“Reflected Glory”? That was Tallula Bankhead!
Why not just call yourself Lyta Alexander? It takes less time! 
First off eris; I think I started rambling when replying a response to your assertation - so I decided to take a little more time to translate it in a way which shows that the point is disagreeable; if indeed it is.
One thing I openned the reply with was the idea that logic seeks to recursively redeem contradiction. I have no ready made answer right now as to why we are all not just experientially consistent; or why spacial resource exists as scarcity in general, however I do understand why logic exists in general; given the first priciple of sorts. Moving along this line doesn’t specifically answer your question/statement though, so I’d better hold my horses until something more concrete than a generalized: “Why does anything exist at all? I don’t know, but it does and this is what you have to do.” I personally disagree with this type of reasoning; and don’t want to be percieved (by myself if anything)as defending myself with it.
As for the quote I selected above; he’s talking about difference, as a fundamental ‘axiom’ without generalizing it. He may use a similar tool to what I use, in that he looks at himself and determines what is impossible for OTHER beings to perform in the future (or in general) in order for him to exist right now.
Other beings including himself, cannot create nothing; ever. This is a phenomenal block on free-will; which through the use of logic, determines that difference cannot exist in the form of a monism (zero and one; as both one and zero are zero).
This is quite possibly the most difficult thought to articulate in logic. 0+1=0 1+1=0 0+0=0 also! 0+1=1, 1+1=2
or 2=(1+1=0). Difference is exceptionally difficult to symbolically represent even if you know the language it’s being communicated in. Why? Because it’s too obvious; it’s everywhere. I believe that he’s unnecessarily contradicting himself in this passage by stating a logical constant that discards logical constancy; without providing a reason which is somewhat obvious. His sensory arguement requires quite a bit of complexity to even emerge; and as such I don’t see much evidence that he recursively validated those complexities in that regard.
If he had stated how fundamental the pervasiveness of difference itself is; that it cannot be represented reducabily as it is irreducable; that would be significantly different than stating that “difference cannot be discerned, because everything is fundamentally unrelated.” Some aspects of logic are related, in that we can formulate similarity from difference; without similarity being exactly the same; and as such, effectively nothing at all.
Part of this involves the trap of thinking “If everything was related; then nothing would exist; therefor since we exist everything can’t be related which means that talking about it is pointless.” That’s a good and dandy, but NOTHING does not exist. That is the problem he’s running into IMO. He’s using the existence of nothing to make the arguement; though I don’t imagine that it was his intended effect.
As to why everything is not just everything; buth rather something along the lines of: “everything else”; I can’t say.
I don’t think this fundamental aspect of reality can be argued against however - but I’m gonna think on it a bit.
In short: I disgree with the conclusion that the last sentence from this quote makes; as he did not effectively demonstrate (to me anyways); that logic is always bound by it’s lack of possession from prior generations; and that this bind is more true of our current state, than truth itself.
-Justhink
Not that Aide. Not that Vorlon Ambassador, either.
Still, it was nice to read an actual debate on these forums that didn’t degrade into philosophical twinkery or pointless flaming. Thanks – you’ve made my day.
Part of this topic involves a mathematical habit which illustrates our ‘lazyness’ along this regard.
1/3 is translated as 0.33333 repeating… 3’s into infinite regress effectively building a finite structure to that degree; which is utilized as motion when it is currentlyu being processed.
The way humans translate this finitely is to tack a 4 on the end.
0.3333334 …and then give a general rule about that, which is effectively as arbirtary as the process itself. They also write a line over 0.333333 (which I don’t know how to do with computer symbols); however this line is left open ended as a great mystery of nothingness to a large degree.
What I don’t see occurring in the teaching of decimal output from fractions is the idea that adding the 4 on the back end is necessarily tweaking numbers outside of where the decimal point is.
You can’t just write 0.3333334 without understanding that you have eluded to the existence of numbers…
- <----- (behind that point)33334
Not only behind that point, but illogical to ever bring in front of that point; which begs another decimal point; with which these processes can be observed.
-Justhink
first off, let me say that without logic, you cannot communicate the validity of your statements, so to say it is meaningless is…meaningless. for example, in arguing against the usefulness of logic, someone said:
consider for a moment, if you will, what you mean by begged, if you are not assuming that logic has meaning.
logic is a set of things we consider “true” because they seem to be so inherently, in this reality. i have argued in the past that in another reality, they may not be so, so logic’s definition is relative (rather than absolute). this is FAR from claiming it is meaningless.
it seems that the major argument to the meaninglessness of logic is that it is built of tautologies, which are meaningless. the claim is that they are meaningless because they are true for all substitutions of propositions for their variables. like:
(p & p->q) -> q
is a tautology. that means the real statement, if we consider it as a proposition is:
(p & p->q) -> q for all p, q.
now, this is tautological, and it states that we can substitute any value for p and q and maintain the validity of this statement. suppose we say:
p = “it is raining”
q = “i have an umbrella”
then we can say if i assume the truth of the statement “if it is raining then i have an umbrella”, we can validly say that any time it is raining, i will have an umbrella. that is, we can achieve something meaningful.
