Where does logic come from?

[peanutaxis]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.

[mighty_duck]

New Jersey.

Now you know.

...

You may want to rephrase the question to get a more meaningful response. What are you really asking here?

[peanutaxis]

New Jersey.

Now you know.

...

You may want to rephrase the question to get a more meaningful response. What are you really asking here?

post 1 edited

[kennethamy]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.

Ohio

[David B]

This is a subject that I think about from time to time, but is always on the back burner, so to speak.

The following link does not, I think, lead to any definitive conclusion, but does, I think, lead to a better informed view of the difficulties in coming to a definitive conclusion.

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

David B

[kennethamy]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.

What does, "informed by observation" mean? Logic is the study of inference. The central question in logic is, supposing that some proposition, p is true, what else must be true, without any other information.

For instance, supposing that the proposition, No snakes are mammals is true, the proposition, no mammals are snakes must be true. Or, supposing that the proposition, Jane is taller than Sophie is true, Sophie is shorter than Jane must be true. We do not know either the former, or the latter, "from observation". We know it because we know the meanings of the words involved, and we can reason. By contrast, supposing that all snakes are reptiles is true, do we know anything about the proposition, all reptiles are snakes? The answer is no, we don't. Suppose that some reptiles are not snakes is true. Must it be true that some snakes are not reptiles. What do you think? Will you be using observation to find out.

Remember, though, the last question is not asking you whether some snakes are not reptiles. That is something to find out from observation. The last question is, rather, supposing that some snake are not reptiles is true, must it be true that some snake are not reptiles. That is not, I think, something that can be discovered by observation.

[Chris Porter]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.

What kind of logic are you talking about? (modal, bivalent, non-Aristotelian, etc)

[RareBird]

Vulcan.

[peanutaxis]

This is a subject that I think about from time to time, but is always on the back burner, so to speak.

The following link does not, I think, lead to any definitive conclusion, but does, I think, lead to a better informed view of the difficulties in coming to a definitive conclusion.

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

David B

Thanks for the link.


I get that we can take a bit of mathematics, say, and run with it and come up with new theories without making observations. But mustn't the original mathematics have come from observaion.

If I theorise that n+1 > n, isn't that dependant on observations from which natural numbers and the word 'greater' were derived.

[kennethamy]

Thanks for the link.


I get that we can take a bit of mathematics, say, and run with it and come up with new theories without making observations. But mustn't the original mathematics have come from observaion.

If I theorise that n+1 > n, isn't that dependant on observations from which natural numbers and the word 'greater' were derived.

That (I am afraid) depends on what you mean. You may be talking about the cause(s) of our mathematical concepts (what philosophers call "the genesis") How exactly we get our mathematical (and logical) concepts, is, of course, a question not for philosophers, but for learning psychologists who do research into such matters. It is an empirical question. But, it probably is true that we derive such concepts from (in general) observation, although it is certain that the mind takes some part in processing the information we get from the world, and molding that information into concepts. But the "raw material" seems to come from observation. However, many linguists, and even some psychologists think that in addition to how the mind processes and molds information into concepts (including mathematical and logical) think that the human mind itself, may contribute something to that information. That, in other words, we have what philosophers have called innate (inborn) concepts or knowledge. And there seems to be evidence that is true. The question of the mind's role in logic and mathematics is what philosophers call, the a priori element in those disciplines. ("A-priori" means "prior to", really "prior to (before) observation". Or "independently of observation").

But there is another issue, which is this: After we have these concepts (however we derive them) and use them, how much does that depend on observation? Suppose we already have the concept of the number two, and the concept of the number three, and the concept of addition. Does the truth of the equation, 2+3=5 depend on observation? Is whether 2+3=5 an empirical issue. Do we have to make observations in order to determine whether 2+3=5? The answer to that seems to be, no. We can determine whether 2+3=5 a priori, or independently of observation. Our knowledge that 2+3=5 is not based (or dependent on) making observations or experiments.

