Is logic a branch of philosophy or maths?

[Strange]

But they have gone further and implemented a whole family of devices and system of logic known as 'tristate', which extends the formal logic discussed above.

 

And we often use 4 (or even 7 or more) state logic to model this.

Four state logic is 0, 1, Z (tri-state) and X (conflict or unknown).

Other states can include H and L (weak 1 and 0), U, W (unknown, weak unknown), - (don't care), and so on.

[Gees]

Studiot;

 

Please consider my following thoughts:

It is a logical fallacy to lump all posters together like this and then say

 

Particularly as you are articulating what I said in my Venn diagram and extracts from the OED.

 

When I was proofing that post, I realized that I should have stated "some" of the posters or "many" posters, but was not sure which word was correct. I remembered that YodaP's post was not in conflict with my thoughts, so I intended to go back over the thread to review, then rewrite my opening sentences, but I got distracted and forgot. So I will accept your little scold.

 

But I do not think that what I articulated was the same as what I read in your Venn diagram.

 

This question lends itself to a Venn diagram for discussion.

 

But only so long as we can agree boundaries and there is only one ring for each of the three words.

 

venn1.gif

 

Now I will be the first to admit that my knowledge of math is very elementary, and I know of no significant difference between a "Venn" diagram and a regular diagram. To me, a diagram is simply a picture of a concept. So when I looked at your diagram, what I saw was a large section of Philosophy, over 50 %, that had nothing to do with logic -- a frightening prospect. Then I noted a large section of Science, over 50 %, that had nothing to do with logic -- a terrifying prospect. Then I saw a large section of Logic, over 50 %, that related only to logic -- which seems impossible, as logic relates to other things.

 

Maybe I do not understand your diagram, in which case, I hope that you will educate me.

 

If I were to diagram these concepts, I would start with a large circle, maybe 4 inches across, and name it Philosophy, because all knowledge starts with philosophy. Then I would put a smaller circle, almost 1/2 the size in the middle of the large circle and name it Science. The science circle would be smaller because it limits itself to the objective and does not deal with theology/religion, leaving a lot of study open to other disciplines. This circle would be centered in the middle of Philosophy because science has become the heart of philosophy.

 

I would not make a separate circle for Logic, but would instead choose a color -- say, blue. Then I would color in all of Philosophy and Science with a light blue, except for maybe a centimeter around the edge of Philosophy, and add a concentrated blue about the size of a dime within Science to represent Logic in Maths, and add a concentrated blue about the size of a dime within Philosophy to represent Formal Logic.

 

It seems that we do not agree on boundaries.

 

I would say that Philosophy does not deal directly with the numbers (probability), that is the province of Mathematics.

 

I agree that Philosophy does not deal with the numbers, but we have our own way of dealing with probability -- we call it wisdom. Although probabilities and numbers are very useful on an objective level to businesses, governments, and policy makers, knowing the probabilities are not always useful to a person on a subjective level. Wisdom is very useful.

 

Gee

 

[studiot]

Hello Gees,

 

Gees

 

Studiot;

 

Please consider my following thoughts:

 

I would say your post was a well reasoned response to the issues.

+1 for the self analysis.

 

I would also say we probably agree on more than you think.

Some alternative words to 'some' or 'many' are 'several' or a 'few'.

 

You should not be afraid of Venn diagrams they are just a pictorial tool.

In general the areas do not correspond to the relative sizes of the zones, this is a diagramitc aid and you can move the circles about to vary the zones.

You can use circles or squares or even magical pentagrams to depict the zones. Circles are just conventional.

Your comment about Philosophy embracing other things is perceptive and akin to the part of the Venn diagram I omitted as is often done by convention.

A complete diagram is usually contaiend within a rectangular box, which is called 'the universal set' or just 'the universe' or even just U.

So everything in the universe that is not included in the zones lies in the area of this box that is outside the overlapping circles.

 

But what you should take away is the concept of 'overlap'. This is the area common to two or more (circular) zones and represent that which is used and specified in both, say logic and mathematics.

 

As to the boundaries.

