I personally feel like absolute doubt might bring one to see "logic" as an axiom.

I feel like I am capable, for anyone trying to use logic to prove something, to use their own "axiom" they think with ("logic") to instigate the doubt in its very own self: considering human is not omniscient, how is it possible to prove that one cannot encounter a questioning that (s)he hasn't thought of about any piece of knowledge one might have thought to have developed/acquired/proven? In other words, how can one prove that something "illogical" cannot exist? As a consequence, it seems like everything can be correct, and everything can be incorrect.

To put it in another way: why can we trust "logic"? Someone trying to answer this question will have to do something that boils down to "using logic to prove logic", which looks like a fallacy I believe.

I think it will be hard to argue this topic in when many forum visiters (yourself included it looks like) have not formally studied Logic as a philosopihy...it has a lot of practical applications that you can't immediately dismiss, like math or programming.

The true paradox doesn't stop with logic being used to prove logic, there is also the problem of using logic to disprove logic. In fact your whole basis for questioning logic is based around logic (which hilariously I would use logic to prove that it doesn't necessarily undermine your position).

The real philosophical nature of logic is that it's the mechanics of truth preservation. It relies on the axiom of non-contradiction and a few others. But the actual mechanics of it, that's quite a silly thing.

To prove, to trust, to reason... These are all words in our language that describe the mechanics of truth; that is, logic.

I seriously question whether this discussion is possible on any level.

Logic is just rules. For something to exist contrary to existing rules simply means you need different rules to explain it. Hence, science. You can't have phenomena that by definition follows no rules. Closest you can get (but not saying such a thing could really exist) is something that follows completely random rules, but that would be the rule it follows in turn.

I feel I didn't word this well, but I can't be arsed to revise it now.

Post has been edited 1 time(s), last time on Mar 25 2013, 7:29 am by Tuxlar.

Mathematics and logic only model the world, they do not define it.

I indeed haven't. However, I plan on starting studies in Philosophy at university next winter.

That's what I thought, but I was curious whether or not people would have some things to share that I might not have thought about.

The problem here seems to be that to determine that "for something to exist contrary to existing rules simply means you need different rules to explain it", you are using logic, which is one of those "set of rules" you are talking about.

Plenty. None of which are particularly prolific.

From what I've understood in my studies of it logic is basically like translating the English language (or any language) into math. Stripping away all the unnecessary stuff and just looking at arguments or claims in a pure true/false way.

Eg.
Acts of punishing the innocent are right.
Here we have an unsupported claim. Now let us turn it into an argument:

If acts of punishing the innocent were wrong, then God would not have killed all the Egyptian firstborns for the sins of their Pharaoh.
God killed the Egyptian firstborns for the sins of their Pharaoh.
Therefore, punishing the innocent is a righteous act.

What you see here is:
PREMISE
PREMISE
CONCLUSION

There are two things you need for an argument to have a conclusion that is true, soundness and validity. Validity is basically a properly structured argument aka no fallacies (this is a very simple explanation) and soundness is that each of the premises is true AND the argument is valid (aka you can't have a sound argument that is invalid - however you CAN have a valid argument that is not sound - one or more of its premises are untrue). How do you know that they are true? Well they have their own supporting arguments, ad infinitum, or something that everyone just agrees on, eg. "the sky is blue."

Now to make it a syllogism, what my Prof referred to as "Loglish".
If A, then B.
Not B.
Therefore, not A.

The structure of the argument is referred to as 'modus tollens' or 'denying the consequent'. (The 'opposite' structure is 'modus ponens' or 'affirming the antecedent'.)

Finally, what the same argument looks like in proper logic:
(A ⊃ B)
~B
∴ ~A

Now here is a modus ponens argument:
(A ⊃ B)
A
∴ B

Modus ponens in English:
If God killed the Egyptian firstborns for the sons of their Pharaoh, then punishing innocents is a righteous act.
God killed the Egyptian firstborns for the sins of their Pharaoh.
Therefore, punishing the innocent is a righteous act.

Now here are the two invalid versions of modus tollens and modus ponens, known as denying the antecedent and affirming the consequent, respectively. These two are formal fallacies.

Denying the antecedent:
(A ⊃ B)
~A
∴ ~B

Affirming the consequent:
(A ⊃ B)
B
∴ A

Anyway that's all I'm going to bother to do for now - you can get into much more depth than this though. I hope you enjoyed your logic lesson for today!

I don't believe the topic is basic deductive logic , oh_man.

My question would be: how do you know that using the "PREMISE-PREMISE-CONCLUSION" method is good? By trying to explain it to me, you will eventually end up having to say that something (logical reasoning, that is) has to be considered to be true before establishing that anything is logical.

So you are referring to this?
http://en.wikipedia.org/wiki/Regress_argument

I am a foundationalist myself.

