Is logic a branch of philosophy or maths?

[andrewcellini]

I'd say natural logic underlies math

what is meant by "natural logic?"

[cladking]

Natural logic is two apples are always composed of an apple and an apple. Or that an apple and an apple make two apples. We quantify this as 1 + 1 = 2. In the real world acceleration is strictly correlated to an object's mass and the force applied. We define units and say f=M X A. These things don't hold true because we do the calculations. They held true even when man still lived in caves. They are real independently of our knowledge or quantification of the terms.

 

Everything happens all the time. Collision between particles and every event involving everything that ever was and everything that will be are occurring now everywhere. All of these events and processes determine the current and will determine the future reality in a chaotic manner and are determined by the past. Each event in the here and now is also affected by every other event in the here and now (probably). These are infinitely complex computations but they aren't actually made because all these events are simply following natural logic. They are all just doing what reality does and what we do is try to isolate the variables in the lab for study. When we identify some of this natural logic we incorporate this into our models and then we see the world in terms of these new models. The models aren't real, the math isn't real, but the logic that composes reality is real.

Edited November 19, 2015 by cladking

[DevilSolution]

Natural logic is two apples are always composed of an apple and an apple. Or that an apple and an apple make two apples. We quantify this as 1 + 1 = 2. In the real world acceleration is strictly correlated to an object's mass and the force applied. We define units and say f=M X A. These things don't hold true because we do the calculations. They held true even when man still lived in caves. They are real independently of our knowledge or quantification of the terms.

 

Everything happens all the time. Collision between particles and every event involving everything that ever was and everything that will be are occurring now everywhere. All of these events and processes determine the current and will determine the future reality in a chaotic manner and are determined by the past. Each event in the here and now is also affected by every other event in the here and now (probably). These are infinitely complex computations but they aren't actually made because all these events are simply following natural logic. They are all just doing what reality does and what we do is try to isolate the variables in the lab for study. When we identify some of this natural logic we incorporate this into our models and then we see the world in terms of these new models. The models aren't real, the math isn't real, but the logic that composes reality is real.

 

When you say "The models arent real, the math isnt real, but the logic that composes reality is real."

 

I hope you understand that all the maths is doing is identifying the logic that composes reality and quantifying it in a formula or such. When you say it's not real do you mean that the equations do not accurately represent the "logic that composes reality"? Such that if we want to find the height of a building that is 70 meters away and we've found the angle of elevation to be 40 degrees from base level and we then apply the formula [math] height = adjacent * \tan(theta)[/math] Which is 70 * tan(40) = 58.73 meters. Now are you saying that 58.73 meters is wrong? the equation is wrong? or measuring in meters is wrong?

 

Just as a side note, if they're not real how come they work so well? Take mechatronics for example (mechanical and electrical engineering), if the maths behind these equations we're using to transmit and receive electrical signals are not real how does a radio stream live audio from someone 10,000 miles away?

Edited November 19, 2015 by DevilSolution

[cladking]

I hope you understand that all the maths is doing is identifying the logic that composes reality and quantifying it in a formula or such. When you say it's not real do you mean that the equations do not accurately represent the "logic that composes reality"?

 

 

None of this logic exists in isolation. It is all bundled up with all the other formulae we know and those we've yet to learn. The logic never affects things in isolation. Reality is the sum total of everything and when we see our models we are overlooking reality. We are overlooking the existence of all we don't know.

 

Such that if we want to find the height of a building that is 70 meters away and we've found the angle of elevation to be 40 degrees from base level and we then apply the formula [math] height = adjacent * \tan(theta)[/math] Which is 70 * tan(40) = 58.73 meters.

 

 

Math works when it is properly applied and all the terms are defined. We often lose sight of proper methodology but, no, this is not the problem. The problem is the inability to see the city because all the skyscrapers are in the way. We see our beliefs and knowledge preferentially to reality.

[Gees]

Andrewcellini;

 

It is very possible that I am missing something here, but I do not see 'logic' as the other posters do, and do not see it as a 'branch' of anything. So please consider my following thoughts.

 

there are a few posts i've seen by members here which are along the lines of "logic is branch of mathematics." is "logic" considered indistinct from "mathematical logic?" if so that seems to be a narrow generalization of what logic is(at least in comparison to the descriptions i can find elsewhere such as https://en.wikipedia.org/wiki/Logic),but i could be wrong and that's why i wanted to ask.

 

ALL of philosophy works through logic and reason. Science and math are branches of philosophy that use logic and reason. So I see logic as more of a foundation than of a branch, and think it would be more correct to call it a methodology or tool for learning. Consider that science does not call the 'scientific method' a 'branch' of science -- as it is more the foundation of science.

