Hi, I noticed my post about this was erased…did I break any rule? or what? :S
or did the question just freak u out…
the question was about the absolute and unquestionable ‘absolute’ truth of math and logic…
c’mon… y do u chicken out! 
notice your post count… this was the only time your post has registered…
welcome to the boards
-Imp
sorry, I thought I’d posted it…
anyways… my question is this…
do you think that math and/or logic is absolutely true and we can be certain that it is and will be true inside all contexts?
or is there the possibility that we could be deluded into believing they are absolute truths ontologically and metaphysically when in fact they are false ‘inside’ the context that ‘contains’ them…
the same as the brain in a vat thing, and any skeptical hypothesis… just about the axioms of logic and mathematics…
for example : (an axiom of logic) existence exists, all red cars are red.
see? they are true, but they are tautologies…
I think this will be an eye opener for most of you, but for the ones who know what I’m talking about, please enlighten me on arguments for and against this hypothesis posed by philosphers like Nietzsche, Foucault, and whomever u wanna quote.
I hope this question isn’t too… 
…to be answered.
Logic does not always work. For example. George Bush is an idiot, George Bush is president, all presidents are idiots.
Also math can be false. using Roman numerals i can Take away 1 from 4 and leave 5…IV - I = V… see what i mean
thats illogical logic you retard haha
logic does always work if you understand it properly.
Are you kidding? This seems sarcastic, but is also presented seriously, so sorry if you are kidding and I just didn’t pick up on it. But in case you weren’t, you should know that these examples are totally and blatantly erroneous.
Well, that question is interesting, because it kind of gets at the roots of philosophy - but also because it ends up being self-referential in many ways!
Here’s what I mean - all truth (by our ken) seems to require some sort of evidence. If I go up to you and assert that China doesn’t exist, assuming you even talk to me at all, you’ll say, “prove it”. Or if I tell you that the solar system only has 8 planets, and you haven’t read the science news, you’d say “why should I believe that?” And there are only two ways in which this kind of proof / argument, fundamentally, can be given.
-
Deductive. We can use first principles and methods of deduction (e.g. logical inference) to arrive at the truth (or falsity) of a more complicated assertion.
-
Induction / Observation. We can observe that certain things are true. Clearly there can be no deductive proof for China’s existence, but since observation works just fine (“duh, I’ve been there, it exists”), that isn’t a problem.
Now apply these means to knowing if logic / math can ever be false. Well, the only way we have of showing it’s false DEDUCTIVELY is through first principles and methods of deduction. Unfortunately, we really only have one such system, and that’s logic. So can we use logic to disprove logic? Sadly no, it’s been PROVEN (interestingly) that logic contains no contradictions, that it can never disprove itself.
So unless you want to try to generate an entirely new system of reasoning besides logic (go for it!), that’s left with trying to prove via observation that logic is false. But that will be EXTREMELY difficult, and most likely it simply isn’t true. Logic relies on only one non-trivial axiom: that (A and notA) can never happen. Something cannot both be true and false.
Now, coffee-shop philosophers like to try to shoot this down by crappy examples, like saying something like “Americans are both worshipped and vilified by the rest of the world”, which of course is at best a paradox (where something superficially seems to be contradictory, but in reality isn’t), and not a true contradiction. Same thing with OldPhil’s examples that I quoted up top.
So basically, no, I don’t think anything is wrong with logic & math. More than that, on a fundamental level, I can’t imagine how anyone could ever argue that there is anything wrong with them. Now, you could assert that logic can’t represent all truths about the universe. I’m slightly skeptical about this, but I think this version is much more likely to be true than asserting that logic ever is actually incorrect.
logic and mathematics are a neat circle. they tell you nothing about anything except the circle of logic or math. they do not apply to empirical events. this is the definitive thread about the shortcomings of logic:
ilovephilosophy.com/phpbb/vi … a90777b10e
-Imp
That’s pretty depressing.
imp can you give me a real life example that prooves a = b, b = c so a = c wrong ?
keyword : real
im not challenging i just wonder if you know of one since you say its conditional wether its correct or not.
That depends, I think, on what you mean by “apply”. I’d say they “apply” inasmuch as you have the ability to translate them into empirical events…just as language “applies” to what happened so long as you have the ability to decode it and translate it into something meaningful about reality…otherwise, this philosophy board is talking a whole lot about … nothing.
Hmm - for a “definitive thread”, it certainly has a lot of incorrect postings. But I’ll admit I only read the first and last pages, because it was long and didn’t seem terribly interesting. If there is a meaty section inside there, could you point me to the page where it all begins? Also, Imp, I will say this: I may not be doing your position justice, since I didn’t read but 2/17 of the thread, but it is quite simply not true that the truth of “if A then B” depends upon the truth of A. The sentence “if A then B” is determined to be true if and only if, whenever A is true, B is also true. If A is false, B can be either true or false, and that doesn’t change the truth of the original sentence. Please let me know if you disagree, or if I am misunderstanding your position in the cited thread.
Certainly when you say that “logic and math do not apply to empirical events”, you are risking a great deal. That assertion presumably is founded on the problem of induction - is that right? There are soooo many misconceptions about what is going with induction, but to look at the matter correctly, and then extrapolate to the link between logic / math and empirical events, you must say precisely this: “We cannot logically prove that logic / math can describe empirical events with any predictability.” That is all you can say - you certainly have zero basis, either logically or empirically, for saying that math does NOT apply.