That was an interesting read. It does look like I'm am using the regress argument against logic reasoning.
May you explain how you cope with the idea of foundationalism? I'll draw a parallel with the topic on moral relativism that I've posted recently: if you accept that certain things do not need justification and are to be said to be true, what is your reaction toward someone that would hold different "foundations"? By using your system, wouldn't you end up struggling with any debate questioning your belief? How would you justify the oppression of that person which holds different beliefs than you (because, say, for example, that person believes that killing you is right, while you do not)? Wouldn't you end up feeling hypocritical at some point?
(I understand that you might simply answer "No, because the beliefs I am holding are what I consider to be true no matter what.", but I'm really having a hard time thinking that you would feel like someone using this same way of justifying his beliefs would be in the wrong.)

I thought about it.

I suppose the best answer is this. Because logic is not something we observe, it's something we create. Why does it work? Because it is defined to work.

I call logic the mechanism of truth preservation because that's what it is defined to be. An intro to logic class will delve far more heavily into this, but an argument is only valid if and only if it is not possible for the premises to be true and the conclusion to be false. This definition is not found or discovered, it is imagined. Logic is but an abstract fantasy used to model the world around us.

So at heart it relies on axioms which must exist for logic to exist.

Perhaps I should point out, though, that the idea of a self-proving idea is intriguing.

It could be based otherwise, for example, in randomness or empiricism.

I consider logic to be nothing more than a tool in mankind's toolbox. We don't use things because they are right or because they're good or perfect or infallible or whatever, we use things because they work. Just as we trust our hammer to smash nails through wood, we trust logic to help us make sense of many things. However, there are limitations like any other tool. For example, if logic is our hammer, we would not expect it to be very good at screwing in a nail or making precision graphic art on whatever project we happen to be working on. In the same manner, it would be silly to use logic in a situation where it doesn't apply, which is mostly when our knowledge of a topic is incomplete or untrustworthy. When situations like these arrive, I would argue it's better to use another tool, like observation, intuition, or even flipping a coin sometimes. When we fail to respect the limitations of the tool we end up making assumptions that lead us to wildly incorrect conclusions which can lead to wildly disastrous circumstances.

But aren't our observations and intuitions relying on logic?

They rely on reasoning centers of our brain. Which can be modeled using logic.

Edit: Vrael you empiricist dog

Logic is based in axioms which are in large part based in our intuitions - observations require some assumptions to be useful/share-able, I like to group those assumptions in philosophy but observations themselves don't require logic per-say

But drawing conclusions based on observations does.

Observation and intuitions? Sometimes intuition does. Observation is different though, there is no form of logic which gives us the power to know anything about the world around us. Logic only takes what we already "know" in the form of premises, and gives us a means to determine additional information from it.

To better illustrate what I mean, consider any of the typical lab-rat experiments, where one button gives food and another button gives electric shock. If a mouse presses the shock button, he immediately will avoid that one further, despite the fact that he knows nothing about the internal workings of that button. There is no logical connection between pressing the button and being shocked, for example, that one press may have been a discharge of accumulated static electricity, and a second press will do absolutely nothing. Or perhaps the button malfunctioned and the electric discharge was related to that. The observation gives us the power to say "pressing this button yielded an electric shock", and our intuition combines this observation with our knowledge of other buttons and their functions to yield the statistical likelihood that "pressing this button again will yield another electric shock." If we were to rely purely on logic, we can make no claims about what will happen the second time we press the button, we would need to make some highly invalid assumptions like "there is a 1-to-1 mapping between the pressing of this button and the result that happens" and "there are no outside influences on the pressing of this button" and so on and so forth.

No, it doesn't. As in my above example, drawing the conclusion that "pressing the button again will yield the result of a second electric shock" is illogical based on the observation given. It's simply likely, which we draw from our experience and prior observations to say, we're not drawing any logical implications between the observation and the conclusion.

Prove I'm an empiricist using logic

Post has been edited 1 time(s), last time on Mar 24 2013, 10:55 pm by Vrael.

I definitely see this discussion as something stemming from the regress argument. I also see myself as somewhat of a foundationalist for the following reason:

I feel that we necessarily experience life from a perspective, and therefore we must choose foundations which frame that perspective; i.e. that it is impossible to completely divorce one's self from the issue of perspective. This axiom could itself be challenged by the regress argument, but I choose to hold it foundational, because I believe it necessary. I don't know how to address to idea of someone with a "different" foundation - I see that only as a different perspective and could use the regress argument to (albeit circularly) prove my axiom.

From that, I choose other foundations to form the basis of an epistemology. I recognize that other people have different perspective, but one thing I choose is that there exist empirically verifiable facts. Everyone I interact with shares this belief, and so I don't have need to question it. Logic is the language of empiricism, and I choose to accept it as accurate as it matches with my experience of the world. I think there is also non-empirical information which necessarily depends on perspective, and a lot of that contributes to a general inability to agree on absolute perspective, and is in some sense inextricable from the idea that perspective is fundamental to existence.