oh my... someone get me a giant hammer i wanna wack this guy on the head.

You can't disprove 1+1=2, because it's a definition. It doesn't require a proof because it is a predefined axiom of arithmetic.

 

Nothing is finite. How do you even know that 1 + 1 = anything? How do you know that you know the stuff that you think you know? Because in reality, the only that that you know for certain is that you exist: "I think, therefore I am." Everything else, you can never know for certain. It could all be fake.

 

Now I ask you two questions. See if you can answer them.

 

1. What are numbers?

 

2. Why does math apply to the real world?

1. Numbers quantify objects, linearly.

1 + 1 = 2 because a single object is quantified as one, and if there is another, the next in progression is known as two. We could count in binary and it would mean the same thing. After all, Dec 25 == Oct 31

2. Because everything is made of a finite number of elements.

 

 

You can't disprove 1+1=2, because it's a definition. It doesn't require a proof because it is a predefined axiom of arithmetic.

 

Nothing is finite. How do you even know that 1 + 1 = anything? How do you know that you know the stuff that you think you know? Because in reality, the only that that you know for certain is that you exist: "I think, therefore I am." Everything else, you can never know for certain. It could all be fake.

 

Now I ask you two questions. See if you can answer them.

 

1. What are numbers?

 

2. Why does math apply to the real world?

 

1. Numbers quantify objects, linearly.

1 + 1 = 2 because a single object is quantified as one, and if there is another, the next in progression is known as two. We could count in binary and it would mean the same thing. After all, Dec 25 == Oct 31

2. Because everything is made of a finite number of elements.

 

 

You are missing the point. How do you know these things? Math might not even exist.

 

"The philosophy of mathematics is, at its core, the study of mathematics from a philosophical perspective rather than a strictly mathematical one. Often times philosophers of mathematics concern themselves with the foundations of mathematics - what mathematics is, what kind of objects, if any it refers to, how we come to have knowledge of these objects, and how we are to think of mathematical objects and theories. Because the philosophy of mathematics often deals in foundations, in some senses it is a deviating branch of metaphysics and epistemology. However philosophy of mathematics is not just foundations - it includes questions about the nature of mathematical explanation, computation, proof, set theory, infinity and more. For this reason we will treat the philosophy of mathematics as a separate subfield, within the larger category of the philosophy of sciences and mathematics.

 

In the midst of a rather interesting discussion of the notion of Aristotle’s Unmoved Mover, Leah Libresco went on a mild digression about the philosophy of mathematics that I couldn’t let go of, and feel compelled to respond to. She says:

 

"I take what is apparently a very Platonist position on math.  I don’t treat it as the relationships that humans make between concepts we abstract from day to day life.  I don’t think I get the concept of ‘two-ness’ from seeing two apples, and then two people, and then two houses and abstracting away from the objects to see what they have in common.

 

I think of mathematical truths existing prior to human cognition and abstraction.  The relationship goes the other way.  The apples and the people and the houses are all similar insofar as they share in the form of two-ness, which exists independently of material things to exist in pairs or human minds to think about them."

 

The notion that there’s something special about math – that it has some sort of metaphysical significance – only makes sense if you ignore the history of how we uncovered math to begin with. It was, despite Leah’s protestations, exactly just the abstraction of pairs and triplets and quartets, etc. The earliest known mathematics appear to be attempts to quantify time and make calendars, with other early efforts directed towards accounting, astronomy, and engineering.

 

Mathematics is nothing more and nothing less a tool that’s useful for humans in solving particular problems. Math can be used to describe reality or construct useful fictions. For example, we know now that the spacetime we live in is non-Euclidian. But that doesn’t make Euclidian geometry useless for everyday life. Quite the contrary – it’s used every day. You can use mathematics to build models of reality that may not actually have any bearing on what’s real. For example, the complicated math used to describe how the planets moved in the Ptolemaic model of the solar system – where everything orbited in circles around the Earth – actually produced very accurate predictions. But it was also wrong. There aren’t actually trillions of physical dollars circulating in the economy – there are just symbols for them floating around.

 

The bottom line is that human beings have brains capable of counting to high numbers and manipulating them, so we use mathematics as a useful tool to describe the world around us. But numbers and math themselves are no more real than the color blue – ‘blue’ is just what we tag a certain wavelength of light because of the way we perceive that wavelength. An alien intelligence that is blind has no use for the color blue. It might learn about light and the wavelengths of light and translate those concepts completely differently than we do.

