Is logic a branch of philosophy or maths?

[studiot]

 

I see what you are getting at. Even if individual tasks do not need logic the framework in which you preform these task does. You do acknowledged this in your post.

 

 

 

Of course.

 

All I have ever asserted is that there are things in Mathematics that are not part of Logic and things in Logic that are not part of Mathematics.

 

I have never asserted that those things are disconnected in some way from those that are in both (of which there are legion).

 

Of course you can't get very far in mathematics without logic.

 

Thinking again about my Turing machine,

 

If I take the definition of a quadrilateral as a closed line drawing with four sides, do I need any logic to look at a line drawing to decide if it is a quadrilateral?

Edited December 20, 2015 by studiot

[ajb]

If I take the definition of a quadrilateral as a closed line drawing with four sides, do I need any logic to look at a line drawing to decide if it is a quadrilateral?

I think so.

 

You have to deduce that the number of sides of your figure is 4 and then that this is the definition of a quadrilateral. All very informal and obvious, but still some elementary reasoning is used.

[studiot]

I suspect it is a borderline case.

Again we are reaching into fuzzy territory, where the boundaries are not crystal sharp.

 

A further thought.

 

I wonder if modern technical and engineering mathematics isn't leaving Logic and Philosophy far behind?

 

Formal logic involves creating 'chains' of reasoning akin to but often much grander than the one about my quadrilateral.

 

But every link is connected; there are no disconnected or isolated links that cannot affect the chain.

 

 

These days, with FE analysis, Event Horizons, and whatnot we are often dealing with many chains that may be separate in one part of the analysis and not in another.

Edited December 20, 2015 by studiot

[John Cuthber]

"Is logic a branch of philosophy or maths?"

One plausible answer to that question is simply "no".

 

consider this

"Is logic language a branch of philosophy or maths?"

After all, both areas use language (and both end up arguing about it), but it's not really a branch of either because it exists outside of both disciplines.

 

Since logic gets used in other things too- for example, it's the way you discern the (probable) meaning of ambiguous statements like "I saw a man eating shark"- it's not a branch of either philosophy or mathematics.

 

Logic is a very useful tool, employed by mathematicians and by philosophers (and by practically everyone else and also by some animals).

[ajb]

I suspect it is a borderline case.

Again we are reaching into fuzzy territory, where the boundaries are not crystal sharp.

Indeed.

 

I wonder if modern technical and engineering mathematics isn't leaving Logic and Philosophy far behind?

I don't know, but for sure the typical mathematician I speak to are not so worried about formal logic and philosophy. However, there are some 'fundamentalists' here in Warsaw that do worry about such things.

[studiot]

Mr Cuthber, for once we are agreed.

 

It must be Christmas. +1

 

ajb

Still there must be some reasoning an informal logic here. Proof by exhaustion relies on the logic that testing every example is sufficient to construct a proof. It seems obvious, but still we have some reasoning here.

 

My points here are not that Mathematics does not employ logic at some stage in a proof by exhaustion,

 

1) but that in some stages of the proof it does not. I think the last important proof by exhaustion was that of the four colour problem. That proof certainly involved substantial logic to construct, but the testing stage could have been, and in fact was, carried out by a dumb machine or monkey.

 

2) As far as I am aware there is no such method of proof, as proof by exhaustion, available in the discipline of formal logic. So it does not appear in both disciplines.

 

A final observation is that there is one gaping hole in the disciplines chosen in this thread.

Philosophy and Logic are basically silent on the issue of seting goals.M

Mathematics, I'm not so sure about.

 

The statements

 

I want to climb that mountain

I want to solve the NP hypothesis

 

are neither logical, nor philosophical.

 

The words practical, sensible, rational all come to mind.

 

It is a good job that English can convey ideas and concpts outside of these three disciplines.

 

Enjoy your Sunday lunch.