 

So why is mathematical logic different? Because it is a purer logic. Many people have come to the conclusion that mathematical logic is better because it is purer, but that is just arrogant swill. Mathematical logic is purer because there are parameters around math that limit what can be considered. No one will ever have to solve: 2 + pink unicorns = fairy dusters forever.

 

Science tries to limit its studies to the objective and what works with testing or in observation. Math limits its studies to numbers and rules regarding numbers. Philosophy has no such luck and studies ALL thought, objective and subjective, so it is by far the most difficult study. Philosophy can not set parameters around thought because thought is unlimited; the only way to stop thought is to stop experience, which would be a little disconcerting for us. So philosophy attempts to break up thought into categories and branches, but it is still a difficult study and still requires reason to work along with logic.

 

Consider what logic actually is; it is the ordering of our thoughts. We try to put our thoughts into an order that will help us to find truth and knowledge. And Cladking is correct; we did not invent logic or order, we observed it in nature, recognized the value of it, and then incorporated it into our thinking. I define something as 'real' if it can cause an effect; logic in and of itself does not cause an effect. Logic has an effect only in conjunction with something else -- even if that something else is only thought.

 

I think that I agree with Swansont; it is the floor wax and the dessert -- when applied correctly.

 

Gee

[studiot]

 

It is very possible that I am missing something here, but I do not see 'logic' as the other posters do, and do not see it as a 'branch' of anything

 

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

 

 

It is very possible that I am missing something here, but I do not see 'logic' as the other posters do, and do not see it as a 'branch' of anything

 

 

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

[cladking]

 

 

 

 

 

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

 

 

Is it? Doesn't your diagram suggest not only an overlap in meaning but also suggests "math", "philosophy", and "science" are just as real as logic? Gees is saying logic is fundamental. I'm suggesting that it underlies, it is, reality itself and we are simply blind to it because we thought ourselves into existence. I'm suggesting that words are constructs and it's not the reality of philosophy and logic that overlap but merely their constructs. We each define these words a little differently and we each use them in different contexts that overlap as well. We hear the definition we expect and there's lots of overlap in the definitions necessary to try to make sense of what others are saying.

 

Of course even I use different definitions for "logic" but I try to make a set meaning that has no variance apparent from context: It is logical to believe logic is reality as determined by the logic I employed to deduce this. "Philosophy" has made so little progress and applied science is far behind the times because of the difficulty of communication. How do you build on the greats of the past if you misunderstand them?

[swansont]

applied science is far behind the times because of the difficulty of communication.

 

Behind what times?

[Strange]

It is logical to believe logic is reality as determined by the logic I employed to deduce this.

 

The logic you used appears to be circular. (If it is logic at all, it sounds like more of your baseless assertions.)

 

applied science is far behind the times because of the difficulty of communication.

 

Applied science is called technology and, ironically, allows you to communicate your opinions and assertions all round the world in an instant with no difficulty at all.

[studiot]

 

Is it? Doesn't your diagram suggest not only an overlap in meaning but also suggests "math", "philosophy", and "science" are just as real as logic?

 

Although the following comment is specific to you and critical it is intended to be helpful in a big way.

 

Please take it in that spirit.

 

I think/wonder if your difficulty discoursing with others is because you respond not to what they actually said but to what you guess/think/wouldlike them to have said.

 

I have noted this elsewhere in other threads which struggle as a result.

 

Look again at my post 17 and ask yourself

 

Where did studiot use the word 'science'?

[DevilSolution]

 

None of this logic exists in isolation. It is all bundled up with all the other formulae we know and those we've yet to learn. The logic never affects things in isolation. Reality is the sum total of everything and when we see our models we are overlooking reality. We are overlooking the existence of all we don't know.

 

 

Math works when it is properly applied and all the terms are defined. We often lose sight of proper methodology but, no, this is not the problem. The problem is the inability to see the city because all the skyscrapers are in the way. We see our beliefs and knowledge preferentially to reality.

 

I think you need to look into reverse engineering and decomposition.

[Strange]

We are overlooking reality. We are overlooking the existence of all we don't know.

...

We see our beliefs and knowledge preferentially to reality.

 

Who is this "we" you keep speaking of? Are you projecting your own shortcomings on to other people?

[cladking]

 

I think you need to look into reverse engineering and decomposition.

 

Excellent point.

 

But don't forget reverse engineering can't really be applied to nature. It can be applied to machines and object which are simple manifestations of theory but all of nature's logic applies to everything outside the lab and isolating these forces can be extremely difficult.

 

Yes, science itself is a sort of a way to reverse engineer nature and it's still working even if it is hung up on the unified field theory.

 

Although the following comment is specific to you and critical it is intended to be helpful in a big way.

 

Please take it in that spirit.

 

I think/wonder if your difficulty discoursing with others is because you respond not to what they actually said but to what you guess/think/wouldlike them to have said.

 

I have noted this elsewhere in other threads which struggle as a result.