So, there are two different questions we have to hold separate:

1. Where does our mathematical or logical knowledge come from? What is its genesis?
2. How do we (once we have mathematical and logical concepts) decide whether a mathematical or logical statement is true or not.

These are two different questions, and may have (and seem to have) different answers.

[wnope]

I personally do not believe there is any objective "origin" of logic. As pointed out above, there are even several types.

We create axiomatic systems (such as those originally described in math or Aristotelian logic) in order to interpret events. I consider it more of a tool, a "heuristic" to help derive conclusions about our universe.

Modern logic, for instance, that of Quine, Frege, and Leibniez, distinctly changed how we use logic to interpret the world. The fact that all of our version of logic still contain unsolved paradoxes and such are further evidence that it is not some objective entity.

However, being a heuristic does not make it any less powerful than it currently is.

[kennethamy]

I personally do not believe there is any objective "origin" of logic. As pointed out above, there are even several types.

We create axiomatic systems (such as those originally described in math or Aristotelian logic) in order to interpret events. I consider it more of a tool, a "heuristic" to help derive conclusions about our universe.

Modern logic, for instance, that of Quine, Frege, and Leibniez, distinctly changed how we use logic to interpret the world. The fact that all of our version of logic still contain unsolved paradoxes and such are further evidence that it is not some objective entity.

However, being a heuristic does not make it any less powerful than it currently is.

Logic, in at least one sense, is the science of inference, and if it has any origin it is Aristotle who first discussed it, and created it as a discipline. Of course, as John Locke said, "God did not give Man two legs, and then left it up to Aristotle to make them logical". Human beings have probably produced inferences as soon as they could think. In fact, inference is the partly what we mean by thinking. Unless animals can draw inferences, it is questionable whether they can think. But if logic is the study of the science of inference, its origin is with Aristotle.

Of course, logic is a tool. That is why Aristotle put his discussion in his Organon which happens to mean, "instrument" or "tool".

[peanutaxis]

I personally do not believe there is any objective "origin" of logic. As pointed out above, there are even several types.

We create axiomatic systems (such as those originally described in math or Aristotelian logic) in order to interpret events. I consider it more of a tool, a "heuristic" to help derive conclusions about our universe.


To "create axiomatic systems in order to interpret events" don't we have to observe events - which is an objective origin?

[kennethamy]

To "create axiomatic systems in order to interpret events" don't we have to observe events - which is an objective origin?

I understand that in order to find a mathematics applicable to his physics, Einstein discovered a system of mathematics which was uninterpreted and had no application, and only then interpret it to fit his physics.

That was also true of non-Euclidean geometries.

So, although we observe events, we don't observe the interpretations, nor the systems we interpret.

[John Page]

I understand that in order to find a mathematics applicable to his physics, Einstein discovered a system of mathematics which was uninterpreted and had no application, and only then interpret it to fit his physics.
Invented, not discovered.
So, although we observe events, we don't observe the interpretations, nor the systems we interpret.
Interpretations are observed events. If this were not so, we would not have any knowledge of them.

[John Page]

Where does logic come from?
Mind + Alphabet + Language + Proposition (which in predicate logic must also be a wff) -> logic happens :)
Is it informed from observation, or is it more fundamental than even observation.
Logic is a process.

[kennethamy]

Invented, not discovered.

Interpretations are observed events. If this were not so, we would not have any knowledge of them.

Einstein discovered them. But others invented them.

Events may occur when no one knows of them.

[John Page]

Einstein discovered them. But others invented them.
Interesting. Which "system of mathematics which was uninterpreted and had no application" were you referring to?
Events may occur when no one knows of them.
Makes no difference to my position.

[wnope]

To "create axiomatic systems in order to interpret events" don't we have to observe events - which is an objective origin?

You can set up an axiomatic system without events. In fact, that's the whole point of a priori knowledge. However, the USEFULLNESS of whatever heuristical form of logic in place is dependant on the Universe.