The Venn diagram relies on the type of logic that divides matters into two camps, with nothing on the boundary or with a foot in both camps.

This is where the representation is seriously limited since, in my view, there are many grey areas between the subjects.

Further as I also showed there are forms of Logic that do not conform to this bipartite classification.

 

So the Venn diagram is a quick and dirty way of presenting the data - that of the relationships between the players - just so long as you don't look to deeply or are careful with how you apply it.

 

But doesn't it work that way for most representations and models?

 

So yes I agree

 

 

Wisdom is very useful

[Gees]

Studiot;

 

Hello Gees,

 

I would say your post was a well reasoned response to the issues.

+1 for the self analysis.

 

Thank you. Although this is the Philosophy forum, it is not often that a well reasoned argument is acknowledged.

 

As to the self analysis, that is the easy part. Like most people, there is a great deal that I know, and there is a great deal that I am clueless about, but the wide gap in between is the part that proves interesting and provides the most fun.

 

But what you should take away is the concept of 'overlap'. This is the area common to two or more (circular) zones and represent that which is used and specified in both, say logic and mathematics.

 

So a Venn diagram's primary purpose is to show the relationship between two or more things as to their entanglement. (Not quantum entanglement, just entanglement.)

 

I could draw three Venn diagrams: The first would be two circles that are separated, and I could name them "boy" and "girl".

 

Then I could draw the same circles overlapping and name the diagram "marriage".

 

Then I could draw the same circles almost eclipsing each other and name the diagram "50th Anniversary".

 

Yes? If this is essentially correct, you do not have to answer.

 

So the Venn diagram is a quick and dirty way of presenting the data - that of the relationships between the players - just so long as you don't look to deeply or are careful with how you apply it.

So you are saying that I over thought it. A common occurrence for me. I would like to say that I will curb the impulse to over think things, but I would be lying. My mind is my favorite playground, so maybe people will just be patient with me.

 

Thanks again.

 

Gee

[studiot]

 

So you are saying that I over thought it

 

No, you weren't to know if you have never met them. They are just very well known in technical circles because they are very useful for what they are.

 

 

Interesting,your choice of texamples about Venn diagrams. I have in mind something similar (Men, Women, Marriage) to show something to another poster (in another thread) here about a case, not mentioned on Wikipedia, (a mathematical term) of surjections .

I only wish he had the same approach to discussion you have.

 

Edited December 11, 2015 by studiot

[Strange]

I could draw three Venn diagrams: The first would be two circles that are separated, and I could name them "boy" and "girl".

 

This is quite a good example. Although, in reality, there is a slight overlap (when you consider physical characteristics). There is a slightly larger overlap when you consider the psychological and social definitions.

[hoola]

It seems that for math to function, a foundation of logic must have preceded it, or else a 6 could be a 9 and reality would fall apart as equations fail, and the BB wouldn't have happened...(jimi hendrix joke withheld)

Edited December 14, 2015 by hoola

[moth]

It seems that for math to function, a foundation of logic must have preceded it, or else a 6 could be a 9 and reality would fall apart as equations fail, and the BB wouldn't have happened...(jimi hendrix joke withheld)

 

And the hippies cut off all their hair.

 

Since you can't use logic to prove boolean algebra is true, it seems like logic is philosophy and math a branch of logic.

 

But that's just my freak-flag waving high.

hi

 

edit:you can't stop jimmy

[hoola]

no, moth. Logic must have established the foundation, and later math can do all kinds of fancy things....hahaha.... and thumb it's nose at it and say "suck my boolean logic"

Edited December 14, 2015 by hoola

[moth]

The straightforward application of logic, that to see back in time we can reverse the dynamics we observe now, leads to singularity.
There are probably ways to work around the singularity,but only observation, not logic, can possibly distinguish the correct origin theory.
If the correct origin theory makes sense logically you still have a chicken egg. Did logic define the universe or does the universe define the logic.

