I am saying that definitions and tautologies are functionally equivalent. They are redundancies. You may, for example, define a triangle in a Euclidean plane in terms of its angles adding up to 180 degrees. There is no functional difference in always being true and having no truth value.
Lib, no offense, but that’s just wrong. The two are fundamentally different. A definition is a notational shorthand. Replace every defined term, and you maintain the meaning of the original statement, even if it is a bit longer. Tautologies are not like this–you can’t replace every tautology with “true” and retain any meaning. See my point?
Yes, I do see your point. And twenty years ago, I would have agreed with you. But after enough immersion, certain matters have presented themselves as rather obvious.
Take your point about definitions, for example. Replacing the terms with new definitions. Do that long enough, and what will you have? A tautology.
A tautology and a contradiction are two sides of the same coin; one is proved by everything, and the other proves everything.
No, no, no. Consider this example:
Start: “x is divisible by 2”
Substitute in the definition of divisibility: “There is some c such that x = 2c”
Substitute in the definition of the existential quantifier: “It is not the case that for all c, x != 2c”
All the definitions are stripped away, but what is left is sometimes true and sometimes false.
Did you mean going the other way? Cause it doesn’t work that way either.
We’re two ships passing in the night. What I’m talking about are what you would call reflexives, e.g., this is that.
By the way, note that every formal argument begins with the spookiest thing imaginable: undefined terms.
That’s probably true. Best just to let it drop, I suppose.
Well, if we may press on just a bit, now that you’re oriented to what I’m talking about… Since your interest is first order predicate logic, I think I can give you an example that will hit home. Consider Peano’s axioms. He speaks of a “successor”, and leaves it undefined (intentionally). What do you suppose would happen if you defined it?
You get a subtheory of Peano arithmetic. That is, your new theory will have all of the theorems of Peano’s arithmetic, and then some. Did you have something else in mind?
Gaaah! What philosopher is this? Your whole post sounds like some horrible and terrifying mixture of postmodern antirealists and those people who deny a priori knowledge. Hmmm…if Immanuel Kant and Hilary Putnam had a baby, what would it look like?
Are you deriding the notions of truth and falsity here, or are you simply attempting to abandon one of the two traditional methods of identifying truth? I doubt you can do merely the latter. If logical inference is denied, then we couldn’t learn anything true about the universe at all, because even our most basic perceptions require the inferential step of concluding “I perceive it, and that perception relates in some way to the world as it really is, therefore the world really is some particular way.” If you believe that, you might as well retire from the SDMB, because there is no ignorance to fight where there cannot be truth.
Sorry, I meant “if you don’t believe that”, referring to the inferential process immediately preceding that last sentence.
as one of the no doubt numerous kids that got nicknamed Mr. Spock, i must strenuously disagree.
the MAJOR problem comes in when dealing with symbols and reality. who decides the meaning of the symbols and does that person have an accurate paradigm of reality.
what does the symbol CAPITALISM mean?
try something simpler like CONTINENT
my random house dictionary says an island is a body of land completely surrounded by water that is smaller than a continent.
LOGICALLY one would think that a continent is a body of land COMPLETELY SURROUNDED BY WATER that is bigger than an island. this works for australia and antarctica, but the americas present a problem. it is either one continent that gets real skinny in the middle of two connected continents. therefore the definition becomes:
a body of land completely surrounded by water and larger than an island or connected to another large land mass by a narrow strip of land called an isthmus.
so north and south america and africa meet the updated definition. but how does EUROPE becom a continent. this is totally illogical. the logic must apply to reality not just symbols. the symbols are simply a convenience.
Dal Timgar
Well, Rex, I do deny a priori knowledge, so that should help. I am sort of an anti-realist in as much as I don’t support realism (though I admit that it is the closest I would come to supporting any of the various stances along those lines), but I don’t accept idealism, and transcendentalism is right out. If that makes me post-modern… :shrug:
I’m not trying to deconstruct or destroy logic or anything. Nor am I trying to show it is stupid, pointless, etc.; only that it is meaningless. It has no referent, and so claims to its truth when compared to statements in English (or whatever) are specious at best, and rooted in conceptual confusion. Also, appeals to the truth of English statements by pointing to rules of logic are also rooted in conceptual confusion.
No, you’re right on track!
Now, continue the exercise, adding more undefined terms and then defining them repeatedly within your new systems. Then again. And again. And so on. If you start thinking about when you will “hit the wall”, you will have come to understand intuitively a familiar notion — namely, that so long as your system is incomplete, it is consistent; but when it is completed, it becomes inconsistent: i.e., x Gen [Neg (x B Neg t)].
That is because of the tautological nature of definitions.
Oh, and the philosopher is mention in the post I made just previously, with a link to a tolerable summary of ideas.