allow me to suggest that the fellow who made this claim had in mind not tautologies, which are implied by all, but contradictions, which imply all. a tautology is a valid statement and its truth can give meaning to the various propositions we substitute for its variables. a contradiction, though implies all things and presumes no meaning in those implications. they are valid trivially.
it has also been claimed that the meaning of the earlier statements (about rain and umbrellas) is derrived from the language and not from the logic. first, consider that the application of “language” to these statements of logic has a purely logical basis: substituting specific propositions for general variables is a concept derrived from first order logic. second, consider the meaning of the language without the application of logic. if we do not believe that logic applies, we can claim that it is raining, that i do not have an umbrella, AND that if it is raining then i will have an umbrella. these statements of course have no meaning. the concept of “if” and “then” is a concept of logic, not just of language. finally consider the relationship between the theorem (which i will pretend you consider meaningfull), and the tautology. all theorems are tautological. it is just that fact that implies that one can prove their validity. so by claiming that logic is meaningless, you are claiming that all theorems are meaningless. in fact, if we accept russell’s definition of “pure mathematics” (all statements of the form p -> q, and i do), you claim that all pure mathematics is meaningless.
also, i would like to restate that logic is based on the concept of truth. if we do not assume that the concept of truth exists, we assume that logic does not. also, we assume that by our present methods, we can say nothing “meaningful” about the world in which truth does not exist. that is to say, i prefer to claim that all concepts defined a priori are meaningful in the context in which they are defined, NOT that they are undefined in all contexts. i hope that you agree.
on another note, how many people here are “mathematicians”, and in what sense of the word? and how many have read russells works on the topics? russell happens to be my favorite philosopher (for reasons independent of logic), so these are just questions of background, not to imply that anyone is a rightful ‘authority’. i’m new here, so i don’t know these things.
lastly, i challenge anyone to aruge to me that logic is meaningless without appealing to my sense of logic.
-d^n such that n is an element of Z
That’s an interesting paradox.
If your message holds, logic becomes meaningless. But once that happens, so does your message, since you relied on logic to provide your point. At which point, of course, logic becomes meaningful again.
::evil grin::
I’ve been attempting to do that, in a way. My point remains this:
Meaningful English sentences are not more or less meaningful for our ability to map them to a rule-bound symbology of logic. They do not mean more or less by being constructed in a manner analogous to logical statements.
Consider, instead, that we said something like this. Logic is the generalization of an argument. How does that sit with people?
Mao Tse Tung once wrote: “Political power grows out of the barrel of a gun”-- the gun being a metaphor for the military.
ITSM that some posters are seeking a meaning to logic within logic, and that’s the wrong place to look. That’s why the OP says logic is “meaningless.”
The right place to look IMHO is in its application to the real world. Here, the appropriate standard is usefulness, rather than meaningfulness. And, the key evidence that logic is useful is this: societies that use logic have militarily defeated those that don’t.
Logic is an abstraction of the real world. The meaning of (P&P->Q)->Q lies in the fact that it summarizes the way many natural language statements behave (as far as their logical properties).
Consider arithmetic. It’s an abstraction of the way the real world behaves, and it’s only true to the extent that the abstraction correctly represents the real world. Example:
2=2 (tautology)
2+2=4 (add 2 to both sides)
2+2-2=4-2 (subtract 2 from both sides)
2=2
Now apply this to the real world. Start with 2 Granny Smith apples in one pile and 2 in another pile:
2 apples = 2 apples (true)
Add 2 crab apples to both piles:
2 Granny Smiths + 2 crab apples = 4 apples (true)
Remove 2 apples from both piles:
(Well, now it matters which apples I remove. Suppose I remove two Grannies from the left pile and two crabs from the right pile. Then I get)
2 crab apples = 2 granny smiths (false)
At least, I would rather have Granny Smiths than crab apples. The math only works to the extent it reflects the real world: all aplles are equal in arithmetic, but in the real world some are more equal than others.
So I would agree with the earlier poster who said that logic is meaningful in the same way physics is meaningful. It approximates the way the world works.
Friend Rob: Actually, that conclusion is true. In adding the crab apples to the Granny Smith apples, you were inherently stating that the two were equivalent.
If the two types aren’t equivalent, you committed the error by putting them together in the first place.
Otherwise, you’re right on.
Gee, Friend Rob, but why can’t we just say the real world is useful because it approximates the way ideals work? (a la transcendental realists a la Platonism)
Then how come it didn’t show me that I had eggs for breakfast?
I was offline for a while, so this reply is a bit belated:
You’re describing a pattern.
To put it in perspective, the word “hammer” doesn’t describe a particular hammer. You can hold up a particular hammer to provide an example of the general concept, but the word “hammer” doesn’t apply solely to the hammer you’re holding up; it describes attributes common to a large collection of real-world objects, past and present.
The same thing holds for “green” and “pain”: they don’t describe particular objects or sensations or events. They describe attributes common to a collection of objects (in the case of “green”) or sensations (in the case of “pain”). In other words, they describe a pattern observed amongst those things.
