there is any arguement of objective reality, it is that each subject experiences a strikingly similar subjective reality even when isolated from other subjects, groups of subjects isolated from other groups experience extremely similar consensual realities, and that it can be logically assumed that processes which are vital to the experiences of a given subject continue to exist when there is no subject to experience them.
When you state that truth is a fictional concept and refuse to define it's meaning as a fictional concept, you are creating a semantic null. Even fictional concepts have meaning.

That's mathmatics. All mathmatical proofs reduce to n=n that's what makes them proofs.

Speaking of proofs - you also name the mathmatical law as well as the work. What you're talking about is the Reflexive Property, I do believe...

Yes. We must start with the initial, raw reality, the substance of being, which is essentially (for us) experience. Subject and object are simply two conceptual constructs that we use as what are essentially place-holders for that which is beyond experience. It's kind of like what Kant says.



Now, I'd agree with Kant that phenomena are all we have access to. However, I would go further and say they are all that is. I'd claim that subject and object are conceptual constructs -- two poles that act as foci around which we organize the conceptual framework we create to deal with our experiences.



Oh, I believe it whole-heartedly. I just accept the fact that, in everday life, it's useful to pretend otherwise. That doesn't make the assumptions I use in everyday life correct.



Given those assumptions, I agree.



Ah, but that could just as easily be explained by the existence of some sort of collective consciousness which we are all a part of. This is still less complicated than positing the existence of a completely different, non-mental substance. (I'm drawing a bit on Berkeley for this. A much fuller and more comprehensive defense of this idea can be found here. A very interesting read, if you have the time to look it over. (And while I'm recommending shit to read, you might also want to check out a short story by Jorge Luis Borges entitled "Tlon, Uqbar, Orbis Tertius" that deals with this subject as well.))



I have two seperate definitions of truth. One, which I will call "lowercase-t" truth, or "truth" (in quotes), is what is effective -- i.e. the conceptual model which satisfies the goal at hand, whatever that goal may be. "Capital-T" Truth, on the other hand, which I also call Reality, is pre-conceptual, pre-judgment, pre-processed, raw experience. Truth cannot ever be described conceptually. (Again, drawing upon Derrida, I don't actually believe this form of Truth entirely exists either; however, let's ignore that for the moment.)

Hopefully this has cleared a few things up. Honestly, the main reason I engage in debates like this is to remind myself exactly what I believe, and to crystallize/refine my descriptions of those beliefs. If, over the course of a debate, I have not discovered something about my beliefs that I myself did not know at the beginning, I consider the debate a failure.

Which therefore calls into question the entire reason for mathematics' existence besides making various people feel smarter than various other people.

A tautology by any other name is still just a tautology. There is no mystical barrier between the sciences that was not put there by some silly fool who thought he would do better if he didn't have to worry about any disciplines but his own. It may make things easier to deal with, but it's hardly the most effective method for understanding the fullest scope of our knowledge - which, I believe, you are striving for, correct? I am not, but I'm perfectly willing to use your definition to my advantage.

The only real statement anyone can make that has no underlying assumptions is that "existence exists," and even that is questionable. Such a claim requires an assumption that "existence" can be defined outside of the perspective of the one experiencing "existence," which it cannot.

A tautology is a needless repetition.
What you're calling tautology is an equation.

-b +/- radical b^2 - 4ac =x
2a

Under your definition, would be a tautology.
so would A^2 + B^2 = C^2.

Do you contend that this is, in fact, the case?

Not really. You're reducing the unknown problem to one previously solved or accepted as a postulate. It's a matter of saying


Of course, you are right in pointing out that the results of the "+" operator are simply a previously agreed on set of axioms. Operating on a mathematical <a href="http://mathworld.wolfram.com/Field.html">field</a> other than the reals, 1+1 may well not be 2

To use everybody's favorite field,

is an equally vaild way of doing things

There's a difference between arithmetic equations, which can be right or wrong, and algebraic equations. 2+2=4 is true, but A^2 + B^2 =C^2 is not necessarily true.

And yes, both those equations are referring to geometrical truths, which cannot be reduced to tautologies. Or can they? Hmmm, I'll have to think about this further.

Even if they can't, however, I can easily argue that geometric "truths" are simply a product of our way of interpreting spatial relations.

(By the way, for the purposes of this discussion, "tautology" means some variation of the statement "A is A". In mathematics, yes, this is called an equation, but it's rather awkward to call the statement "a man is a male human being" an equation. What I call a "tautology" is what Kant would call an "analytic statement".)

