Philosophy of mathematics and origins

[gezz]

I'm not sure I'm posting this in the right section but here goes...

For anyone that has studied both philosophy and mathematics, at any level really, i would like to know whether you think maths is a rationalist or empiricist study?

For anyone who is purely a mathematician (and i salute you =-p ), do you think mathematics could be discovered without experience of the physical world?

For example if i were locked away in a scentless, intangible, soundless, pitch-black, tasteless cupboard since birth, yet had the mental faculties necessary to think logically, would i be able to come up with any mathematical truths?

This is more of a debatable question, and there are many schools of thought on the subject, but this is a question that has been in my head for a long time now and I've only recently discovered this forum. I'd be interested to hear what you all have to say.

Thanks.

 

[symbolipoint]

gezz,
Humans must act in the physical world. Humans are both reasonably intelligent and a few are curious; so that inspection and investigation with and through the physical world can not be avoided. Whether developing or discovering Mathematics, the physical world must be used. We must obtain data from the physical world before we could think about ways to manage & interpret that data.

'symbolipoint'

 

[Math Is Hard]

note: Moved from General Math to Philosophy under "Philosophy of Science, Math, Logic" subforum -MIH

 

[gezz]

That's definitely a valid viewpoint there, and from a practicality mindset i would have to agree with you. But again i find myself wondering if at one point sensory experience could be cut off for mathematics to continue.

For example, I'm sure less visual learners can make perfect sense out of calculus without having to imagine what any of it would mean in terms of shapes or lines.

The amount of proofs we are able to generate, and the ways in which maths can be thought out, certainly imply to me that without application the need for any sensory experience fades from mathematics the more it is studied.

Again i know this is debatable and i hope no one minds me prodding for answers, but is there any way of defining what we need to experience to understand maths?


Oh, and thanks Math Is Hard, i was in the complete wrong section, making it pretty obvious I'm new here, lol

 

[wuliheron]

The last stage of sensory deprivation is where the individual experiences an endless parade of perfect geometric objects. Similarly, many animals can count up to five. Thus it seems the roots of mathematics are inherent in the brain.

 

[JonF]

I think we couldn’t discover math without empirical observations. But math in of it self is pure, just our discovery isn’t. Formal math is a set of logically deduced inferences from definitions and axioms, which by definition is almost rational.

 

[Jedlmind]

The idea you are touching on is Platonism, where the truth does not exist in physical or mental worlds (or space and time). Stating that mathematics is not created; it is discovered from this ultimate realm of truth...

I read this in the first chapter of "The Road to Reality" (all the further I have managed to get) but definitely a larger than life idea (literally).

You can read about it here
http://plato.stanford.edu/entries/platonism/

 

[Rade]

..For example if i were locked away in a scentless, intangible, soundless, pitch-black, tasteless cupboard since birth, yet had the mental faculties necessary to think logically, would i be able to come up with any mathematical truths?

Well, check your false premise--you see, in this situation you would not be able to think "logically", because logic requires a process of identification and integration of that which is perceived. Since in your example by definition nothing can be perceived, then no logic is possible, and the answer to your question is no, you would not be able to come up with any mathematical truth. Horror of horrors, it is even possible to consider that such an experiment with a new born would be possible--now here seems a good topic for ethics thread.

 

[Mike2]

Well, check your false premise--you see, in this situation you would not be able to think "logically", because logic requires a process of identification and integration of that which is perceived. Since in your example by definition nothing can be perceived, then no logic is possible, and the answer to your question is no, you would not be able to come up with any mathematical truth. Horror of horrors, it is even possible to consider that such an experiment with a new born would be possible--now here seems a good topic for ethics thread.

I disagree. Even without reference, just being aware of the question of one's own existence is enough to derive everything. For all of logic can be based on the axioms of negation and implication. As soon as you consider the possibilities of your existence or not, you can understand logic. As soon as you know there are more than one possibility (existence or not), you can count and come up with mathematics and probabilities. And as soon as you understand math and logic, I believe you can derive the laws of physics. This may not tell you that you are in a cupboard. But it would tell you what other possible things there are in the world.