For instance, I may formulate the axiom "A= not A" but it would not be applicable to the universe as we know it.

Spoken language, in fact, rarely uses good logic. We still haven't come up with a good justification for the most things.

Think about math for a moment. Before calculus (and there was a relevant reference to non-Euclidean geometry), our conception of "math" was entirely different than today. Would you say, then, that today's mathematics come from an "objective" source of some sort? Did it come from an objective source in the pre-Leibniz/Newton days?

[peanutaxis]

You can set up an axiomatic system without events. In fact, that's the whole point of a priori knowledge. However, the USEFULLNESS of whatever heuristical form of logic in place is dependant on the Universe.

Ahh. That makes sense.:)


Think about math for a moment. Before calculus (and there was a relevant reference to non-Euclidean geometry), our conception of "math" was entirely different than today. Would you say, then, that today's mathematics come from an "objective" source of some sort? Did it come from an objective source in the pre-Leibniz/Newton days?


Yes I see your point, I think. I would not claim that all math was derived from observation, but I would suggest that the basis of that math comes from observation. i.e. the starting point comes from observation......like natural numbers (set theory?)

[kennethamy]

Interesting. Which "system of mathematics which was uninterpreted and had no application" were you referring to?



The Lorenz equations.

Non-Euclidean geometries.

[kennethamy]

Ahh. That makes sense.:)




Yes I see your point, I think. I would not claim that all math was derived from observation, but I would suggest that the basis of that math comes from observation. i.e. the starting point comes from observation......like natural numbers (set theory?)

What does "starting point" mean? Are you talking about time? If you mean how we get the concepts of math. like addition, or division, or of numbers, there is controversy about that, but most psychologists (and philosophers) agree that both the mind and the senses are involved, as in most learning. The more interesting question, though, is how, once we learn the concepts, we "verify" that, for instance, the Pythagorean theorem is true. Is that by observation?

[John Page]

The Lorenz equations.
1. I don't see how you make the claim that the Lorenz equations were "uninterpreted". In what sense were they uninterpreted?

2. You said "Einstein discovered a system of mathematics which was uninterpreted and had no application, and only then interpret it to fit his physics." Einstein died in 1955 and the Lorenz equation was published 1963. Are you suggesting he traveled forward in time to discover them?

You are not making sense to me. What am I missing?

[kennethamy]

1. I don't see how you make the claim that the Lorenz equations were "uninterpreted". In what sense were they uninterpreted?

2. You said "Einstein discovered a system of mathematics which was uninterpreted and had no application, and only then interpret it to fit his physics." Einstein died in 1955 and the Lorenz equation was published 1963. Are you suggesting he traveled forward in time to discover them?

You are not making sense to me. What am I missing?

http://en.wikipedia.org/wiki/Lorentz_transformation

I confused the Lorentz equations with the Lorentz Transformation. I hope you will forgive me. The Lorentz Transformation was discovered in the early 20th century.

[John Page]

http://en.wikipedia.org/wiki/Lorentz_transformation

I confused the Lorentz equations with the Lorentz Transformation. I hope you will forgive me. The Lorentz Transformation was discovered in the early 20th century.
No problem. I'm still unclear in what sense you say they were "uninterpreted". Are you indicating that they had not been used to describe the relativity between different frames of reference?

[kennethamy]

No problem. I'm still unclear in what sense you say they were "uninterpreted". Are you indicating that they had not been used to describe the relativity between different frames of reference?

As I understand it, Lorentz had invented them as a nice piece of math. Einstein, later, was looking for mathematics to work with for his special theory. He came on the transformation, and used that. Until then, the transformation had no application. It was pure math.

Like non- Euclidean geometries.