(Oh, Emy, minor note: I was looking over one of my earlier posts, when I agreed with you about there being a reality that includes you, me, and the debate. The debate is not a seperate entity, you realize. It's simply something that exists in my mind, and also exists in your mind. So, even if we pretend that you and I exist absolutely and are not in fact conceptual constructs, there need not be any third entity. I'd have put this in an edit of that particular post, but I thought you'd have a better chance of seeing it if I added it to this one.)

They can be. When you (took/take) highschool level geometry, you (will be/should have been) asked to write a proof of one of those equations, with their appropriate given assumptions and an index of postulates and theorems.
does that mean that you're agreeing to the existance of truth?

Provisional, practical "truth", yes.

I made a bit of a mistake in the post where I gave two definitions of truth for you. I forgot to mention that I was questioning neither of those two when I was claiming that the concept of "truth" is fictional (and moreover, nonsensical). The type of "truth" whose existence I was questioning would fall under a third definition: the correspondence between "objective reality" and "subjective reality". I do not believe in the existence of "objective reality" and "subjective reality" as discrete, seperate entities, and thus cannot believe that the concept of their correspondence even makes sense. However, I'd given that definition of truth in the original debate, so your claim that I was denying the existence of something which I had never given a definition of is invalid.

Oh, boy, the nature of proof.

A proof is a series of statements of known truths that together establish the necessity of a given truth. Not all proofs provide equations. (Unfortunately.) Here is one such:

Proposition. (Euclid) There are infinitely many prime numbers, where by "prime" I shall denote a natural number p with precisely two positive integer divisors, 1 and p. Note in particular that 1 is not prime; it has only one positive integer divisor.

Proof. Presume by contrast that there are only finitely many primes, p_1 = 2, p_2 = 3, ... , p_n. Construct the number q = p_1 * p_2 * ... * p_n. Note that p_i does not divide the number (q + 1) for any 1 <= i <= n, because (q + 1) = ((p_1 * ... * p_i-1) * (p_i+1 * ... * p_n) * p_i) + 1. Then either (q + 1) is itself prime or there is a prime less than (q + 1) which divides it, but is not any of p_1, p_2, ... , p_n. A contradiction with the presumption is thus established, so there cannot then be only finitely many primes. Q.E.D.

In my first year of undergraduate study, I once suggested to a professor whom I wanted to annoy that all math is tautology. He was, indeed, annoyed, and should some upstart tell me the same thing now, I would be equally annoyed. This famous proof of Euclid's is a very strong counterexample to frosh-Tamayo's suggestion.

Some proofs do provide equations, and indeed those ones tend to be more practically useful.

Proposition. ("Chinese Remainder Theorem") Let n_1, n_2, ..., n_k be k distinct positive integers such all pairs (n_i, n_j) of such numbers, where i <> j, are relatively prime. (That is, if i <> j, then we know that there is no integer m >= 2 such that m divides both n_i and n_j.) Let m = n_1 * ... * n_k. Then there is an isomorphism between (Z/m)*, the multiplicative group of units of the integers modulo m, and (Z/n_1)* * ... * (Z/n_k)*, the Cartesian product of all groups of units of the integers modulo n_i for all 1<= i <=k.

Proof (<-). Let (t_1, ... t_n) be an element of (Z/n_1)* * ... * (Z/n_k)*. Then (t_1 * (m / n_1) + ... + t_k * (m / n_k)) (mod m) is a unique element of (Z/m)*.

Proof (->). Obvious.

This particular theorem is very useful in all kinds of places, and as I showed, it actually provides a recipe for translating various quantities between different representations. However, without the proof, the proposition is not a tautology at all, but just that -- a proposition whose truth or falsehood is in doubt.

Sure, any simple arithmetic equation like "2 + 2 = 4" can be viewed as tautology, but can you prove the Prime Number Theorem: the number of primes less than a natural number n is asymptotic to n/log n as n increases to positive infinity? Do you care? You should. Your bank account's security depends on this fact. It is not obvious, however, and (like Fermat, I cop out by saying) a proof wouldn't fit easily here on a topic on the message board.

Analytic statements like Euclid's Theorem, the Chinese Remainder Theorem, or the Prime Number Theorem are not only necessarily true but meaningful to all kinds of people -- and not just mathmos. They are as true as true can be: given precisely determined predicates, a new, necessary statement can be made.

Why are these necessary statements not acceptable as truth?

I hope you do know that 1+1 isn't a tautology or a simple subjective labling. Bertrand Russell took about a hundred pages and eventually did prove that 1+1 = 2 is provable, not some postulate of algebra / arithmetic.


