What Is Logic?

1. Oct 13, 2004

XxFREEofFILTHxX

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

2. Oct 13, 2004

dekoi

1.) Logic is a root of reason. Reason is either 1: a product of human/intellectual developement |or| 2: a Divine gift.

2.) Depends on whether you believe in a central authority or not (God). If you believe in God, and that God created all, then God defines reason. One can refute this, by saying humans have free will and thus, they use their will to define reason. However, reason is based on an objective truth (if in fact, you believe in God). If you are a humanist, then you clearly define your own logic (because you believe you are your own authority).

3. Oct 14, 2004

Goongyae

1a. "What Is Logic"

Logic is a reliable method for taking one set of truths and manufacturing new truths from them. Using a finite number of axioms, plus logic, one has access to many truths (though not all). Seeing as how it's impossible to prove the consistency of simple systems like arithmetic, I admit that it's possible logic can also yield false results. The theorem about cutting up a grapefruit into a finite number of pieces and then fashioning a solid sphere the size of the sun comes to mind.

1b. "What Is It A Product Of?"

Logic, like science, is something people invented because it proves useful empirically. Most people who reject logic have died out by now. In particular, the bunga bunga tribe was horribly impaled by their foes when they refused to accept the parabolic trajectories of their javelins.

2. "Does It Define Things Or Is It Being Defined By Other Higher Things?"

It's merely a tool that has proven useful to people. So, the answer is that people are the higher things that have defined their logic. I think suggesting much beyond that would take a lot of hubris.

Last edited: Oct 14, 2004
4. Oct 14, 2004

Humbucker

Logic is weighing your behavior against the consequences.The choice is yours.

5. Oct 14, 2004

wuliheron

The term "logic" refers to the catagory of analytical tools based on the principle of Reductio ad absurdium (reduction to the absurd). In turn, this principle is derived from our demonstrably emotive ability to give or find meaning in the world around us.

Logic provides merely one type of description of things among many. For example, natural language is repleat with vague terms such as love, pile, bald, etc. which logic has little to say about.

6. Oct 14, 2004

XxFREEofFILTHxX

1. but how did you conclude these statements?
2. Is logic wrong and full of errors?
3. By what do we conclude what is logic, and what is not?
4. On what is Logic based on?
5. What is proof?

7. Oct 14, 2004

XxFREEofFILTHxX

Dekoi, The opinion base in the existence god should not make a difference...........what defines logic?

8. Oct 14, 2004

Prometheus

Logic is an abstract form of reasoning that is based on the model of the Indo-European language grammar. Non I-E languages do not consider, and never developed, logic in the way that it developed in the west.

Logic is a method of formulating thought. It is not a way to prove anthing, except in a theoretical manner. For example, logic could never be used to provide a proof that god exists, because such proof requires axioms, which are beyond the scope of logic.

9. Oct 14, 2004

dekoi

Prometheus:
Logic can very much prove something. Proving God does not require axioms; the proofs themselves use logic/reason to build up into a general law (an axiom).

XxFREEofFILTHxX: If God exists, he has defined logic for us. Logic and/or reason, in this case, would be founded on the natural law.

10. Oct 14, 2004

hypnagogue

Staff Emeritus
I think what Prometheus meant to say is that the formal rules of logic alone are not enough to prove anything; we must start with certain premises that we assume to be true (axioms) and manipulate these axioms using the rules of logic to derive further premises. In this regard, Prometheus is quite right. Given no axioms to work with, logic cannot do much of anything, somewhat like a baker cannot do much of anything if he has a recipe but no ingredients.

This depends on one's definition of God. If the minimal requirements for a God be that it is omnipotent and omniscient, then it's not hard to suppose a kind of omnipotent, omniscient God that has nonetheless not defined logic for us.

Remember that we are talking about an abstract philosophical concept when we use the word 'God.' Perhaps some religions suppose a God who defines logic (whatever that might mean exactly), and in the context of such a religious definition of God your statement would hold. But please keep in mind that PF does not support discussions about God in the context of religion.

11. Oct 14, 2004

hypnagogue

Staff Emeritus
XxFREEofFILTHxX, a good introduction to the topic of logic is available on wikipedia.org: http://en.wikipedia.org/wiki/Logic

Please read over this article. It may clear up some lingering confusions you have and help shape any future questions you might have.

12. Oct 14, 2004

Prometheus

Well-phrased.