[John Page]

Originally Posted by John Page
No problem. I'm still unclear in what sense you say they were "uninterpreted". Are you indicating that they had not been used to describe the relativity between different frames of reference?
As I understand it, Lorentz had invented them as a nice piece of math. Einstein, later, was looking for mathematics to work with for his special theory. He came on the transformation, and used that. Until then, the transformation had no application. It was pure math.

Like non- Euclidean geometries.

Here's my question again. "I'm still unclear in what sense you say they were "uninterpreted".'

[kennethamy]

Here's my question again. "I'm still unclear in what sense you say they were "uninterpreted".'

No referents were given to their symbols. They had no application. That is what "uninterpreted" usually means. In fact, in that context, that is what "uninterpreted" means.

[John Page]

No referents were given to their symbols. They had no application. That is what "uninterpreted" usually means. In fact, in that context, that is what "uninterpreted" means.
:confused: If this is true, the Lorentz Transformations have no meaning.

[kennethamy]

:confused: If this is true, the Lorentz Transformations have no meaning.

Save as a piece of pure mathematics, uninterpreted, that's right. Mathematicians often produce uninterpreted mathematics. That is what pure, as contrasted with, applied, mathematics is all about. Go see the movie, "A Beautiful Mind".

Look, I am really not interested in conducting a private conversation with you on this forum. It is all input. And you are exceedingly hostile.

[John Page]

Save as a piece of pure mathematics, uninterpreted, that's right. Mathematicians often produce uninterpreted mathematics.
Nonsense, pure mathematics by definition is embodied in a language which has no meaning unless it is interpreted.

Seems by uninterpreted you mean something like "It's implication for other discplines and branches of mathematics was not appreciated by the inventor."
Look, I am really not interested in conducting a private conversation with you on this forum. It is all input. And you are exceedingly hostile.
This is not a private conversation. I am not being hostile. The interpretation of math/logic by the mind is directly relevant to the OP.

[kennethamy]

Nonsense, pure mathematics by definition is embodied in a language which has no meaning unless it is interpreted.

Seems by uninterpreted you mean something like "It's implication for other discplines and branches of mathematics was not appreciated by the inventor."

This is not a private conversation. I am not being hostile. The interpretation of math/logic by the mind is directly relevant to the OP.

"Uninterpreted" means, "uninterpreted". I gave you a simple (enough) example.

'X' and 'Y' are uninterpreted symbols in the expression, "X + Y= Z" The equation may be either true or false depending on how 'X", 'Y', and 'Z' are interpreted.

I do not mean by "uninterpreted" what you impute to me, since that is not what "uninterpreted" means. I try to use words with their ordinary meanings.

[John Page]

'X' and 'Y' are uninterpreted symbols in the expression, "X + Y= Z" The equation may be either true or false depending on how 'X", 'Y', and 'Z' are interpreted.
Equivocation, you raised "uninterpreted" in relation to "system of mathematics", not symbols alone. See below.
I understand that in order to find a mathematics applicable to his physics, Einstein discovered a system of mathematics which was uninterpreted and had no application, and only then interpret it to fit his physics.

[peanutaxis]

Quote:
Originally Posted by wnope View Post
You can set up an axiomatic system without events. In fact, that's the whole point of a priori knowledge. However, the USEFULLNESS of whatever heuristical form of logic in place is dependant on the Universe.

Ahh. That makes sense.

Quote:
Originally Posted by wnope View Post
Think about math for a moment. Before calculus (and there was a relevant reference to non-Euclidean geometry), our conception of "math" was entirely different than today. Would you say, then, that today's mathematics come from an "objective" source of some sort? Did it come from an objective source in the pre-Leibniz/Newton days?


Yes I see your point, I think. I would not claim that all math was derived from observation, but I would suggest that the basis of that math comes from observation. i.e. the starting point comes from observation......like natural numbers (set theory?)

[peanutaxis]

I personally do not believe there is any objective "origin" of logic. As pointed out above, there are even several types.

If someone started a thread questioning "is there an objective origin of physics" wouldn't the answer be an obvious yes?