 

In the same way, since the only truly good mathematicians among the animals are ourselves, we assume that if we encounter other systems of intelligence that they’ll have the same concepts of math was we do. But there’s no evidence to base that assumption on. For all we know, there are much easier ways to describe physics than through complicated systems of equations, but our minds may not be capable of symbolically interpreting the world in a way that allows us to use those tools, any more than we’re capable of a tool that requires the use of a prehensile tail.

 

Math is a useful descriptor of both real and fictional concepts. It’s very fun to play around with and its essential for understanding a lot of subjects. But it’s just a tool. Not a set of mystical entities.

 

Here are some good readings on the philosophy of math:

 

Introductory Readings

Books

 

Stewart Shapiro - Thinking About Mathematics. Shapiro's book is a masterpiece of introductory philosophy - it's easy to read and covers nearly all the ground you would hope, starting with a brief gloss of the history of philosophy of mathematics and moving forward into the major schools of foundations, with equal focus on both the historical views (e.g. Russell/Whitehead, Frege and Brouwer) and contemporary movements (e.g. Hale/Wright, Field, Shapiro).

Encyclopedia Articles

 

As always the SEP is of great help. In particular, the following articles are essential:

 

Philosophy of Mathematics

Frege's Logic, Theorem, and Foundations for Arithmetic

Platonism in the Philosophy of Mathematics

Intuitionism in the Philosophy of Mathematics

Formalism in the Philosophy of Mathematics

Fictionalism in the Philosophy of Mathematics

Kurt Gödel

Set Theory

Explanation in Mathematics

Constructive Mathematics

Further Readings

Anthologies

 

Philosophy of Mathematics: Selected Readings ed. Benacerraf and Putnam - this is the bible of philosophy of maths, containing almost two dozen of the most important papers ever written in the subject. It's a bit out of date at this point, but still a classic. Rather than listing all of the must-read papers in the philosophy of mathematics one should just read this book cover to cover.

 

The Oxford Handbook of Philosophy of Mathematics and Logic ed. Shapiro - This book has articles on every major movement in philosophy of maths and logic written in a fantastically accessible way. It is a massive resource to anyone with interest in the field.

 

Primary Texts (Books)

 

L.E.J. Brouwer - Cambridge Lectures on Intuitionism

Richard Dedekind - Essays on the Theory of Numbers

Gottlob Frege - Grundlagen der Arithmetik or The Foundations of Arithmetic

Gottlob Frege - Grundgesetze der Arithmetik or The Basic Laws of Arithmetic. OUP has the first full translation of the Grundgesetze forthcoming, translated by Ebert, Rossberg, Wright and Cook. Reading it alongside Richard Heck Jr.'s Reading Frege's Grundgesetze is highly recommended.

Hartry Field - Science Without Numbers: A Defense of Nominalism

Bob Hale and Crispin Wright - The Reason's Proper Study

Stewart Shapiro - Philosophy of Mathematics: Structure and Ontology"

Edited September 27, 201312 yr by Zappa

 

 

 

You can't disprove 1+1=2, because it's a definition. It doesn't require a proof because it is a predefined axiom of arithmetic.

 

Nothing is finite. How do you even know that 1 + 1 = anything? How do you know that you know the stuff that you think you know? Because in reality, the only that that you know for certain is that you exist: "I think, therefore I am." Everything else, you can never know for certain. It could all be fake.

 

Now I ask you two questions. See if you can answer them.

 

1. What are numbers?

 

2. Why does math apply to the real world?

 

1. Numbers quantify objects, linearly.

1 + 1 = 2 because a single object is quantified as one, and if there is another, the next in progression is known as two. We could count in binary and it would mean the same thing. After all, Dec 25 == Oct 31

2. Because everything is made of a finite number of elements.

 

 

You are missing the point. How do you know these things? Math might not even exist.

 

The philosophy of mathematics is, at its core, the study of mathematics from a philosophical perspective rather than a strictly mathematical one. Often times philosophers of mathematics concern themselves with the foundations of mathematics - what mathematics is, what kind of objects, if any it refers to, how we come to have knowledge of these objects, and how we are to think of mathematical objects and theories. Because the philosophy of mathematics often deals in foundations, in some senses it is a deviating branch of metaphysics and epistemology. However philosophy of mathematics is not just foundations - it includes questions about the nature of mathematical explanation, computation, proof, set theory, infinity and more. For this reason we will treat the philosophy of mathematics as a separate subfield, within the larger category of the philosophy of sciences and mathematics.

