## How I see logic

I think it was in 4th grade elementary school, that I first heard of logic.  The teacher introduced it, with some examples to illustrate the use of logic.  I recall that it seemed rather easy to do logic.  All that I had to do was use clear thinking.  So I never did actually try to learn the rules of logic.  I just went by clear thinking, as appropriate.

I am posting this as one of the posts on my own views of philosophical topics.  No doubt my view of logic is partly shaped by the fact that I am a mathematician.  And, as a mathematician, I of course use a lot of logic.  But my basic view is still much the same as in 4th grade.  That is, I see logic as clear thinking.  It is a formalized or formalizable view of clear thinking, but it is nevertheless something that comes from clear thinking.

### What is logic?

Apparently, there is some controversy as to what we mean by logic, as indicated in the wikipedia article on Definitions of Logic.  I take it to be a rule based system of inference.  Some people take logic to be the same as thought.  But if logic is taken to refer to thought, then it is an empirical question as to whether it is rule based.  If we take logic to be rule based, then the empirical question becomes that of whether thought is an application of logic by the brain.  I think it better to take logic to be rule based, leaving the question of how thought works as a project for cognitive scientists.

### The limitations of logic

Logic is used to derive consequences of assumed premises.  But it does not give you the starting premises.  Those have to come from elsewhere.

Remembering back to high school geometry, one of the important parts was the proof of the Pythagoras theorem about right angled triangles.  The proof started with a clever construction.  Then, using that clever construction, the theorem was proved.  Once you have the clever construction, the proof is a matter of logic.  But logic does not give you that clever construction.  That had to come from somewhere else.

Computers, using logic, can play chess very well.  The rules of chess become part of the premises used in logical deductions.  The rules of chess were invented by humans, but logic is not something that could be used to invent such rules.

A carpenter builds a house.  He uses timber (wooden beams), and nails them together with a hammer.  When he has finished, the hammer won’t be part of the house, but the timber and nails will be.  The hammer is just a tool.  Similarly, I see logic as just a tool.  It can be used as an aid in reasoning.  But, when the reasoning is done, we see that the essential components, such as the premises, are not provided by the logic.

### Logic is formal

• Premise 1: All fibblywogs are globsups.
• Premise 2: John is a fibblywog.
• Conclusion: Therefore John is a globsup.

We did not need to know the meaning of “fibblywogs” nor of “globsups” to apply this logic.  The logic uses only the formal structure of the argument, not its content.

It is not necessarily a problem that logic is formal, but we should be aware of that formality.  When doing mathematics, it is important that we reason based on the formal structure, and that we don’t allow the meanings of the terms to distract us.  However, that seems to be different from ordinary common sense reasoning, as practiced by people.  In such common sense reasoning, the content (the meanings of the statements being considered) is often an important part of the argument.

### Why does logic work?

There seem to be some misunderstandings about logic.

I used Google to search for “why does logic work” (with the quotes), and came up with some weird answers.  Try it, and see what shows up.  Some people seem to think that logic is a gift from God, and that it works is evidence supporting theism.

Most Atheists believe that everything that exists is material, that everything that actually exists is part of the physical world.   The laws of logic are not physical.   The Atheistic worldview eliminates the possibility of logic being real or reliable.   At the same time, Atheists try to use logic to reason.   When they do so, they are demonstrating that their worldview is not internally consistent and that their worldview is not valid.   The worldview of the Atheist cannot be a valid worldview because the worldview requires that the Atheist use the laws of logic, yet the Atheist’s worldview does not allow the laws of logic to exist   since they are not material.   Atheism is self-refuting because the Atheist must assume something (logic) that disproves Atheism in order to prove Atheism.

That is really quite silly.  Logic is used with language, not with things in the world.  You can see this from the fact that logic is formal.  So logic works with language, because people invented language for clear communication, and thus invented it to support logical reasoning.  However, natural language is a bit messy, and logic does not fully work with it.  The sorites paradox is an example of a case where logic does not work with linguistic expression.

### Summary

As should by now be clear, I see logic as a rather limited tool, and as unlikely to be sufficient to explain human intelligence.

Tags:

### 4 Comments to “How I see logic”

1. I remember reading this before, and now felt like going back to this again. Mostly I think it’s good what you write, but some things I react to, like
“logic does not fully work with natural language” – seems to assume that logic partially works with natural language, but shouldn’t the modes of logic rather be “not at all” or “entirely” here?
“unlikely sufficient to explain human intelligence” – speaking of (un)likeliness seems to assume that logic is about speculation of probabilities of empirical matters

One tricky thing is that the word “logic” is a part of our natural language, and thus its meaning has a kind of arbitrariness… I remember reading that Ramsey, quoted by Wittgenstein, claimed that logic is a normative science (and I don’t think Wittgenstein rejected this).

Like

• “logic does not fully work with natural language” – seems to assume that logic partially works with natural language, but shouldn’t the modes of logic rather be “not at all” or “entirely” here?

Perhaps I am missing your point. What I wrote was a natural language statement, a pragmatic assessment of the usefulness of treating language as if logic. I’m not seeing why that should be limited to a binary choice.

One tricky thing is that the word “logic” is a part of our natural language, and thus its meaning has a kind of arbitrariness…

I agree with that. I’m a mathematician, which presumably influences what I mean by “logic”. And that seems to be different from what philosophers often mean.

Like

• My point is basically to make clear the distinction between the logical and the empirical. Or in other words, distinction between grammatical and material. The idea that logic could to some extent “work” with natural language appeared to me to rely on an assumption that it can somehow deal with empirical matters. Maybe it wasn’t what you meant…
Anyway, I believe this distinction is important. Didn’t Wittgenstein claim something like that all philosophical problems arise from confusion between logical and empirical claims…?

Like

• My point is basically to make clear the distinction between the logical and the empirical. Or in other words, distinction between grammatical and material.

Yes, I agree with that. Using your terminology, my post was mostly commenting on the grammatical. But I guess I was, to some extent, also commenting misuses of logic that mix those elements.

Of course, I was not saying that we can only use a formal language. Rather, its a matter of needing to be especially precise with language.

As a mathematician, it would not have occurred to me that one needs to make a distinction between the logical and the empirical. We pretty much take that for granted. So I was a bit taken aback when the Uncommon Descent blog (an ID blog) absolutely insisted on applying logic directly to the empirical.

Like