We create axiomatic systems (such as those originally described in math or Aristotelian logic) in order to interpret events. I consider it more of a tool, a "heuristic" to help derive conclusions about our universe.

A physicist couldn't then answer: "[in physics]We create axiomatic systems in order to interpret events, therefore there is no objective origin of Physics." How come you can do this to logic?


Modern logic, for instance, that of Quine, Frege, and Leibniez, distinctly changed how we use logic to interpret the world. The fact that all of our version of logic still contain unsolved paradoxes and such are further evidence that it is not some objective entity.

However, being a heuristic does not make it any less powerful than it currently is.

Could you give an example?

[naturalist.atheist]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.

From nature. Our neurons are logic. It is a useful evolutionary trait to be able to infer that if there is fresh water there will be wildlife. So look for fresh water. There are a large number of such inferences that are not only useful but are a matter of life and death. So over time nature selects for nuron circuits that encode rules of inference that are consistent with nature as we experience it. Of course move into a different realm where the rules of inference of nature are different and then things don't seem so logical anymore.

[wnope]

Ahh. That makes sense.:)




Yes I see your point, I think. I would not claim that all math was derived from observation, but I would suggest that the basis of that math comes from observation. i.e. the starting point comes from observation......like natural numbers (set theory?)

What you are actually referring to is set theory. The natural numbers themselves are based on a set of axioms just like geometry is made up of axioms.

When you count something, you are sorting objects into larger groups. For instance, if five rocks are in front of you, you can make a group of "3" and a group of "2." You can add these groups together to get a group of "5."

We APPLY numbers to what we observe. When we count, we are just creating larger and larger sets. So numbers, in the sense that we use them mathematically, are just another tool.

[wnope]

If someone started a thread questioning "is there an objective origin of physics" wouldn't the answer be an obvious yes?



A physicist couldn't then answer: "[in physics]We create axiomatic systems in order to interpret events, therefore there is no objective origin of Physics." How come you can do this to logic?



Could you give an example?

I'm not sure why you think we cannot create an axiomatic model of reality. That's the whole point of heuristics. There is an objective universe, but we have no direct way to know it. Instead, we create tools to model the reality.

Newton created laws that predicted how the universe would behave. It was true for everyone. You would have said "we can call that 'fact.'" But then you get quantum physics which destroys the idea of determinism.

There is no way to exactly predict or explain the universe, we aren't capable of finding that out. We can only aim for model closer to the universe.

[wnope]

If you want an example, just scan the "history of logic." (http://en.wikipedia.org/wiki/History_of_Logic#Traditional_logic)

[John Page]

I'm not sure why you think we cannot create an axiomatic model of reality.
I think its because it is an 'open system' that defies axiomatization.

We also have the limitations of the human faculty of imagination. :)

[Cacofonix]

On the original question, as opposed to that one of wearing more hats haha, I think it is a bloody brilliant question. It, if we are connectivists, would seem to be wired and about the senses and analysis of the senses, therefore all about inference of the outer world and how it is wired - turns out to be quantum mechanics.

My guess about all that would be that the studies of the fundmentals of life and the fundamentals of physics will converge as Penrose and others would say.

[naturalist.atheist]

My guess about all that would be that the studies of the fundmentals of life and the fundamentals of physics will converge as Penrose and others would say.

Too mystical for me and completely unnecessary. We are exploring reality. If we keep looking we will probably find out how it works. No need to presume anything. Besides my bet is that things turn out to be far more amazing than anything Penrose can imagine, as great as he thinks he is.

[wnope]

I think its because it is an 'open system' that defies axiomatization.

We also have the limitations of the human faculty of imagination. :)

I'm sorry, I screw up when I type off the top of my head. I meant that I didn't see how he could think we can know exactly how the universe works.

[peanutaxis]

What you are actually referring to is set theory. The natural numbers themselves are based on a set of axioms just like geometry is made up of axioms.