 

In the midst of a rather interesting discussion of the notion of Aristotle’s Unmoved Mover, Leah Libresco went on a mild digression about the philosophy of mathematics that I couldn’t let go of, and feel compelled to respond to. She says:

 

"I take what is apparently a very Platonist position on math.  I don’t treat it as the relationships that humans make between concepts we abstract from day to day life.  I don’t think I get the concept of ‘two-ness’ from seeing two apples, and then two people, and then two houses and abstracting away from the objects to see what they have in common.

 

I think of mathematical truths existing prior to human cognition and abstraction.  The relationship goes the other way.  The apples and the people and the houses are all similar insofar as they share in the form of two-ness, which exists independently of material things to exist in pairs or human minds to think about them."

 

The notion that there’s something special about math – that it has some sort of metaphysical significance – only makes sense if you ignore the history of how we uncovered math to begin with. It was, despite Leah’s protestations, exactly just the abstraction of pairs and triplets and quartets, etc. The earliest known mathematics appear to be attempts to quantify time and make calendars, with other early efforts directed towards accounting, astronomy, and engineering.

 

Mathematics is nothing more and nothing less a tool that’s useful for humans in solving particular problems. Math can be used to describe reality or construct useful fictions. For example, we know now that the spacetime we live in is non-Euclidian. But that doesn’t make Euclidian geometry useless for everyday life. Quite the contrary – it’s used every day. You can use mathematics to build models of reality that may not actually have any bearing on what’s real. For example, the complicated math used to describe how the planets moved in the Ptolemaic model of the solar system – where everything orbited in circles around the Earth – actually produced very accurate predictions. But it was also wrong. There aren’t actually trillions of physical dollars circulating in the economy – there are just symbols for them floating around.

 

The bottom line is that human beings have brains capable of counting to high numbers and manipulating them, so we use mathematics as a useful tool to describe the world around us. But numbers and math themselves are no more real than the color blue – ‘blue’ is just what we tag a certain wavelength of light because of the way we perceive that wavelength. An alien intelligence that is blind has no use for the color blue. It might learn about light and the wavelengths of light and translate those concepts completely differently than we do.

 

In the same way, since the only truly good mathematicians among the animals are ourselves, we assume that if we encounter other systems of intelligence that they’ll have the same concepts of math was we do. But there’s no evidence to base that assumption on. For all we know, there are much easier ways to describe physics than through complicated systems of equations, but our minds may not be capable of symbolically interpreting the world in a way that allows us to use those tools, any more than we’re capable of a tool that requires the use of a prehensile tail.

 

Math is a useful descriptor of both real and fictional concepts. It’s very fun to play around with and its essential for understanding a lot of subjects. But it’s just a tool. Not a set of mystical entities.

 

Here are some good readings on the philosophy of math:

 

Introductory Readings

Books

 

Stewart Shapiro - Thinking About Mathematics. Shapiro's book is a masterpiece of introductory philosophy - it's easy to read and covers nearly all the ground you would hope, starting with a brief gloss of the history of philosophy of mathematics and moving forward into the major schools of foundations, with equal focus on both the historical views (e.g. Russell/Whitehead, Frege and Brouwer) and contemporary movements (e.g. Hale/Wright, Field, Shapiro).

Encyclopedia Articles

 

As always the SEP is of great help. In particular, the following articles are essential:

 

Philosophy of Mathematics

Frege's Logic, Theorem, and Foundations for Arithmetic

Platonism in the Philosophy of Mathematics

Intuitionism in the Philosophy of Mathematics

Formalism in the Philosophy of Mathematics

Fictionalism in the Philosophy of Mathematics

Kurt Gödel

Set Theory

Explanation in Mathematics

Constructive Mathematics

Further Readings

Anthologies

 

Philosophy of Mathematics: Selected Readings ed. Benacerraf and Putnam - this is the bible of philosophy of maths, containing almost two dozen of the most important papers ever written in the subject. It's a bit out of date at this point, but still a classic. Rather than listing all of the must-read papers in the philosophy of mathematics one should just read this book cover to cover.

 

The Oxford Handbook of Philosophy of Mathematics and Logic ed. Shapiro - This book has articles on every major movement in philosophy of maths and logic written in a fantastically accessible way. It is a massive resource to anyone with interest in the field.

 

Primary Texts (Books)

 

L.E.J. Brouwer - Cambridge Lectures on Intuitionism

Richard Dedekind - Essays on the Theory of Numbers

Gottlob Frege - Grundlagen der Arithmetik or The Foundations of Arithmetic

Gottlob Frege - Grundgesetze der Arithmetik or The Basic Laws of Arithmetic. OUP has the first full translation of the Grundgesetze forthcoming, translated by Ebert, Rossberg, Wright and Cook. Reading it alongside Richard Heck Jr.'s Reading Frege's Grundgesetze is highly recommended.

