Philopshy 'owns' everything

[steve_bnk]

http://talkfreethought.org/showthread.php?51-Math-Subforum&p=8753#post8753

Originally Posted by steve_bnk

Originally Posted by Underseer

Originally Posted by beero1000
Personally, I'd rather see it with the science boards. Currently, most of the math type posts on FRDB go into Science Discussions anyway.



Why? Math falls under idealism/rationalism, whereas science comes from evidence-based epistemologies. They're totally different branches of philosophy.

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Mathematicians invent mathematics.

Philosophers invent -isms.
Meaningless distinction. The vast majority of academic disciplines are technically branches of philosophy.


A tpic debated on the old forum.

Some take a position that philosophy functions as some collective agency that created science and other disciplines.

The term philosophy itself is ill defined.

Love of knowledge, search forknowledge, search for wisdom? Search for knowledge certainlyencompasses most everything, however the assertion that all fallsunder some function called philosophy is false.

 

[Philos]

Steve,

My 2p.

When we are trying to 'do' philosophy, I think the philosophy is the bit we struggle with. Once we think we know something, philosophy has long gone.

Of course the above sentence isn't philosophy.

Alex.

 

[fromderinside]

Its not that philosophy doesn't cover everything, it does. Its that philosophy doesn't originate everything. As you said, essentially, physicists, engineers, biologists, psychologist, agronomists, etc, invent mathematics. Philosophers don't.

As to ownership I leave that to the ones who originate, patent the specific construct. I see philosophers as historians of information in the real world.

 

[Tom Sawyer]

Also, philosophers are the ones who make sure that the burgers are ready on time so that the scientists can have a good meal before they get back to work.

 

[Underseer]

Its not that philosophy doesn't cover everything, it does. Its that philosophy doesn't originate everything. As you said, essentially, physicists, engineers, biologists, psychologist, agronomists, etc, invent mathematics. Philosophers don't.

As to ownership I leave that to the ones who originate, patent the specific construct. I see philosophers as historians of information in the real world.

Mathematicians didn't invent math either. Modern mathematicians insist that all of mathematics is based on set theory, but math doesn't come from set theory because math is a heck of a lot older than set theory. In reality, the most likely origin of math is counting. Once you have counting, you can quickly find reasons to develop addition and subtraction (say, to make keeping inventories easier), and from there it's another short leap to multiplying and dividing.

Ultimately, counting is a consequence of the early development of languages in which developing languages needed to describe quantities with greater and greater specificity.

So if we use the origin of mathematics as a means of determining how to classify it, math is a branch of linguistics.

One could argue that mathematics is a branch of empiricism because the development of counting came as a result of humans interacting with the physical world and trying to describe the things in it, but I'm pretty sure that math-as-empiricism is a minority view among those who study the philosophy of mathematics.

However, even if we assume that the origins of mathematics is empiricist/evidentialist in nature, I think we can all agree that empiricism plays zero role in the modern practice of mathematics. No mathematician would try to prove a theorem using experimental evidence, which is why I don't think it should be classified with empiricist disciplines like science.

 

[beero1000]

Its not that philosophy doesn't cover everything, it does. Its that philosophy doesn't originate everything. As you said, essentially, physicists, engineers, biologists, psychologist, agronomists, etc, invent mathematics. Philosophers don't.

As to ownership I leave that to the ones who originate, patent the specific construct. I see philosophers as historians of information in the real world.

Mathematicians didn't invent math either. Modern mathematicians insist that all of mathematics is based on set theory, but math doesn't come from set theory because math is a heck of a lot older than set theory. In reality, the most likely origin of math is counting. Once you have counting, you can quickly find reasons to develop addition and subtraction (say, to make keeping inventories easier), and from there it's another short leap to multiplying and dividing.

Ultimately, counting is a consequence of the early development of languages in which developing languages needed to describe quantities with greater and greater specificity.

So if we use the origin of mathematics as a means of determining how to classify it, math is a branch of linguistics.

One could argue that mathematics is a branch of empiricism because the development of counting came as a result of humans interacting with the physical world and trying to describe the things in it, but I'm pretty sure that math-as-empiricism is a minority view among those who study the philosophy of mathematics.

However, even if we assume that the origins of mathematics is empiricist/evidentialist in nature, I think we can all agree that empiricism plays zero role in the modern practice of mathematics. No mathematician would try to prove a theorem using experimental evidence, which is why I don't think it should be classified with empiricist disciplines like science.

Counting is arguably much older than linguistics, and so is simple arithmetic. Many other animals have number concepts and can keep track of changing numbers of objects, essentially performing addition and subtraction.

Most mathematicians hold that mathematical terminology and techniques are invented, and then mathematicians discover the relationships between those mathematical concepts. While set theory is foundational for modern math, set theory itself rarely appears. If one really wanted to dig all the way down to bedrock one could find Peano and ZFC, but other than the logicians and set theorists most mathematicians just count and use naive set theory in their day to day work.

In modern times the 'pureness' of mathematics is slowly disappearing. The four color theorem was proved by computer analysis of thousands of cases. Much of the uproar among mathematicians when that came out is that it was not possible for a human to verify the proof. What if there was a bug in the code? Since then, more implementations have come out the same, and much of the hesitance about computer proofs is disappearing. Is that experimental?

There are also many fields that vary continuously from very applied/experimental to very pure/theoretical, and one end informs the other. If someone works on one of those, are they an empiricist or not? Is there a strict cutoff for people working on theoretical  molecular self-assembly where their terminology, problems, and interest come from biology/chemistry, but their papers are full of proofs and no experiments?