Axioms. What axioms? next paragraph?


When you count something, you are sorting objects into larger groups. For instance, if five rocks are in front of you, you can make a group of "3" and a group of "2." You can add these groups together to get a group of "5."

We APPLY numbers to what we observe. When we count, we are just creating larger and larger sets. So numbers, in the sense that we use them mathematically, are just another tool.

[peanutaxis]

I'm not sure why you think we cannot create an axiomatic model of reality. That's the whole point of heuristics. There is an objective universe, but we have no direct way to know it. Instead, we create tools to model the reality.

Newton created laws that predicted how the universe would behave. It was true for everyone. You would have said "we can call that 'fact.'" But then you get quantum physics which destroys the idea of determinism.

There is no way to exactly predict or explain the universe, we aren't capable of finding that out. We can only aim for model closer to the universe.

Oh. Right. I think I get you. So even something basic like counting numbersis really only a representative internalization of the 'real world'.

Yeah I was also thinking of starting a thread on whether our models of reality are really..........models of reality (Newton vs. Einstein thing)

[peanutaxis]

On the original question, as opposed to that one of wearing more hats haha, I think it is a bloody brilliant question. It, if we are connectivists, would seem to be wired and about the senses and analysis of the senses, therefore all about inference of the outer world and how it is wired - turns out to be quantum mechanics.

My guess about all that would be that the studies of the fundmentals of life and the fundamentals of physics will converge as Penrose and others would say.

Hats?

I've often wondered whether, as we study the universe, we are actually studying the human brain - the final frontier(?)

BTW, have people watched the videos on The Science Network?
http://beyondbelief2006.org/Watch/
Ramachandran has some very interesting thing to say about neuroscience. Session 4 I believe.

[wnope]

Oh. Right. I think I get you. So even something basic like counting numbersis really only a representative internalization of the 'real world'.

Yeah I was also thinking of starting a thread on whether our models of reality are really..........models of reality (Newton vs. Einstein thing)

Right, so what you have to do is try and divorce yourself from your interpretation of the world via sensory perception alone and via heuristics.

We observe thinks falling in a certain way. We observe this quite often.

What we do, then, is try and shape our model of the universe with our heuristical tools so that it best represents how the universe may actually work.

It would appear initially that scientific laws of physis and such are objective simply because the model we have in place to describe physical acts is, on a macro level, extremely consistent. Our model predicts with much exactness how much energy a ball will transfer to the ground when we drop it. But, as the Newton/Einstein example shows, we learned over time that on a smaller level things do not act according to our model. Thus, we have reshaped our model of the universe to include quantum physics.

As long as you separate between the tentative model of the universe we establish via heuristics and the objective universe being modeled, you will have a much better understanding of the true nature of reality...assuming we ever figure it out ;)

[peanutaxis]

Right, so what you have to do is try and divorce yourself from your interpretation of the world via sensory perception alone and via heuristics.

We observe thinks falling in a certain way. We observe this quite often.

What we do, then, is try and shape our model of the universe with our heuristical tools so that it best represents how the universe may actually work.

It would appear initially that scientific laws of physis and such are objective simply because the model we have in place to describe physical acts is, on a macro level, extremely consistent. Our model predicts with much exactness how much energy a ball will transfer to the ground when we drop it. But, as the Newton/Einstein example shows, we learned over time that on a smaller level things do not act according to our model. Thus, we have reshaped our model of the universe to include quantum physics.

As long as you separate between the tentative model of the universe we establish via heuristics and the objective universe being modeled, you will have a much better understanding of the true nature of reality...assuming we ever figure it out ;)

Cheers, that neuron path was not quite complete, so to speak (& perhaps literally!).

[Iacchus]

Where does logic come from?

I really want to know!

Is it informed from observation, or is it more fundamental than even observation.It's funny, how I started a thread with the same title (http://www.iidb.org/vbb/showthread.php?t=186876), about five or six months ago.