#philosophyofmathematics — Public Fediverse posts

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics ( #mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics ( #mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

https://youtu.be/jtPgdy80YZ8

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

https://youtu.be/jtPgdy80YZ8

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

https://youtu.be/jtPgdy80YZ8

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

https://youtu.be/jtPgdy80YZ8

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

https://youtu.be/jtPgdy80YZ8

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Danuta Gierulanka (1909–1995) was a Polish mathematics educator, psychologist, philosopher, and translator. She was associated with #RomanIngarden and known for her work in #phenomenology and the #philosophyOfMathematics.

What does it mean (to you) to understand a piece of mathematics?

#math #PhilosophyOfMathematics #understanding

What does it mean (to you) to understand a piece of mathematics?

#math #PhilosophyOfMathematics #understanding

What does it mean (to you) to understand a piece of mathematics?

#math #PhilosophyOfMathematics #understanding

What does it mean (to you) to understand a piece of mathematics?

#math #PhilosophyOfMathematics #understanding

What does it mean (to you) to understand a piece of mathematics?

#math #PhilosophyOfMathematics #understanding

This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.

https://youtu.be/bHKvT1ZACLY

The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?

It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!

It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.

It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.

I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.

#PhilosophyOfMathematics #MathematicalFoundations

This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.

https://youtu.be/bHKvT1ZACLY

The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?

It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!

It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.

It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.

I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.

#PhilosophyOfMathematics #MathematicalFoundations

This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.

https://youtu.be/bHKvT1ZACLY

The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?

It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!

It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.

It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.

I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.

#PhilosophyOfMathematics #MathematicalFoundations

This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.

https://youtu.be/bHKvT1ZACLY

The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?

It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!

It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.

It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.

I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.

#PhilosophyOfMathematics #MathematicalFoundations

This Topos Institute seminar (Kevin Carlson presenting) is an interesting topic -- do we actually need infinite sets to do mathematics? But, I think he takes a long and questionable route to the meat of the topic.

https://youtu.be/bHKvT1ZACLY

The fallacy here is that the answer to "why is there so much consensus in modern mathematics" cannot be a mathematical answer! It has to be grounded in something else: sociology, history, or psychology. It's all very well to point at the structural approach as a unifying point of agreement, but that by itself does not answer "why"?

It could be: humans have some set-sense like they have a language-sense, and so building things on sense connects to a lot of people. That might be JP Mayberry's point, in his appeal to "Euclidean set theory." But that's not a mathematical claim!

It could be: people who do not get on board with the structuralist approach don't succeed at being modern mathematicians.

It could be: we are living in an era that encourages that consensus instead of discouraging it, for reasons that will be evident only in retrospect.

I think part of the answer is that modern mathematics has achieved consensus by successfully eliminating "truth" as a topic of debate and instead making it a topic of study, in a very postmodernist way. You can insist to your dying day that you're a intuitionist or an ultrafinitist or whatever, and the only response you can get is mathematicians studying what is or isn't provable in your version of logic! It is no longer possible to disagree what mathematics is, because the modern conception swallows any such disagreement into a mathematical object.

#PhilosophyOfMathematics #MathematicalFoundations

Philosophy of maths questions:

Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".

Are proofs the only explanations that pure maths has to offer?

Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?

Is it even sensible to ask these questions in the context of pure maths?

Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?

#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics

Philosophy of maths questions:

Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".

Are proofs the only explanations that pure maths has to offer?

Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?

Is it even sensible to ask these questions in the context of pure maths?

Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?

#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics

Philosophy of maths questions:

Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".

Are proofs the only explanations that pure maths has to offer?

Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?

Is it even sensible to ask these questions in the context of pure maths?

Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?

#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics

Philosophy of maths questions:

Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".

Are proofs the only explanations that pure maths has to offer?

Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?

Is it even sensible to ask these questions in the context of pure maths?

Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?

#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics

Philosophy of maths questions:

Say I want to ask for an explanation of some mathematical phenomenon (that is, to ask "Why is it true that <X>?"). You might offer a formal proof of <X>, but that doesn't feel like an explanation to me because a proof is essentially a statement that <X> is logically implied by the assumptions. So the proof, as an explanation, is equivalent to "because I chose these assumptions".

Are proofs the only explanations that pure maths has to offer?

Are there other forms of mathematical explanation (e.g. involving reference to assumptions outside the minimal axioms required for a formal proof)?

Is it even sensible to ask these questions in the context of pure maths?

Is it different when we shift to applied maths and have to recognise that the maths is a model of the system of interest (so there's a possibly fallible mapping between the maths and the system of interest and the mathematical axioms presumably correspond to assumed truths in the system of interest)?

