Is logic based on knowledge?

[shackleton]

Point of question:
Things people thought logically impossible one-hundred years ago are now common sense. With this in mind, are the axioms that make up our logical conclusions based soley on what we know to be true as of now? When new knowledge comes to light it changes our axioms and therefore changes our comclusions. So I ask...are logical conclusions based on knowledge. If they are, can anything be known to be absolutely, logically true?
We as finite beings cannot know all possible variables, so how can we come to a completely logical conlcusion based on our limited knowledge of facts.

Example: At one time it was thought impossible for a human to run a 4 minute mile. This was based on the fact that noone had done it before, so as far as they are concerned it was logically impossible. Now it is something many people can do.

If logic is based on knowledge, how do we know that God could not do something that we deemed logically impossible? God knows all the possible variables, so what is logically possible for him would be different from what we would deem logically possible for God. We are basing our knowledge of what God can and can't do based on the information God has given us. How do we know that there is not knowledge out there that we are incapable of understanding. Adam and Eve would not have been able to understand the theory of Relativity based on what they knew to be true. Who knows what man will have discovered hundreds of years from now...if the Lord tarries.

 

[CatechumenPatrick]

First of all, what do you mean by “logical”? Do you mean the laws of logic--logic as in validity--such as the law of non-contradiction? If so, then could you please give one example of something considered logically impossible in the past that is now considered logically possible?
To skip ahead to your example, you state, “At one time it was thought impossible for a human to run a 4 minute mile. This was based on the fact that noone had done it before, so as far as they are concerned it was logically impossible. Now it is something many people can do.” In this example, you are using "logic" in an everyday, non-technical, non-precise manner. It may have been thought impossible for a human to run a mile in four minutes in the past, but it was not logically impossible. A human running a four-minute mile does not contradict any law of logic--it is not a matter of logic. If you said, “A human by definition cannot run a four-minute mile, yet today humans run four-minute miles, therefore something that is logically impossible one hundred years ago is logically possible today,” then perhaps you would be correct. Alas, there is nothing in the concept of “human” that necessitates running a four-minute mile to be a logical impossibility.
Clear up your use of the word “logic” and “logically impossibility” and then ask the question again, otherwise I don’t think it is intelligible.

 

[VaughanRSmith]

What Patrick said, plus:

From my limited knowledge of logic, I would say no to your question. The way we use logic will always remain the same, because object A can never be not-A. However, our presuppositions govern the use of that logic. If I assume that the world is flat (A), then I cannot logically come to the position that it is round (not-A) unless my governing presupposition is changed. The way I change that is through logical means also.

My 2c.

 

[Cheshire Cat]

you are confusing logical possibility with physical possibility.

 

[shackleton]

Maybe running a four minute mile is a bad example. I was referring to the laws of logic and contradiction.
If I am trying to find out if something is possible, and I have determined that it boils down to a question of feasibility based on the laws of logic. If person A has a limited understanding compared to person B, their concepts of what is possible is going to be different based on what they know. Person B knows more than person A so they are going to have different ideas as to what is possible.
Person A is going to think a thing impossible, based on what he knows, but person B knows that it is either possible or impossible based on the greater knowledge of the subject.

 

[Brian Bosse]

Hello Erik,

Things people thought logically impossible one-hundred years ago are now common sense.

Can you give me an example of one such thing? The reason I ask is that I doubt this claim very much. I suspect you may be using the term ‘logic’ in a different sense than its technical usage.

With this in mind, are the axioms that make up our logical conclusions based soley on what we know to be true as of now?

The axioms of logic are the foundation for rationality. Such axioms would include the law of non-contradiction, excluded middle, modus ponens, etc… Axioms of this type are not determined by our experience. Rather, they are so foundational that our rationality depends upon these truths.

So I ask...are logical conclusions based on knowledge.

No. These axioms are preconditions to knowledge. That is to say, if I have knowledge, then the laws of reason (logic) exist.

If they are, can anything be known to be absolutely, logically true?

You are using terms fast and loose. What do you mean by logically true? Something is logically true if and only if it is a tautology. For example, the statement “A implies A” is logically true. There is no A that can undermine its truth. (An interestng question would be to ask what happens if A asserts that it is not the case that A implies A.) ‘“A implies B’ implies ‘not-B implies–A’” is logically true. These types of truth are about the most certain truths you and I can know.