[hoola]

the void fragmented to chaos, regions within the chaos froze out to assemble logic, logic then organizes a primitive mathematics using chaos as a primary signal source....later, the accumulation of information invents endless equations, such as pi, E, sq.rt of 2 and etc.... As self-sustaining equations co- evolve, the chaos signal is no longer needed. Based upon it's own extrapolations, what I call the "informational black hole" develops, delivers the finalized data stream for the first physical representation, the singuarity. I see the singualrity as a lone virtual particle, the same as we see today, but without it's anti-particle to cool things down, as power source for the big bang.

Edited December 14, 2015 by hoola

[Shelagh]

Logic is not a branch of mathematics; it is applied in mathematics.There are five branches of logic: Categorical Logic, Truth-Functional Logic, Predicate Logic, Modal Logic and Informal Logic. You'll find more information about logic here:

 

http://www.manyworldsoflogic.com/whatIsLogic.html

[studiot]

Yes logic and mathematics are separate but overlapping disciplines.

 

Unfortunately my nice tidy venn diagram cannot do this full justice since certain processes, different in each, have the same name.

[ajb]

Logic is not a branch of mathematics; it is applied in mathematics. There are five branches of logic: Categorical Logic, Truth-Functional Logic, Predicate Logic, Modal Logic and Informal Logic. You'll find more information about logic here:

I do not think a clear distinction can be made between mathematical and applied mathematics. Nor am I sure that trying to make such a distinction helps when it comes to such large mathematical theories. Most people I know who work on logic would probabily not see themselves as applied mathematicians.

[Shelagh]

It is logic that is applied, not mathematics! This link is to an overview of logic and the philosophy of mathematics. It is intended for the general reader. It has appeared in the volume The Examined Life: Readings from Western Philosophy from Plato to Kant, edited by Stanley Rosen, published in 2000 by Random House:

 

http://www.personal.psu.edu/t20/papers/philmath/

[studiot]

Neither Mathematics nor Logic is a branch of the other.

 

They possess common processess. It would not be fair to ascribe a common process as belonging to one or the other and simply applied by the second.

You cannot say that a ball belongs to cricket and is applied by soccer or vice versa.

 

But they also both posess process not available in the other.

Edited December 19, 2015 by studiot

[ajb]

It is logic that is applied, not mathematics!

Applying logic is not quite the same as developing the formalism of logic and indeed fundamental mathematics. Of course the two are not completely distinct.

 

Also in mathematics one uses informal logic all the time. However, my work is far from 'logic'. The people I know work in logic, fundamental mathematics and model theory are all quite a strange bunch!

 

 

Neither Mathematics nor Logic is a branch of the other.

They are, of course, tightly related, especially when it comes to fundamental questions in mathematics.

[Shelagh]

The topic seems to be descending into pedantic semantics.

 

One may ask whether logic is part of philosophy or independent of it. According to Bochenski [2, §10B], this issue is nowhere explicitly raised in the writings of Aristotle. However, Aristotle did go to great pains to formulate the basic concepts of logic (terms, premises, syllogisms, etc.) in a neutral way, independent of any particular philosophical orientation. Thus Aristotle seems to have viewed logic not as part of philosophy but rather as a tool or instrument1 to be used by philosophers and scientists alike. This attitude about logic is in agreement with the modern view, according to which the predicate calculus (see 1.2 below) is a general method or framework not only for philosophical reasoning but also for reasoning about any subject matter whatsoever.

[studiot]

 

They are, of course, tightly related, especially when it comes to fundamental questions in mathematics.

 

 

Of course they are.

 

But it is possible to carry out (some) mathematics without logic and I think , some logic without mathematics (though I fully admit to being less expert here)

 

As a for instance there is no logic involved in proof by the method of exhaustion or the old surveyors' method of counting by transferring stones from left pocket to right pocket.

As an example of the difference i spoke of, proof by induction in mathematics refers to quite a different process from induction in formal logic.

 

Edited December 19, 2015 by studiot

[Strange]

The topic seems to be descending into pedantic semantics.

 

 

You don't get much more pedantic than logicians.

[ajb]

But it is possible to carry out (some) mathematics without logic and I think , some logic without mathematics (though I fully admit to being less expert here)

I am not sure. Even very elementary mathematics requires some informal logic and reasoning. In reverse, I suspect that all logic is rather based on mathematics as the human brain seems wired to think mathematically, we normally do not realise this.