 

Look again at my post 17 and ask yourself

 

Where did studiot use the word 'science'?

 

 

I undestand your point. I often respond to the logical conclusion of what people are saying rather than the statement itself. I believe this better highlights my objection while cutting to the chase.

 

I didn't remember the diagram and since I consider "science" a subset of "philosophy" I was just covering all the bases.

 

 

 

Applied science is called technology and, ironically, allows you to communicate your opinions and assertions all round the world in an instant with no difficulty at all.

 

I wasn't referring to technology. Technology is always in virtual lockstep with theory and never lags more than half a step.

 

By applied science I mean the application of new knowledge and technology to culture, language, and the economy.

[studiot]

 

 

 

Cladking

 

 

 

Studiot

Although the following comment is specific to you and critical it is intended to be helpful in a big way.

 

Please take it in that spirit.

 

I think/wonder if your difficulty discoursing with others is because you respond not to what they actually said but to what you guess/think/wouldlike them to have said.

 

I have noted this elsewhere in other threads which struggle as a result.

 

Look again at my post 17 and ask yourself

 

Where did studiot use the word 'science'?

 

 

 

 

Cladking

I undestand your point. I often respond to the logical conclusion of what people are saying rather than the statement itself. I believe this better highlights my objection while cutting to the chase.

 

I didn't remember the diagram and since I consider "science" a subset of "philosophy" I was just covering all the bases.

 

Rather proves my point.

 

You didn't respond to either of my statements, just your guess as to what they might have been or might have meant.

 

You put in a lot of typing here.

 

At best it is only one extra click to quote, and a few extra seconds to write

 

X is what you said, Y is the logical conclusion which leads me to respond.....Z

 

Doing this would save a lot of confusion all round.

[Strange]

I wasn't referring to technology. Technology is always in virtual lockstep with theory and never lags more than half a step.

 

By applied science I mean the application of new knowledge and technology to culture, language, and the economy.

 

So by "applied science" you mean "the use of technology".

 

No wonder you think there are so many problems with language - you appear to be unable to use it.

I often respond to the logical conclusion of what I think people are saying rather than the statement itself. I believe this use of the strawman fallacy allows me to repeat my baseless assertions.

 

FIFY

[TheGeckomancer]

Why is math not a division of philosophy? That's what I have always felt. Distinguishing math from logic is a pointless exercise if they are both extensions of philosophy. In my opinion it is the most rigorous and well defined area of philosophy.

Edited November 28, 2015 by TheGeckomancer

[studiot]

Why is math not a division of philosophy? That's what I have always felt. Distinguishing math from logic is a pointless exercise if they are both extensions of philosophy. In my opinion it is the most rigorous and well defined area of philosophy.

 

Because there are elements of mathematics that are not reflected in philosophy

 

(treatment of chance for example)

 

and elements of philosophy that are not reflected in mathematics

 

(discussion of what is existence? for example)

[TheGeckomancer]

Hence why I said the most rigorous and well defined area of philosophy. Philosophy does deal with chance. It just doesn't explicitly enumerate it, unless math is a division of philosophy. And math does touch on the nature of existence. Mathematicians all the time are trying to explore the nature of reality, nature of existence, what is real etc. If math is not a division of philosophy it's a separate discipline that is trying to supplant philosophy.

Edited November 28, 2015 by TheGeckomancer

[studiot]

 

And math does touch on the nature of existence

 

Perhaps you are not aware that the statement "There exists" has a very precisely defined meaning in Mathematics, as well as its own symbol.

And this meaning is different from the definition used in other disciplines, including general English and in Philosophy.

 

 

If math is not a division of philosophy it's a separate discipline that is trying to supplant philosophy.

 

 

Yes it is a separate discipline, but it is nonsense to suppose it has any desire or will or capability to supplant any other discipline.

 

 

Philosophy does deal with chance

 

Actually it deals with aspects of chance, not dealt with by Mathematics.

 

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

[andrewcellini]

 

Perhaps you are not aware that the statement "There exists" has a very precisely defined meaning in Mathematics, as well as its own symbol.

And this meaning is different from the definition used in other disciplines, including general English and in Philosophy.

to expand upon this, when one says "there exists...such that..." they are talking about abstract objects (specifically "at least one __," and the objects in question can be, for example, members of set of real numbers) in the universe of discourse such that certain statements regarding the object are held true.

 

trivial example: for some real number, r, r*r = r + r

 

this is clearly different from, say, ontological existence, which is what geckmancer seems to be confusing it with.

Edited November 28, 2015 by andrewcellini

[studiot]

 

to expand upon this, when one says "there exists...such that..." they are talking about abstract objects (specifically "at least one __," and the objects in question can be, for example, members of set of real numbers) in the universe of discourse such that certain statements regarding the object are held true.