Bah! A=A is only true VERY conditionally.
Difference is true down to the core of everything regardless of what one says or does. To that degree, A=A is contradicting itself. Those "A’s are not the same, nor can ever be the same; you can’t even express them as the same without replicating it spacially.
As for eris’s OP; I disagree with you eris =)
Logic seeks non-contradiction, existential validity. In terms of the mind and the body; I personally think of them as having different metabolic systems which subsist off of fundamentally different ‘foods’ for nourishment.
The body is interested in survival “I do exist”; the mind is interested in existence “Do I exist?” If the mind can prove free-will by simply not doing anything; and to that degree controlling the bodies inclination; it will. If it notes a contradiction in this process (i.e. the body is still doing something), it will rise again and attempt to live that much longer until it can resolve this dilema. The mind is always working on recursively redeeming its own free-will in regards to having had been born - in order to prove it’s existence.
Linguistically, and even moreso, ‘the conveyence of profundity’ is observed when the mind finds something which proves to it that something comes from nothing; that nothing to this degree exists, and that it has validated its will through ‘knowing’ that nobody is right and nobody can figure ‘it’ out (by negating itself - but negating everyone else in the process, so it’s ok). This process tends to be automated to the degree that people by-in-large (particularly the child-bearing portion of the population) will reward evidence of this use of logic (quitting to solve the existential problem so that the survival problem seems securely fastened - that generations still continue, regardless).
I do not however find the tool of logic meaningless, in so much as it does eventually allow one to ‘mentally’ consider itself in respect to all perspectives; and in using contradiction as a filtering process for more explanation, ultimately seeks to harmonize itself with all the data so that an informed decision about it’s own existence can recursively be had without a shadow of doubt; whether it chooses to stay or to exit, it at least felt that it existed. I personally suggest that the use of terms which funnel existence through synonyms for ‘everything’, ‘nothing’, ‘anything’; is resultant from an incomlete mapping of the cognitive stage of permanence, and is a much easier way for the mind to simulate proof of it’s existence. However, the continual enactment of this simulation is evidenced to degrade the material survival interest at large; and also seeks to degenerate the mind itself into living off of ‘junk food’ which clearly negates its own purpose via its own criteria.
Part of psychological maturity is the clear understanding and consistent application both behaviorally and linguistically; consistently; of coming to terms with and realizing that nothing cannot be interacted with in order to resolve its requirement of proof for existence. The mind needs to fundfamentally understand that many of its beliefs, opinions and convictions are directly resultant from a lack of very specific phenomenal stresses; this lack, giving it the luxury to be delusional in regards to it’s generalized belief of purpose.
These delusions are theft, and constitute the re-enactment of the birth ‘rape’ of non-consent into existence itself; incorrectly utilizing the very tool of logic by proving you are right because you can do it, regardless of other perspectives which contradict such purpose.
I think we can all equally agree that a person cannot un-exist themselves; as logically this would prove that they couldn’t have existed to make that formulation or determination in the first place. The goal of self-determined proof then lies in the capacity to provide unillateral tools for self-determination without impacting the will or consent of another being or perspective; in order to not ‘tautilogically’ prove this to ones self; but rather to know that this is true. This is achieved by automating resources necessary for survival; abstracting them outside of the field of controlled economy so that people can feel the pressure of truth which lies behind the delusion and/or deception; that they can interact with free-will on a peer basis, rather than subsist off of black boxes resultant from an incomplete mapping of the conceptual truth of permanence “something comes from something else”
-Justhink
Except that the appearance of a contradiction in logic is not related to what any of the free variables mean, whereas the determination of a contradiction in English is not related to the syntax of the sentence (nor its ability to be manipulated while retaining sense re: a translation).
So, I’m not saying logical sentences in English are meaningless. Still. 
These strike me as different ways of saying this: logic is useful when an argument that is considered logical (according to its own rules) does map to non-logical statements derived from empirical observation (an external reference).
This reminds me of a discussion we had back in the “What’s wrong with this definition of science?” thread, when debating whether mathematics could be considered a science. I pointed out that most scientists recognize four fundamental or “hard” sciences: mathematics, physics, chemistry, biology. IIRC, you preferred to think of mathematics as a tool, not a science, because it did not, in the main, describe anything about physical reality. (Feel free to correct my recollection!)
I propose an analogy: mathematics is to empirical science (like chemistry) as logic is to empirical reality. I propose it in part because I need to introduce a concrete example into this abstract discussion.
Many mathematical statements (equations) are internally consistent, and therefore valid. We may not be able to connect every one of these equations to some empirical reality. But when we can, we find that mathematics does successfully predict reality. For instance, one learns in 12th grade calculus that integrals – however bizarre and useless they seemed at first – can be used to determine the volume of a cherry chocolate chip Bundt cake. The mechanics of the integral may not correspond to any of our empirical or intuitive experiences, but there’s no denying that time after time, the integral is proved correct by filling up the cake pan with water and pouring it out into a measuring cup.