 

[Rade]

...Even without reference, just being aware of the question of one's own existence is enough to derive everything...

A blind person from birth in a box, while clearly aware of its own existence, has no ability to derive anything outside the box if it has 0.0 % experience via perception of what is outside--it can derive only one thing from being aware--that it exists.

 

[HallsofIvy]

A blind person from birth in a box, while clearly aware of its own existence, has no ability to derive anything outside the box if it has 0.0 % experience via perception of what is outside--it can derive only one thing from being aware--that it exists.

But that is, none the less, perception. I also imagine that such a person would also have perception of various bodily functions. He would not have perception of what is OUTSIDE the box, but that just brings us back to the original question- why do you think it is necessary to have perception of the OUTSIDE of some specific space in order to be able to use logic?

 

[Mike2]

A blind person from birth in a box, while clearly aware of its own existence, has no ability to derive anything outside the box if it has 0.0 % experience via perception of what is outside--it can derive only one thing from being aware--that it exists.

Being aware of oneself can only be done in terms of how one fits in with every other thing he percieves. If you can't distinguish yourself from other things, then you can not be aware of yourself as a separate entity. Ususally, we humans need to come across various things in order to catagorize their differences and commonalities. Those catagories become references in our minds about which we form correlations between facts. Those correlations become theories of reality - how things work together. But a mind of sufficient intelligence could catagorize the different thoughts in his head, give arbitrary reference to them, and deduce the same correlations and theories. We humans usually need to consider true and false in terms of other things that exist or not. But if true and false can be conceived only from thinking about ones own existence or not, then logic and math can be be developed and from that the laws of physics.

 

[Rade]

But that is, none the less, perception. I also imagine that such a person would also have perception of various bodily functions. He would not have perception of what is OUTSIDE the box, but that just brings us back to the original question- why do you think it is necessary to have perception of the OUTSIDE of some specific space in order to be able to use logic?

I was not suggesting that logic could not be used. I was responding to the claim that the person in the box could derive "everything". Logically, since deriving everything requires knowledge of both what is inside the box and outside, perception of only what is inside box is at least 50% less than "everything". I agree with your claim, logic is possible if one can perceive only self.

 

[Rade]

...Being aware of oneself can only be done in terms of how one fits in with every other thing he percieves. If you can't distinguish yourself from other things, then you can not be aware of yourself as a separate entity...

While in a box, a person is aware of at least two things, that it exists, that is exists in a confined space outside itself. I agree with you that based on this alone, the person could develop logical (non contradictory) thinking. But recall that in the OP the person in the box was not able to perceive anything, not even self, yet logic was stated to be present. This is my objection to the OP--logic cannot be present unless some perception of either self or other is possible.

 

[Mike2]

While in a box, a person is aware of at least two things, that it exists, that is exists in a confined space outside itself. I agree with you that based on this alone, the person could develop logical (non contradictory) thinking. But recall that in the OP the person in the box was not able to perceive anything, not even self, yet logic was stated to be present. This is my objection to the OP--logic cannot be present unless some perception of either self or other is possible.

It sounds as if you're saying that logic is a cognitive ability of intelligence - that logical thinking cannot be developed by intelligence without perception of other "things". But intelligence itself is the ability to think abstractly apart from the need to refer to other "things". So, yes, logic can be understood by intelligence that thinks abstractly. The question is can intelligence develop spontaneously in a black box.

 

[Colin1]

...I'm sure less visual learners can make perfect sense out of calculus without having to imagine what any of it would mean in terms of shapes or lines

I don't see how. They could conceivably make sense of the formulae involved and even how to solve a set problem but surely PERFECT sense implies intimate knowledge of what 'it would mean in terms of shapes or lines'. If you were taught sheet music and nothing but sheet music until you understood it, could you then be thrown at a piano and be expected to give a virtuoso performance? I doubt it, there is a tangible need for real-world application of knowledge.

The amount of proofs we are able to generate, and the ways in which maths can be thought out, certainly imply to me that without application the need for any sensory experience fades from mathematics the more it is studied

I don't agree. Industry certainly doesn't agree. Nor can I see at any time in the future the contract for a skyscraper being given to anyone with no 'sensory experience'