We as finite beings cannot know all possible variables, so how can we come to a completely logical conlcusion based on our limited knowledge of facts.

What do you mean by “completely logical conclusion”? Without knowing at all what A is or what B is, I can logically deduce that “A implies C” if ‘“A implies B’ and ‘B implies C’”.

Example: At one time it was thought impossible for a human to run a 4 minute mile. This was based on the fact that noone had done it before, so as far as they are concerned it was logically impossible. Now it is something many people can do.

OK, this helps matters. The proposition “It is impossible for a human to run a 4 minute mile” cannot be properly said to be a logical impossibility. It may be said to be a physiological impossibility. There is a big difference between the two. Here is a logical impossibility: “Brian can run a 4-minute mile” and “Brian cannot run a 4-minute mile” taking both propositions at the same time and all of the terms in the same sense.

If logic is based on knowledge, how do we know that God could not do something that we deemed logically impossible?

Logic is not based on knowledge. Rather, knowledge is based on logic. Logic is based in the nature of God. It is part of who God is. Logic is a reflection of the way God thinks. In this sense, one can affirm with Gordon Clark that logic is God. Now, it may be possible that there is a proposition that is true yet appears to us as contrary to some other truth without it actually being so. It is possible that our limited knowledge would create this situation. In this case, the two beliefs are not actually contrary even though we cannot see why they are not. I call this apparent contradiction.

Sincerely,

Brian

 

[Vytautas]

Point of question:
Things people thought logically impossible one-hundred years ago are now common sense. With this in mind, are the axioms that make up our logical conclusions based soley on what we know to be true as of now? When new knowledge comes to light it changes our axioms and therefore changes our comclusions. So I ask...are logical conclusions based on knowledge. If they are, can anything be known to be absolutely, logically true?

You seem to be concerned with having your axioms being changed in light of new evidence. This assumption however, that we base our axioms on evidence, is false, since your basic assumptions determine what counts as evidence in the first place.

Example: Determine if all the snarks in the room will change our definition of what a snark is. All you have to do is gather up all the snarks and examine them if our assumptions of snarkness are correct or not. Can’t do it? It is because you have to begin with a definition of what is a snark in the first place in order to find the snarks.

If logic is based on knowledge, how do we know that God could not do something that we deemed logically impossible? God knows all the possible variables, so what is logically possible for him would be different from what we would deem logically possible for God. We are basing our knowledge of what God can and can't do based on the information God has given us. How do we know that there is not knowledge out there that we are incapable of understanding.

Why do you want to find out the hidden things? Are not the revealed things enough?

Deuteronomy 29:29 “The secret things belong unto the LORD our God: but those things which are revealed belong unto us and to our children for ever, that we may do all the words of this law.”

 

[shackleton]

After thinking about it, I guess what I am trying to say is that if one enters incorrect axioms, (based on faulty knowledge), one will come to wrong conclusions, but I guess that has more to do with the person and his incorrect use of logic, than with logic itself...

 

[shackleton]

Logic is not based on knowledge. Rather, knowledge is based on logic. Logic is based in the nature of God. It is part of who God is. Logic is a reflection of the way God thinks. In this sense, one can affirm with Gordon Clark that logic is God. Now, it may be possible that there is a proposition that is true yet appears to us as contrary to some other truth without it actually being so. It is possible that our limited knowledge would create this situation. In this case, the two beliefs are not actually contrary even though we cannot see why they are not. I call this apparent contradiction.

I like this, that makes sense when put that way. Others were explaining it as if logic was something God was subject to, which I did not agree with, I agree with it the way you put it.
Thanks.

 

[shackleton]

Why do you want to find out the hidden things? Are not the revealed things enough?

Deuteronomy 29:29 “The secret things belong unto the LORD our God: but those things which are revealed belong unto us and to our children for ever, that we may do all the words of this law.”

Because someone in another thread posed question of the feasiblity of God creating a rock soo big that even He could not lift it. The answer became one of whether it was logically posssible. Rather than ask this there I posed my own question.

 

[Vytautas]

Because someone in another thread posed question of the feasiblity of God creating a rock soo big that even He could not lift it. The answer became one of whether it was logically posssible. Rather than ask this there I posed my own question.

I got the impression that you were asking if our knowledge and God's knowledge is of the same kind, or of a completely different kind. You were asking about knowledge, not about power.