Hartry Field - Science Without Numbers: A Defense of Nominalism

Bob Hale and Crispin Wright - The Reason's Proper Study

Stewart Shapiro - Philosophy of Mathematics: Structure and Ontology

 

 

 

http://www.reddit.com/r/philosophy/wiki/readinglist

You are missing the point. How do you know these things? Math might not even exist.

 

The philosophy of mathematics is, at its core, the study of mathematics from a philosophical perspective rather than a strictly mathematical one. Often times philosophers of mathematics concern themselves with the foundations of mathematics - what mathematics is, what kind of objects, if any it refers to, how we come to have knowledge of these objects, and how we are to think of mathematical objects and theories. Because the philosophy of mathematics often deals in foundations, in some senses it is a deviating branch of metaphysics and epistemology. However philosophy of mathematics is not just foundations - it includes questions about the nature of mathematical explanation, computation, proof, set theory, infinity and more. For this reason we will treat the philosophy of mathematics as a separate subfield, within the larger category of the philosophy of sciences and mathematics.

Isn't that what I just said? Your argument isn't even making sense anymore. Philosophy in general doesn't make sense. Kind of like getting a degree in Philosophy, it's worthless and you'd be an idiot to attempt it.

Math makes the world work. Everything you own was designed using some form of math.

Even before calculus was discovered, brewing barrels for whisky were made by trial and error to find the optimum shape.

(look it up if you don't believe me)

Fast forward 1000 years, and we can use calculus to derive the shape they found by trial and error in one semi simple equation using polar coordinates.

Sure math might not be real, but it sure as hell is real for every person who uses it in their daily life. (ALL OF US)

I swear, anytime philosophy is brought up in an argument, it's just to fuck with people. It has no real value in this world. "You cant prove I exist!" "Neither can you!" LETS THROW STONES ARE EACHOTHER TILL WE DIE LOLOLOL

Oh- and if math doesn't exist, then I don't exist. Because clearly you're dreaming and it's time to wake up and face reality.

Edited September 27, 201312 yr by dreamliner

 

You are missing the point. How do you know these things? Math might not even exist.

 

The philosophy of mathematics is, at its core, the study of mathematics from a philosophical perspective rather than a strictly mathematical one. Often times philosophers of mathematics concern themselves with the foundations of mathematics - what mathematics is, what kind of objects, if any it refers to, how we come to have knowledge of these objects, and how we are to think of mathematical objects and theories. Because the philosophy of mathematics often deals in foundations, in some senses it is a deviating branch of metaphysics and epistemology. However philosophy of mathematics is not just foundations - it includes questions about the nature of mathematical explanation, computation, proof, set theory, infinity and more. For this reason we will treat the philosophy of mathematics as a separate subfield, within the larger category of the philosophy of sciences and mathematics.

Isn't that what I just said? Your argument isn't even making sense anymore. Philosophy in general doesn't make sense. Kind of like getting a degree in Philosophy, it's worthless and you'd be an idiot to attempt it.

Math makes the world work. Everything you own was designed using some form of math.

Even before calculus was discovered, brewing barrels for whisky were made by trial and error to find the optimum shape.

(look it up if you don't believe me)

Fast forward 1000 years, and we can use calculus to derive the shape they found by trial and error in one semi simple equation using polar coordinates.

Sure math might not be real, but it sure as hell is real for every person who uses it in their daily life. (ALL OF US)

I swear, anytime philosophy is brought up in an argument, it's just to fuck with people. It has no real value in this world. "You cant prove I exist!" "Neither can you!" LETS THROW STONES ARE EACHOTHER TILL WE DIE LOLOLOL

Oh- and if math doesn't exist, then I don't exist. Because clearly you're dreaming and it's time to wake up and face reality.

 

 

You come off as both ignorant and arrogant here. Philosophy has a lot of merit, and just because you are not a person who can not understand what philosophy is, does not mean you have to bash other people.

 

"I swear, anytime philosophy is brought up in an argument, it's just to fuck with people. It has no real value in this world."

 

It is not to "fuck with people" and it does have value because it is the most real thing that we have.

Girls = Time * Money (girls are time and money)

 

Time = Money (time is money)

 

Therfore, Girls = Money * Money

 

Money = Sqrt(evil) (money is the root of all evil)

 

Therefore, Girls = sqrt(evil) * sqrt(evil)

 

So I conclude that Girls = Evil.