I'd like to propose my logic for deciding morality. To begin, I state that to have any kind of philosophy, we must be free to debate it. Therefore, the basis of things begins with we (by which I mean any two individuals) must have freedom to debate. From that, I start with the assumption that we all must exist because what's the point in debating someone who doesn't exist, but is merely part of your own reality. Moving from that, I say that such things as murder or hurting someone is immoral because allowing it would allow someone hurt the people having the debate. It also means that there should be no inhibitions on freedom of speech.

Punishment on people that does not inhibit their exercise of free speech is acceptable because without enforcement, there is no way to prevent them from interfering in a debate if they choose to do so.

I'm sure there's some glaring loopholes in it, but that's why I'm posting it.

Yes, but Bertrand Russell was a wanker.

(Won't be able to seriously respond to any of the DC threads I had been posting in until after this semester's finished, BTW. But [MacArthur]I shall return![/MacArthur])

Yes, I know that. He showed that the statement "1+1=2" is a theorem of arithmetic, if one builds arithmetic on his brand of logic. Not an entirely bad thing to do, but ....



That too! Nevertheless, he was possibly the most powerfully intelligent wanker of the twentieth century, which is saying something. Only John von Neumann came close. The thing is, though, Russell spent something like thirty years of his life writing Principia Mathematica -- the most significant intellectual wanking ever: Godel published the famous Incompleteness Theorem halfway through the writing of Principia but even that didn't stop him.



Not bad at all! Then again, I agree with you quite closely, so I'm having trouble trying to find any of those holes you said you thought might be there ....

We just discussed this in my philosophy class. My opinion on this is that we can only prove that "I" (for everyone) exists, and only through the input of sensation. By that, I mean, that if we cannot sense anything (blind, deaf, no nose, no tongue, completely numb) - we have nothing to base our thoughts off of.



Without thoughts or a mind, how can we tell that we exist?



Everything apart external from "myself" (or yourself) only tells us that we exist. Because "I" think "you" exist, meaning that "I" must exist to make that conclusion in the first place.

So how 'must' "you" exist in the first place? I can prove that "I" exist, through my own perceptions. But I don't think things independently from "you." Justifying an external existance from "myself" through 'what would be the point?' is kind of irrelivant. They have nothing to do with each other (in my mind). The point lies in the fact that "I" perceive "you" and "your" responses, so it can affect the way "I" think, whether or not "you" actually exist.



*quotation marks around "I" and "you," because what I'm talking about doesn't apply only to myself or to the 'you' of this debate. It's just a certain perspective.

If I may be so bold --



It is better to make one's definitions plain than to put scare quotes around words and hope that one's audience can guess the altered meanings of the words so quoted. Please do not take this as a personal attack; it is not intended to be. It is a respectful attack on your position. I want to understand your statement, and I am failing to do that, and I believe my failure stems from ill-defined premises.

As for Descartes' cogito: I name it thus because it is thus he wrote it originally, in Latin. Now in Latin, one rarely needs to use personal pronouns at all, because verbs are inflected as to number and person. In English, however, we need them: cogito, ergo sum means "I think, therefore I am". The English translation makes the presumption of an I who exist to think far more obvious than the Latin original. In short, the cogito might indeed be translated to "Since I exist to think, I exist" -- which is unfortunately a vacuous statement.

edit: Latin nouns and adjectives are certainly inflected, but not for person, duh

Okay, sorry. I'm not quite sure how to put this. Uhm... (you see, I'm in my first ever philosophy class after being in my first psychology class - which is why that was my first post in the thread.) Sorry it's confusing.



Everything external from my body only tells me that I exist because I perceive it.
Likewise, everything external from your body tells you that you exist because you perceive it.
And everything external from his body tells him that he exists because he perceives it.

etc.



So how 'must' you exist in the first place? I can prove that I exist through my own perceptions. But I don't think things independently <b>as</b> you. Justifying something's external existance (from myself) through 'what would be the point[?]' is kind of irrelivant. They have nothing to do with each other (in my mind). The point lies in the fact that I perceive you and your responses to exist, so that it can affect the way that I think, whether or not you actually exist.

Likewise:
So how 'must' I exist in the first place? You can prove that you exist through your own perceptions. But you don't think things independently <b>as</b> me. Justifying something's external existance (from yourself) through 'what would be the point[?]' is kind of irrelivant. They have nothing to do with each other (in my mind). The point lies in the fact that you perceive me and my responses to exist, so that it can affect the way that you think, whether or not I actually exist.


I think I have some editing errors in there that may have also clouded your way of thinking. I guess this is all pretty much a technicality. But I hope you understand what I'm saying now.

Descartes was also a wanker.

Who isn't?