 

I am not well versed in logic, but as soon as you start to formalise logic you are using mathematics. I am not sure if one can really disentangle informal logic from mathematics.

 

That said, nobody has clearly defined mathematics, so as Shelagh has pointed out, this may all just be a matter of semantics. Therefore, tying to make a clear distinction between philosophy and mathematics when it comes to logic may be futile and unhelpful.

 

 

As a for instance there is no logic involved in proof by the method of exhaustion or the old surveyors' method of counting by transferring stones from left pocket to right pocket.

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.

 

As an example of the difference i spoke of, proof by induction in mathematics refers to quite a different process from induction in formal logic.

Indeed. (Not everyone likes proofs by induction probabily for that reason)

 

 

The topic seems to be descending into pedantic semantics.

I am not surprised. Generally I am against putting subjects of human interest in neat boxes, it seldom actually helps the development of the subject. For example, I am not too worried about any distinction between pure and applied mathematics. Similarly, I am not sure that trying for put logic in the box called Philosophy or the box called Mathematics is really helpful. How you approach and think of logic may of course be strongly guided by your other interests. As I favour a mathematical approach rather than a philosophical one to almost everything, it is not surprising that logic feels more like mathematics than philosophy to me.

 

Then we have missed some related questions that spin-off from this. These questions are, in my opinion unanswerable. Is mathematics a science, an art, or a branch of philosophy? (All three maybe?)

 

"However, Aristotle did go to great pains to formulate the basic concepts of logic (terms, premises, syllogisms, etc.) in a neutral way, independent of any particular philosophical orientation."

So Aristotle was building an abstract framework to formulate 'logic' and ask question in 'logic'. This is mathematics!

Edited December 20, 2015 by ajb

[Shelagh]

So Aristotle was building an abstract framework to formulate 'logic' and ask question in 'logic'. This is mathematics!

Maybe you should explain that to Aristotle. I don't have his email address, so I can't help you to contact him.

[ajb]

Maybe you should explain that to Aristotle. I don't have his email address, so I can't help you to contact him.

Meaning you disagree?

 

Based on the quote that you gave it sounds like he was working quite mathematically. It is quite possible that he did not see it that way as mathematics has come a long way since his time.

[studiot]

Good morning, ajb,

 

(and Ms Shelagh are you not talking to me?)

 

The is a minimum capabilty that is required in order to apply a process belonging to any form of logic.

For instance a Turing Machine has the capability to make a decision.

 

You do not have to have this in order to perform some mathematical tasks (i.e. perform some mathematics)

 

For instance my Austalian Aboriginal Surveyor's Assistant cannot count, does not know what number he has counted, indeed does not even have the concept of number.

Yet he has achieved the mathematical task of accurately counting the number of chains laid using the stones.

A trained monkey or machine could have done the same.

 

Yes others can apply logic or its fruits or to the result but counting the chains is nevertheless a piece of mathematics.

 

Here is another more vivid example.

 

Take a die and roll it.

Copy or photograph the symbols on the upturned face.

 

You have achieved the mathematical task of the selection of a random number.

 

Did it take logic?

 

No.

 

Could a Turing Machine have performed this task?

 

No.

 

Why not?

 

Because the Turing Machine has to make a decision before it can move on and complete a task.

But no decision is required in this example since you copy whatever is there.

 

It may be that a small mathematical task is part of a larger mathematical task, which does require logic, but there remain some sub tasks that do not.

Edited December 20, 2015 by studiot

[ajb]

You do not have to have this in order to perform some mathematical tasks (i.e. perform some mathematics)

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.

 

Usually there is two 'kinds of logic' at play in mathematics.

 

i) Very few mathematicians will go to formal logic to prove results. One just accepts that if really asked then one more-or less could. I mean we start from some starting assumptions and work from there. This has to be taken in the light of the incompleteness theorems: all mathematics cannot be reduced to pure logic.

 

ii) Then there is the more informal logic, which the standards will vary branch to branch of mathematics. All mathematicians use informal logic all the time: 'A implies B' etc.