 

Stick that in your juice box and SUCK IT.

Some dickhead literally made all this shit up one day so kids in school would commit suicide. 

Research mathematical realism. 

 

"Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same."

 

 

Therefore, neither our mind nor senses can deceive our interpretation of mathematics. It is simply something that we discover to be factual and existent.

 

eg. 1+1=2

 

^.^

Edited September 27, 201312 yr by Mysteryy

Research mathematical realism. 

 

"Mathematical realism, like [/size]

realism in general, holds that mathematical entities exist independently of the human [/size]mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same."[/size]

 

 

Therefore, neither our mind nor senses can deceive our interpretation of mathematics. It is simply something that we discover to be factual and existent.

 

eg. 1+1=2

 

^.^

Which is why philosophy doesn't dictate what mathematics is.

You are missing the point. How do you know these things? Math might not even exist.

 

The philosophy of mathematics is, at its core, the study of mathematics from a philosophical perspective rather than a strictly mathematical one. Often times philosophers of mathematics concern themselves with the foundations of mathematics - what mathematics is, what kind of objects, if any it refers to, how we come to have knowledge of these objects, and how we are to think of mathematical objects and theories. Because the philosophy of mathematics often deals in foundations, in some senses it is a deviating branch of metaphysics and epistemology. However philosophy of mathematics is not just foundations - it includes questions about the nature of mathematical explanation, computation, proof, set theory, infinity and more. For this reason we will treat the philosophy of mathematics as a separate subfield, within the larger category of the philosophy of sciences and mathematics.

Isn't that what I just said? Your argument isn't even making sense anymore. Philosophy in general doesn't make sense. Kind of like getting a degree in Philosophy, it's worthless and you'd be an idiot to attempt it.

Math makes the world work. Everything you own was designed using some form of math.

Even before calculus was discovered, brewing barrels for whisky were made by trial and error to find the optimum shape.

(look it up if you don't believe me)

Fast forward 1000 years, and we can use calculus to derive the shape they found by trial and error in one semi simple equation using polar coordinates.

Sure math might not be real, but it sure as hell is real for every person who uses it in their daily life. (ALL OF US)

I swear, anytime philosophy is brought up in an argument, it's just to fuck with people. It has no real value in this world. "You cant prove I exist!" "Neither can you!" LETS THROW STONES ARE EACHOTHER TILL WE DIE LOLOLOL

Oh- and if math doesn't exist, then I don't exist. Because clearly you're dreaming and it's time to wake up and face reality.

 

You come off as both ignorant and arrogant here. Philosophy has a lot of merit, and just because you are not a person who can not understand what philosophy is, does not mean you have to bash other people.

 

"I swear, anytime philosophy is brought up in an argument, it's just to fuck with people. It has no real value in this world."

 

It is not to "fuck with people" and it does have value because it is the most real thing that we have.

How can philosophy make me money? If someone is paying you to make logical decisions on their behalf, they're borderline retarded.

It math was some made up joke, then we wouldn't have computers right now.

Read up on discrete mathematics.

Understand how your processor works.

I will say it again- The only thing that math does is quantify objects. Nothing more, nothing less. Leave the philosophical bullshit out of it and come back with a real argument.

Please tell me how philosophy is real and math isn't. I really am curious.

Edited September 28, 201312 yr by dreamliner

2? ..

 

If someone is paying you to make logical decisions on their behalf, they're borderline retarded.

 

What do you think every Prime Minister/President does? Pays people to make decisions for them.

Well that escalated quickly...I don't have the time to read all your wikipedia copy/pasted posts, but I simply stated you cannot disprove 1+1=2 using mathematical tools because all your mathematical tools are based off the definition of 1+1=2 (not that one in specifically, but in general, the axioms of arithmetic). 

 

All your philosophical shit about "what is real" doesn't mean anything, you can't say "Math doesn't exist" unless you are questioning the existence of everything, which isn't really going to lead you anywhere. Math is just a human construct to represent the world. It is based upon the fundamentals of logic (i.e, true, false, implications, etc). And logic is just how the universe works. If all ohhungrys are awesomes, and all awesomes are fuckingreat, then all ohhungrys are fuckingreat. It's just a basic definition which can't be disproven, because there is no lower, simpler level.

 

That being said, math and philosophy are both just extensions of logic, so you really shouldn't hate too much on either one. 

 

And to that guy that said "How do you even know math is real", I kinda skimmed over your post and it looks like it's just questioning if math is some innate part of the universe or just something we made up to quantify shit. I'd put my money on math being a man-made quantifier. 

 

 

Me and math = 0