Please prove something using logic. You might try proving that god exists, or something simpler. Please indicate how a proof using the rules of logic can prove that anything exists with no axiomatic requirements.

13. Oct 14, 2004

dekoi

Prometheus, i must have misunderstood you as Hypnagogue stated.

However, why could axioms not be produced by logic as well? Why do you state they are outside the scope of reason? I can answer this question myself (likely the same answer you will reply with), although it is very vague.

Hypnagogue: imo, i find it very difficult (as well as a professor i know) to express philosophical thoughts regarding an omnipotent power without -- at a latter point -- making a connection with theology. However, i will try

Last edited by a moderator: Oct 14, 2004
14. Oct 14, 2004

cogito

Not quite. Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises. So, it is false that we must start with certain premises merely assumed to be true. We can start with no premises, and derive necessary truths. What is the case is that these theorems are true in any possible world, and hence quite uninformative about the particularities of the actual world (i.e., you can't derive any contingent truths about the actual world).

15. Oct 14, 2004

Tom Mattson

Staff Emeritus
What brand of logic is it that can do this?

Logic, as it is normally understood, consists of rules of valid inferences from one statment to another. How do you reason something from nothing?

16. Oct 14, 2004

Goongyae

"Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises."

Incorrect, have you not heard of Goedel's theorem? Even in the simple mathematical system of arithmetic it can be demonstrated that there are truths that are impossible to prove.

17. Oct 14, 2004

cogito

I'm familiar with both Goedel's incompleteness proof, which proves that all consistent formalizations of number theory will include undecidable propositions (propositions for which the axioms of the system will not allow one to determine their truth-value), and his completeness proof, which proves that first-order predicate calculus is complete and sound. When I used the term 'formal logic', in my original quote, I was referring to first-order predicate calculus (which is what the term 'logic' [in the deductive sense, rather than in, say, a Bayesian inductive sense] almost invariably refers to) and not to extensions of it that require set-theory. I should have been more clear about this, but I'm used to talking about logic with philosophers and not mathematicians. Thanks for keeping me honest!

18. Oct 14, 2004

cogito

First-order predicate calculus. You reason from nothing by temporarily assuming some proposition, and seeing what follows from it. You discharge this assumption in various ways. If an assumption leads to a contradiction, then you know that the negation of the assumption is a theorem. If your assumption leads to some conclusion, then you know that the conditional comprised of the assumption as its antecedent and the conclusion as its consequent is a theorem. There are other ways of deriving theorems, but these two methods are very common.

19. Oct 15, 2004

wuliheron

1) Demonstrably, words only have meaning according to their use in a given context. Hence the term logic could be used by someone to refer to a love of chickens, but obviously that is not the context used here. The implied context is the normal uses of the word, which includes both formal and informal logic.

Because all types of logic normally refer to the concept of reason, the foundation of logic is obviously the concept of the absurd because reason has no demonstrable meaning outside the concept of the absurd. That is, the idea that some things are just impossible, undesirable, and meaningless. When analyzed, every form of logic thus far investigated has been based on the principle or axiom of Reductio ad Absurdium.

In turn, the concept of meaningful/meaningless demonstrably arises from our ability to emote. My computer can do endless logical functions flawlessly, but it cannot place logic in any kind of meaningful context. It is an idiot savant which cannot tell the difference between the logical and the irrational.

One famous case study involves a man who lost the ability to emote due to a head trauma. He could not hide his condition for any length of time whatsoever. Like a computer with an incredible number of preset responses, all he had left was his memories of how to respond. Any novelty whatsoever always threw him for a loop (Danger Will Robinson, does not compute!)

2) Logic is a specific type of tool and, as such, is limited by definition. Still, I call a wrench "wrong" or "full of errors" when I attempt to do something with it that it was not designed to do. However I can use it occationally as a hammer or whatever, something it was not really designed to be used as. If I use logic for something it simply cannot do, it is my use of the tool that is "wrong" or "full of errors", not the tool itself.

4) Ditto

5) Again, demonstrably words only have meaning according to their function in a given context. Logically speaking, logic cannot be used to prove it's own axioms because this would violate the principle of reductio ad absurdium. Hence, the ultimate proof for logic is whether or not it fits our ideas of the absurd. Whether or not we feel it is absurd.

20. Oct 15, 2004

dekoi

If logic requires some sort of earlier premises, would that not cause us to assume there is an original, absolute, and objective truth or premise in everybody?