But since logic and math have done a phenomenal job of describing the universe in all of scientifically recorded history, if you have any faith in induction whatsoever, you will believe that they will continue to do so. Even if you don’t have any faith in induction, you have no basis whatsoever to say that they will not apply in the future - all you can say is “I have no idea what will happen, because there isn’t enough information.”
yep, it’s in the thread
-Imp
read the thread. language itself talks about a whole lot of nothing…
-Imp
I’d reply, but what’s the use?
Oni - that can’t be wrong. It is so, by the definition of “=”.
shinton - logic is not applicable to empirical reality, it is only applicable to statements about empirical reality.
This is the great confusion (one of them) in that horrendous thread Imp linked. Logic applies to statements only. Statements are not empirically “real”.
Whether statements are applicable to empirical reality is another thing entirely. That is outside the purview of logic.
Logic explicates what we mean by the word “tautology”. In that way, it is indisputably “true”. But a tautology, again by definition, has no “content”.
This “translation” of which you speak occurs within language, and not within logic. It is actually “pre-logical”.
Imp, I went on to page 2 of the “definitive thread”, and I’m more disappointed than I was with page 1 and page 17. I really have no reason to read any more unless you tell me that there’s something better beyond page 2.
You say this on page 2:
The quote is correct, but you are entirely misunderstanding it (or else I’m misunderstanding you). Validity is not dependent upon the truth of the premises - rather, it is dependent upon whether or not the truth of the premises leads to the truth of the conclusion. That’s a big difference.
If A is true, and if the sentence “if A then B” is valid, then B should be true as well. This is the only requirement for validity. Thus the sentence “if unicorns exist, then they rule maliciously in Africa” is absolutely valid, because you cannot show me a unicorn that exists that does NOT rule maliciously in Africa. This is because you cannot show me a unicorn that exists. This sort of example annoys people who don’t have much experience with logic, and understandably so - it seems like cheating - but it is absolutely a correct example. Just because unicorns DON’T exist doesn’t make the sentence invalid. The only thing that could make the sentence invalid would be if a unicorn existed who did not rule maliciously in Africa.
and as I look into my crystal ball of “science” I predict an illogical future…
read the first 8 or 9 pages of the link… I don’t want to rehash the same argument…
-Imp
with a brilliant mind of logic, i predict a perfectly logical future 
not a bright one at that.
sigh guess ill be reading all that tommorow.
I’ll buy that it is confusing, and I’ve been perusing that thread, but I’m not sure that I’ll buy that logic is not applicable to empirical reality.
Here’s my thought process. What came first in all likelihood for humans? Language? Doesn’t appear to be the case. Logic? Nope–doubtful…at least not what we regard as “formal logic”. Logic was built on assumptions about reality. Why can’t this person be here and there at the same time? Well, my experience suggests that’s true. LOOK! Here, a link between the two is established–the statement is true by virtue of experience, but suppose you only had the experience? If you read the statement you’d say “Ah ha, that is PRECISELY what is happening”. The two are interchangeable. Language is capable of capturing pieces of empirical reality–if it didn’t, it’d be hard talk about whatever it is we’ve experienced in a meaningful way. The common point of origin is our experience in reality.
At some point, logic became a more abstract beast–it began to ask questions ABOUT itself. It began to become one step removed from empirical reality because I suspect, in part anyway, that when you start asking assumptions that are based on empirical reality about themselves without the benefit of all of the other assumptions being known or stated, it yields a system that is different from “actual reality” while still incorporating bits of it into it. Hence, you end up with a system that operates on “statements” in some places, but when you drill down sufficiently far, you begin to find things that are “experientially true”. Why is this logical principle held? LOOK!
The trick is interpreting the statements that are “hybridized”. Maybe they DO relate to something empirical, maybe they don’t.
I’m not sure where a statement starts and logic starts is a fundamentally different place.
I’ll agree with you here.
Again, I’m not sure that it IS pre-logical. I’m not sure formal logic isn’t simply a Frankenstein monster of some very primitive survival mechanism that gave us reality.
Firstly, stay away from that thread. It’s a mess.
I’m not sure what you mean. You seem to deny that language came first, and then that logic came first. One surely came before the other.
I’m guessing language. I agree that language can reflect reality, and never meant to deny it, but only to claim that this is separate from logic. It is language that assumes certain things about reality.
Logic was always logic. It’s development was of scope. Logic has a wider scope now (I am discounting mistakes as not part of logic at all). Logic applies to more statements now than it did at first.
Logic performs operations upon statements. These operations are designed to produce tautologies that are not always apparent in everyday speech. It’s pretty simple. The statements themselves may reflect reality, or they may not. Logic cannot control this - it must take the statements as it finds them. Logic can be prevented from relflecting reality by those statements - the money shot is always in the language.
Twiffy is essentially correct, although it is doubtful that his example is a true inference. It needs some polishing up to be anything but a triviality in inferential form. But I guess it makes his point well enough. We can make inferences about unicorns, however.
Essentially, if the statements reflect reality, logic won’t remove that quality.