I think everybody agrees that we should only believe things that are rational and logical. But who invented logic? Was it a specific person like Aristotle?

As far as I know Aristotle is pretty much considered the father of formal logic. Amazingly, we really didn't move too far past what he did until the 19th/20th century with guys like Frege and later Godel.

But logic did not exist before him? I don't think that's right.

Quote:

---

I think everybody agrees that we should only believe things that are rational and logical.

---

Well, I don't know about this, but I guess it depends on what you view as "rational and logical". To many, believing in God, much less that He took on flesh, died on a cross and rose again 3 days later, would be extremely irrational and illogical.

TexAgs91 said:

---

Logic was not created. It was discovered.

---

That makes sense. Does it come from God in some way? Or is it God himself?

Also, how was it discovered?

That's true. But nobody believes something they find irrational.

It seems to me that logic should be traced back to animals pre-dating humans. I don't know exactly what criteria I'd ascribe to an animal that can make 'logical' decisions, but I think primates certainly qualify.

Create Account said:

---

TexAgs91 said:

---

Logic was not created. It was discovered.

---

That makes sense. Does it come from God in some way? Or is it God himself?

---

Logic is an indication that the universe operates according to natural law, not supernatural law.

I agree with that. My question still remains. A "non-created" thing always existing sounds like God.

kurt vonnegut said:

---

It seems to me that logic should be traced back to animals pre-dating humans. I don't know exactly what criteria I'd ascribe to an animal that can make 'logical' decisions, but I think primates certainly qualify.

---

Or course this is a different answer than TexAgs91. Who was the first primate to think rationally and how did it happen?

Create Account said:

---

Also, how was it discovered?

---

There was an article written called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Math does describe the universe so well though that to understand physical reality at all, you'd have to have at least some minimum level of understanding of logic.

I don't think there is a clear answer. There are animals that display capacity for logic, those that don't, and shades of gray in between. It is arbitrary to say that a particular shade is the cutoff.

And they are adorable.

Create Account said:

---

I agree with that. My question still remains. A "non-created" thing always existing sounds like God.

---

Not necessarily. A non-created thing might be completely inert. That doesn't sound like god.

I think mathematics and logic are constructs that are outside of this or any universe. They are the only things I can think of that "just are". But they are not physical. They do not change in time. While they can describe actions, they do not act. While they can describe thought processes, they do not think. This doesn't sound like god either.

Neither logic nor mathematics are real. They are models for describing and / or predicting how reality behaves.

So, logic did not exist before it was expressed as a system of thinking. People may have used a system of deduction or passively used the same tools that logic uses, but logic is simply a formal method of describing concepts. This is no different than saying that people added one rock to another rock to make two rocks, but that isn't math. That is a situation that can be described by math.

Logic has nothing to do with natural law or God, unless you want to start talking about the metaphysical aspects of Logic, which Aristotle and Plato both did (and are in some ways enshrined in Christian theology of the Word, Logos -- which shares a common root with Logic, the greek word for word / idea / reason).

Logic is based around the law of non-contradiction.

Eastern cultures embrace a "both-and" approach which violates the law of non-contradiction, while the west tends to think in terms of "either-or".

It's my understanding that thinking in terms of "either-or" orginated from the Greeks.

In determining what is true, only either/or works, because otherwise everything is true meaning nothing is true.

I have also observed that liberals tend to adopt both/and worldview while conservatives tend to think more in terms of either/or.

On the other hand, modern analytic philosophy has shown that mathematics cannot adequately define reality to completion without violating logic.

Basically reality isn't subordinate to either.

I'm not sure I understand your explanation of the spirit of noncontradiction. It doesn't say either-or vs both and.

The law of noncontradiction says if X is not equal to Y then X cannot be equal to Y simultaneously. Not quite the same as either X or Y vs X and Y. Can you explain what you meant?

I tend to just think it was named, not invented or discovered.

k2aggie07 said:

---

On the other hand, modern analytic philosophy has shown that mathematics cannot adequately define reality to completion without violating logic.

Basically reality isn't subordinate to either.

---

Why?

Gdel's incompleteness theorems showed that for a consistent formal system you cannot completely define it axiomatically, and that any formal system cannot prove that it is consistent. Basically there will never be a unifying total fundamental physical or mathematical definition of the universe ... without violating the law of noncontradiction.