 

Agreed, although rather than say 'true' which opens another can of worms, I prefer to say 'is compatible with the stated axioms of the discourse, along with their derived theorems'

 

For example the fundamental theorem of algebra asserts crudely that every polynomial has a root (and therefore 'the existence' of complex numbers)

 

So

[math]\exists z:z = \sqrt { - 1} [/math]

 

Means that the square root of minus 1 is compatible with the rules of algebra when we include the complex numbers.

 

Edited November 29, 2015 by studiot

[DevilSolution]

 

Agreed, although rather than say 'true' which opens another can of worms, I prefer to say 'is compatible with the stated axioms of the discourse, along with their derived theorems'

 

For example the fundamental theorem of algebra asserts crudely that every polynomial has a root (and therefore 'the existence' of complex numbers)

 

So

[math]\exists z:z = \sqrt { - 1} [/math]

 

Means that the square root of minus 1 is compatible with the rules of algebra when we include the complex numbers.

 

 

Like, slightly side stepping your conversation and the debate in general, could you or do you entertain the notion that mathematics (however we derive it) as being the primary tool for explaining the universe, i mean fundamentally explaining the universe?

 

If that notion is true, or atleast perceived to be then we as a species shall always be stuck between the devil and the deep blue.

 

On the one hand we have a format that can accurately predict this and that and therefore we can make things deterministic and on the other we have existential and subjective beliefs that can be neither proven nor disproved (not in general but in a meta physical sense). At the end of every answer is another "why" and until we can uniformly agree that such and such a notion is absolute, we will always find ways of discrediting the others notion or beliefs (usually through some form of logic). Now this is where we get down to the nitty gritty, logic is a fundamental premise to both philosophy and mathematics, through use of reasoning or symbolic writings. What the mathematicians fail to see that the philosophers dont is that logic by its very definition, defines what is, what was and what can be. But as a drunken philosopher would say, only we are defined by logic, or to be more precise, we are constrained as an intellectual species and bound by logic. Just because we cant see or comprehend beyond logic doesnt mean that it doesnt exist, even in the physical realm. Its the same notion as each individual being bound by their own personal intellect, there is a limit to which you can comprehend things and beyond that you cant mentally sustain or pertain to know or understand.

 

And i suppose thats where we digress, philosophers and mathematicians and all other freaks of nature alike. We either accept that as a human being we are bound by the laws of logic or we choose to believe that we as humans can expand our comprehension by allowing the notion that something exists beyond the realms of logic.

 

It's almost like a self acceptance ideology, you can accept the fact we are bound by logic or choose to believe that there exists something outside the realms of comprehension.

 

I dont see what the point is of entertaining such a concept, i suppose some of us wake up with hang overs and some of us dont, your seen as a problem if you do but no body questions the thirst.

 

There is no square root to 1 in nature, you can drink a cup of tea out of a glass but it doesnt make it up for the fact you dont have a cup.

 

Well a penny for my thoughts and your lotto numbers would be up. Oh and if your a philanthropist give me some rep points for staying awake for over 48 hours,

I deserve something. Even if its for the pity of my moronic attempt to explain something beyond my comprehension.

[studiot]

Yes I awarded you +1 for staying awake for 48 hours, but had to take it away again for rambling whilst in that condition and particularly because my lotto numbers didn't come up.

 

Sorry.

 

There are several things wrong with your rambles.

 

Here is the shortlist.

 

No I do not think that Mathematics is constructed to explain the universe.

 

There are plenty of things and matters that are outside the boundary of my Venn diagram.

So there are plenty of things in the universe that methematics does not address.

This, of course, is also true of Logic and Philosophy and indeed every other discipline.

 

Mathematics and Logic do not set goals.

That is an important statement because that is why human activity is not constrained by either.

As an aside, nor does Physics set goals.

That is part of the reason they both address the question of 'how' rather than 'why'.

 

Human activity also includes rational thought, sensible sensible thought (and their opposites).

These are not the same as the logic.discussed in this thread.

 

You should perhaps read the scifi novels about A and NullA by AE Van Vogt which explore the boundaries of formal logic.

 

https://en.wikipedia.org/wiki/The_World_of_Null-A

 

It is also instructive to study how electronics engineers have diverged from formal logic.

 

Firstly the customary presentation of formal logic requires two connective 'and' & 'or'.

Theoretically this can be cut down to one, 'nor', but this is rarely done.

 

Electronics engineers however have built a huge industry based on the nor gate.

(Yes I know that and & or gates are also available but nor gate implementations are usually more efficient.)

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.

 

I look forward to more accurate predictions for next week's lotto.

 

[andrewcellini]

in order to prevent further divergence from the topic, i think this topic should be closed.

 

i was personally provided with enough good and thought provoking answers and further questions to rethink my original question.

[studiot]

Please don't close it yet.

 

I am still waiting for next week's lotto numbers.