 

[fromderinside]

Mathematicians didn't invent math either.

....

.... I think we can all agree that empiricism plays zero role in the modern practice of mathematics. No mathematician would try to prove a theorem using experimental evidence, which is why I don't think it should be classified with empiricist disciplines like science.

I think I implied that by leaving them out of those who I think did invent mathematics.

....

uh,  Feynman comes to mind.

 

[fromderinside]

I believe the pureness of mathematics has been up in the air for millennia. Wasn't it Russell and Whitehead who, at the turn of the twentieth century. set out to make mathematics, er, consistent by producing  Principia Mathematica which Godel promptly destroyed, even though Russell had already conceded as much, with  Godel's incompleteness theorems?

 

[Underseer]

Its not that philosophy doesn't cover everything, it does. Its that philosophy doesn't originate everything. As you said, essentially, physicists, engineers, biologists, psychologist, agronomists, etc, invent mathematics. Philosophers don't.

As to ownership I leave that to the ones who originate, patent the specific construct. I see philosophers as historians of information in the real world.

Mathematicians didn't invent math either. Modern mathematicians insist that all of mathematics is based on set theory, but math doesn't come from set theory because math is a heck of a lot older than set theory. In reality, the most likely origin of math is counting. Once you have counting, you can quickly find reasons to develop addition and subtraction (say, to make keeping inventories easier), and from there it's another short leap to multiplying and dividing.

Ultimately, counting is a consequence of the early development of languages in which developing languages needed to describe quantities with greater and greater specificity.

So if we use the origin of mathematics as a means of determining how to classify it, math is a branch of linguistics.

One could argue that mathematics is a branch of empiricism because the development of counting came as a result of humans interacting with the physical world and trying to describe the things in it, but I'm pretty sure that math-as-empiricism is a minority view among those who study the philosophy of mathematics.

However, even if we assume that the origins of mathematics is empiricist/evidentialist in nature, I think we can all agree that empiricism plays zero role in the modern practice of mathematics. No mathematician would try to prove a theorem using experimental evidence, which is why I don't think it should be classified with empiricist disciplines like science.

Counting is arguably much older than linguistics, and so is simple arithmetic. Many other animals have number concepts and can keep track of changing numbers of objects, essentially performing addition and subtraction.

Oooh, that's terribly interesting.

However, if we're talking about math, then it's pointless to talk about people having a concept of numbers before having the language to talk to each other about numbers. The ideas in question have to be something humans can communicate with each other before we can call it "math," at least in my opinion. I have to imagine that languages started out describing quantities rather vaguely ("many," "few"), then increasing in specificity until we get to proper counting. Prior to that, the concept of numbers would have been too vague and shifting to relate to the concept of numbers as they exist in mathematics, wouldn't you say?

[...]

In modern times the 'pureness' of mathematics is slowly disappearing. The four color theorem was proved by computer analysis of thousands of cases. Much of the uproar among mathematicians when that came out is that it was not possible for a human to verify the proof. What if there was a bug in the code? Since then, more implementations have come out the same, and much of the hesitance about computer proofs is disappearing. Is that experimental?

[...]

Ouch. Mathematicians are used to living in a world where everything is true or false. They're not used to life in the empirical world where every idea has to be regarded with suspicion and constantly re-tested. I hope this trend doesn't cause trouble.

 

[Togo]

Counting is arguably much older than linguistics, and so is simple arithmetic. Many other animals have number concepts and can keep track of changing numbers of objects, essentially performing addition and subtraction.

Oooh, that's terribly interesting.

However, if we're talking about math, then it's pointless to talk about people having a concept of numbers before having the language to talk to each other about numbers.

Newborns manage counting quite easily. A neonate human can work out 1+1=2, 2-1=1, and so on, within a few minutes of birth. Baby chimps have the same ability. They can't communicate these concepts until later.

Similarly, mathematical ideas and language spread in very different patterns from each other. If they were closely linked, I'd expect to see mathematical ideas flowing along language paths.

I'd say the basis of mathematics is more likely cookery, or possibly pottery. These are the first disciplines in which you need to add substances together, look at the result, and then work out whether or not to add more or less of each substance the next time. If your stew tastes awful with two pinches of salt, you need to know how many you added (2), work out a lesser number to add next time, and appreciate that the whole stew somehow contains the original values even though they no longer exist as discreet objects - i.e. abstract numerical reasoning.

 

[Underseer]

Counting is arguably much older than linguistics, and so is simple arithmetic. Many other animals have number concepts and can keep track of changing numbers of objects, essentially performing addition and subtraction.

Oooh, that's terribly interesting.

However, if we're talking about math, then it's pointless to talk about people having a concept of numbers before having the language to talk to each other about numbers.

Newborns manage counting quite easily. A neonate human can work out 1+1=2, 2-1=1, and so on, within a few minutes of birth. Baby chimps have the same ability. They can't communicate these concepts until later.

Similarly, mathematical ideas and language spread in very different patterns from each other. If they were closely linked, I'd expect to see mathematical ideas flowing along language paths.

I'd say the basis of mathematics is more likely cookery, or possibly pottery. These are the first disciplines in which you need to add substances together, look at the result, and then work out whether or not to add more or less of each substance the next time. If your stew tastes awful with two pinches of salt, you need to know how many you added (2), work out a lesser number to add next time, and appreciate that the whole stew somehow contains the original values even though they no longer exist as discreet objects - i.e. abstract numerical reasoning.

I'm guessing that the guys who crafted stone tools would have been the first to need to keep inventories.