“(P & (P->Q))->Q” is the same way. It describes, not a particular object, but a pattern observed in a large collection of real-world things (not objects or sensations in this case, but events and facts, or perhaps configurations of events of facts).
There’s more in that vein, but on preview I see FriendRob beat me to it. However, I would like to add this:
I told you. One of your premises (P->Q, specifically) was false to begin with. I don’t see how an incorrect logical argument has anything to do with your point.
Because it is only incorrect… [drumroll]… based on reality! Which is where we must be for meaning. Still. 
But logic is supposed to describe a pattern of all things? Again: a sign we may place in front of everything.
Let’s take a legitimate example, Math Geek, to hopefully solidify my objection.
An event that has an English sentence of the logical form
(P & (P->Q))->Q
is:
“I got into a front-end collision. Front end collisions set off airbags. My airbag is set off.”
What makes this true/meaningful? Its form [(P & (P->Q))->Q]? Or that Front end collisions set off airbags and I had a front end collision?
Well it all seems to obviously come down to how you define having “meaning”.
Start with Peano’s postulates, define the necessary operations and so forth. Then one day some one discovers that
x[sup]n[/sup] + y[sup]n[/sup] = z[sup]n[/sup] has no nontrivial integer solutions when n > 2.
Here is how I picture erislover responding to such a statement (tongue in cheek, of course ;)): “(Yawn) Yeah, tell me something I didn’t already know! Peano’s postulates imply that, it’s nothing new!”
And, in some strict sense, he’d be right, of course; (Peano’s postulates) => (Fermat’s last theorem) is a tautology; once you have P’s Ps you have to have FLT, too.
But it’s a pretty damned impressive tautology. Given knowledge (P’s Ps) and knowledge from inference (FLT) certainly seem to be very different beasts. Logic, of course, is a tool that takes given knowledge and extends that to knowledge from inference; now whether that tool is more appropriately called “meaningful” or “useful” may not be necessarily clear, and is something that really depends on the definitions of the words.
Anyway, at the very least, have I got your position right, erislover?
I like this statement. I think it works with my earlier example about getting from A to D through the mathematics of integrals (B and C).
Sure, we don’t have to determine the volume of a cake pan via mathematics. We can do it the old-fashioned, inverse-Archimedean, empirical way by filling up the cake pan with water and using a measuring cup to figure out how much water that is – we can get from A to D “directly” (leaving aside the question of whether that is really what is going on), without going through B and C. But in this particular case, we’re using the empirical method to satisfy ourselves that going from A through B and C does get us to D. We need this kind of confirmation because B and C are steps which we may not be able to describe in plain English sentences – that is, they may have no meaning to which we can attach rational, intuitive or familiar ideas.
This confirmation is also important because it suggests to us that B and C do have some meaning, even if we can’t express it, because they connect two points of empirical reality (A and D) which we do recognize. More importantly, the confirmation suggests that B and C might be useful in other situations. Just because we can’t describe “outside” doesn’t mean we can’t view “outside” as a useful way to get from door A to door D without going through the building… though I wouldn’t advise this line of reasoning when confronted with, say, airlocks on a space station. As cabbage indicates, it all depends on what you consider “useful”.
In this case, B and C could be useful in measuring the volume of objects which we cannot, for whatever reason, measure using the empirical method described for the cake pan – a mine shaft, for instance, or a crater on the moon. We might never be able to confirm the volumes of those objects empirically. But we feel reasonably confident that B and C can get us there, even if, on an intuitive-empirical-rational-linguistic level we can’t actually describe how.
“If Americans believe in vitamins, let them take them.” — Meher Baba
It doesn’t matter whether we use mathematics to determine the volume of the pan. The number only has sense when we are talking about the volume of a pan. Clearly using such an example to show that logic has meaning isn’t quite working against my argument, which is that the meaning comes from the real world.
Math Geek might think I should abandon the example of the eggs for breakfast. Why doesn’t it happen that I should abandon
(P & (P->Q))->Q
? Why is it that my example doesn’t fit this form? —I mean, what is it about logic that forbids it? Honestly, I’ve looked over the book I have on introductory logic and I don’t see a provision for not discussing intention there.
I have already addressed this, though. I don’t care if we actually try and measure the quantity or not. The point is that it refers to something in the first place, which (I contend)
(P & (P->Q))->Q
does not.
This is my take of ‘the ball’ as far as the OP is concerned.
Logic seeks to recursively redeem all contradiction into non-contradiction; using the evidence of it’s existence as the proof that non-contradiction provides a standardization embedded in all of reality from which to declare an ego and be correct.
However, the very existence of contradiction contradicts the very premise that truth of purpose exists to this degree; as logic would suggest that the inability for contradiction to exist as a perception would nullify the existence of perception itself into a state of “already completed”; at which point perception itself seems meaningless, and necessarily contradictory.
-Justhink
LOL, that’s hilarious. “Contradictions can’t exist.” “But there’s a contradiction, 1=2.” “But that can’t be.” “But I’m looking at it. Here, I’ll write it again.”