The language of mathematical manipulations allows us to get from A to B to C to D, even when all of the steps along the way don’t fit an observable “reality”. Empirically, we may be able to confirm only A and D (the dimensions of the cake pan and the volume of water in the measuring cup); B and C (the steps in doing the integral) may have no empirical reality of which we are aware, or which we can imagine. That doesn’t make B and C invalid statements any more than it makes mathematics as a whole meaningless, pointless or useless. It just means we can’t prove them right or wrong by pointing to an external reference.
So I have to ask: does our inability to “map” B and C to an empirical reality point to a limit in those statements (or in mathematics), or to a limit in our knowledge and experiences as human beings?
Do you take my point, or have I missed the mark?
Either way, nice chatting with you again, erl! 
(btw: The Company has closed us down and I shall be gainfully unemployed as of 1 Jan. 
“And there was much rejoicing…”)
Torturous. You analogy re: our previous discussion is smack-on (which, really, should be no surprise as logic is more or less a subset of mathematics).
By trying to give logic meaning, you keep referring to reality (whether we have observed this “part” or “event” in reality or not is irrelevant). My point is that, in the quest for meaning, you’re done before you ever get to logic. Once you leave reality, you leave meaning, even if you’re “just stepping outside for a quick smoke.” You go to logic to manipulate strings that you substitute with English sentences based on observation. Fine. And perhaps you even come to a conclusion up there that, hey, maybe [this] is the triple point of carbon dioxide from your logico-mathematical workings (i.e.- logic has accepted uses, I won’t deny that). You still come to reality to test it (1), and if you find yourself to be wrong, you don’t throw logic/math away (2).
If nothing, then, proves or disproves it (1 and 2), and it doesn’t strictly concern itself with statements about reality (even if we are able to use it that way), then in what sense does it mean anything? What does it mean? Cervaise asks, what does a hammer mean? This either proves my point (nothing!), or it misses it completely. We can also ask, what does “hammer” mean when used as a noun? I can hold up a hammer to answer that question. What do we hold up (point out, etc) to answer the question, “What does logic mean?” I can reference pain and green better than that! You know? And they don’t even designate objects!
“When we’re talking about [such-and-such], it means [blah blah].” Yes, when we already have extra-logical content in the form of a conversational or otherwise [English] context it means something. Who could deny that?
[PS: 
All the pharmas are going nuts laying people off and cutting budgets. We’ve had a terrible sales year for pharma research instrument sales and have had to lay two people off. That may not sound like much, but it is over 10% of our company (though maybe only 5% of our salary expenditure). Good luck finding work. Honest. But if you move to MA looking for some upstart biotechs you’ve got one guy to drink beer with, anyway! ;)]
[basking in the reflected glory of Jerevan and erislover]
Ahh… now these are Great Debates.
Not quite. Rather I’m saying, because certain parts of logic do have meaning which is demonstrable in empirical reality, we shouldn’t be so quick to assume that the other bits, although they do not correspond to any reality which we as humans can know and/or describe, are absolutely meaningless. But on this I know we will differ: you subscribe to materialism, and I am willing to accept that there may be aspects to reality which elude my five senses.
Or to put it another way: how else would you define “meaning”, if not according to some human experience? (Careful, it’s a trick question! )
Agreed. I don’t throw it away. I certainly don’t throw away the intermediate steps which get me from A to D successfully, even if I cannot imagine an empirical reality – or, if you like, come up with English sentences – to which they correspond. Again I ask: does this not imply meaning in B and C? Or is it not hubris to conclude: because I cannot perceive a reality which corresponds to/is to described by B and C, then none exists – B and C have no meaning?
You seem to want to dismiss logic as generally meaningless, even while acknowledging that “logic has accepted uses”. To me that’s like getting from A to D through B and C, then throwing out B and C because you’re back on recognizable ground. Or to borrow your analogy: it’s like going out through door A, to smoking area B, along path C to door D (in a different part of same building as A), and then denying the meaning, if not the existence, of “outside”.
No one. But as Libertarian has been pointing out, all language is eventually self-referential. I would say, “All language is metaphor.” That is how our human minds operate. Or are you saying that something which cannot be expressed in rational English has no meaning, no existence?
We had a similar discussion in the thread you started about personal phenomena – such as “pain” and “green”. Ultimately we end up having to accept that we each mean the same thing when we use those descriptors, or we accept that we cannot communicate in any real way at all.
Thanks, but between severance and the possibility of a consulting gig with The Company at other sites – how ironic is that, when they don’t have a job for me? – I should be OK for a while. But if I’m ever in Mass…