Put another way... either we'll never know everything, or we'll know everything including an error.

Man is mortal

Socrates is a man

Ergo, Socrates is mortal

1.) Godel's theorems are about formal systems. Physics is not that, and therefore Godel does not apply.

2.) Godel did not show that a complete formal system cannot be defined axiomatically, i.e. Tarski geometry.

k2aggie07 said:

---

Gdel's incompleteness theorems showed that for a consistent formal system you cannot completely define it axiomatically, and that any formal system cannot prove that it is consistent. Basically there will never be a unifying total fundamental physical or mathematical definition of the universe ... without violating the law of noncontradiction.

Put another way... either we'll never know everything, or we'll know everything including an error.

---

Ok, yes. I saw Hawking's talk at A&M and he discussed that.

If mathematics exists outside the universe it doesn't have to describe itself. And it would have to be if it was able to describe alternate universes.

dargscisyhp said:

---

1.) Godel's theorems are about formal systems. Physics is not that, and therefore Godel does not apply.

2.) Godel did not show that a complete formal system cannot be defined axiomatically, i.e. Tarski geometry.

---

Hm.

Physics may not be a formal system but mathematics is, no? How can you describe a physical system without mathematics?

The first theorem says that in a formal system there are certain statements that cannot be shown to be true or false. The second shows that the system can't be self-proving to completion.

My understanding is then that a complete formal system has unverifiable axioms in it (either it is complete or verifiable, but not both).

I'm not a philosopher (just have a good buddy that is) so it's entirely possible I'm mangling this, but this is how I've understood it.

When I think of logic, I think of a formal set of rules that one can agree to follow when making an argument.

Argument and persuasion existed for a long time before formal logic, but Aristotle seems to be the first one that basically says:

"Let's argue about the Universe. Here are the rules that you must follow to have a valid argument. If you fall outside of these rules, your argument is disqualified."

This treatment of logic and math by some on here has strong shades of Platonism, that is, that outside and independent of us there are mathematical (or logical) concepts, constructs, ideals, whatever. Plato called them forms.

I think the entire universe is a construct.

k2aggie07 said:

---

I'm not sure I understand your explanation of the spirit of noncontradiction. It doesn't say either-or vs both and.

The law of noncontradiction says if X is not equal to Y then X cannot be equal to Y simultaneously. Not quite the same as either X or Y vs X and Y. Can you explain what you meant?

---

Holding two contradictory world views as both being correct from a moral point of view, would be both this and that are correct, but the definitions contradict.

Like saying all religions are true, violates the law of non contradiction. I guess it's heading down the road of morality and off topic to the origin of logic.

Quote:

---

Physics may not be a formal system but mathematics is, no? How can you describe a physical system without mathematics?

---

At worst there will be some number of statements that are true that cannot be proven deductively from an axiomatic system. As a physicist, we're perfectly happy to look for empirical answers to such questions. If, for instance, one of the limitations of our axiomatic system is that we don't know whether or not 1+1=2, the physicists answer is to pick up one rock in one hand, and another rock in the other hand. Cool, we have a new axiom. Godel's theorem applies to a fixed axiomatic system, and physicists can add axioms willy nilly.

That being said, if physics ever gets to the point where Godel's theorem becomes relevant, we will be talking about something far beyond what physicists refer to as a theory of everything right now.

One last point: Godel's incompleteness should only be applied to formal systems, and even in mathematics it's not all-encompassing. See my previous example of Tarski geometry as a counterexample.

Yes ok, I see what you mean. But, the project of a unifying equation is basically impossible. And agreed about the point where it matters.

k2aggie07 said:

---

But, the project of a unifying equation is basically impossible.

---

If you demand that such a unifying equation positively answer whether or not every mathematical statement is true in that system, probably. I say probably because I still find it conceivable, though improbable, that if/when physics is finally axiomatized it may be in a system where Godel does not apply. But the unifying equation that physicists are searching for is far less ambitious than this, and so again, as far as physics is concerned, I don't think Godel applies.

Don't forget the second theorem. If it is complete it also won't be consistent. So it's not just mute on its internal consistency, it can't be both complete and consistent. That's a bit daunting at least for philosophy.

Heinlein said something like a philosopher was a scientist with no thumbs. So, as a philosopher you can't consider that its practically irrelevant in a grand sense (though it has immediate application in computers among other things).