#math #maths #mathematics #philosophy #explanation #PhilosophyOfMathematics

Next week, I’m heading off to North America for a few talks. (I’d committed to these talks before last year’s election and I have mixed feelings about the trip, but I’m going, nonetheless.)

If you're in the LA area, in or around Calgary, or New York, and you’re into philosophical logic, why not drop by? Details of the talks are here https://consequently.org/presentation/

#philosophy #logic #philosophyOfMathematics #metaphysics

Next week, I’m heading off to North America for a few talks. (I’d committed to these talks before last year’s election and I have mixed feelings about the trip, but I’m going, nonetheless.)

If you're in the LA area, in or around Calgary, or New York, and you’re into philosophical logic, why not drop by? Details of the talks are here https://consequently.org/presentation/

#philosophy #logic #philosophyOfMathematics #metaphysics

Next week, I’m heading off to North America for a few talks. (I’d committed to these talks before last year’s election and I have mixed feelings about the trip, but I’m going, nonetheless.)

If you're in the LA area, in or around Calgary, or New York, and you’re into philosophical logic, why not drop by? Details of the talks are here https://consequently.org/presentation/

#philosophy #logic #philosophyOfMathematics #metaphysics

Next week, I’m heading off to North America for a few talks. (I’d committed to these talks before last year’s election and I have mixed feelings about the trip, but I’m going, nonetheless.)

If you're in the LA area, in or around Calgary, or New York, and you’re into philosophical logic, why not drop by? Details of the talks are here https://consequently.org/presentation/

#philosophy #logic #philosophyOfMathematics #metaphysics

#HelenDeCruz - #Mathematics in #Evolution

https://www.youtube.com/watch?v=NMufdC0ku4k

#Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfEvolution #Numbers #Realism #AntiRealism #Platonism #StructuralRealism #LawsOfNature #LawsOfPhysics #Abstractedness #CloserToTruth #RobertKuhn

#HelenDeCruz - #Mathematics in #Evolution

https://www.youtube.com/watch?v=NMufdC0ku4k

#Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfEvolution #Numbers #Realism #AntiRealism #Platonism #StructuralRealism #LawsOfNature #LawsOfPhysics #Abstractedness #CloserToTruth #RobertKuhn

#HelenDeCruz - #Mathematics in #Evolution

https://www.youtube.com/watch?v=NMufdC0ku4k

#Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfEvolution #Numbers #Realism #AntiRealism #Platonism #StructuralRealism #LawsOfNature #LawsOfPhysics #Abstractedness #CloserToTruth #RobertKuhn

#HelenDeCruz - #Mathematics in #Evolution

https://www.youtube.com/watch?v=NMufdC0ku4k

#Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfEvolution #Numbers #Realism #AntiRealism #Platonism #StructuralRealism #LawsOfNature #LawsOfPhysics #Abstractedness #CloserToTruth #RobertKuhn

#HelenDeCruz - #Mathematics in #Evolution

https://www.youtube.com/watch?v=NMufdC0ku4k

#Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfEvolution #Numbers #Realism #AntiRealism #Platonism #StructuralRealism #LawsOfNature #LawsOfPhysics #Abstractedness #CloserToTruth #RobertKuhn

#RobertLawrenceKuhn - on the #Origin and #Significance of #Zero

https://www.youtube.com/watch?v=jPbf6-2s6Sk

#JohnLeslie #Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfScience #Science #Nothing #Nothingness #Existence #Physics #LawsOfPhysics #LawsOfNature #Consciousness #PhilosophyOfConsciousness #Emergence #Cosmology #PhilosophyOfCosmology #Existence #Universe #Infinity #Mind #God #CloserToTruth #RobertKuhn

#RobertLawrenceKuhn - on the #Origin and #Significance of #Zero

https://www.youtube.com/watch?v=jPbf6-2s6Sk

#JohnLeslie #Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfScience #Science #Nothing #Nothingness #Existence #Physics #LawsOfPhysics #LawsOfNature #Consciousness #PhilosophyOfConsciousness #Emergence #Cosmology #PhilosophyOfCosmology #Existence #Universe #Infinity #Mind #God #CloserToTruth #RobertKuhn

#RobertLawrenceKuhn - on the #Origin and #Significance of #Zero

https://www.youtube.com/watch?v=jPbf6-2s6Sk

#JohnLeslie #Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfScience #Science #Nothing #Nothingness #Existence #Physics #LawsOfPhysics #LawsOfNature #Consciousness #PhilosophyOfConsciousness #Emergence #Cosmology #PhilosophyOfCosmology #Existence #Universe #Infinity #Mind #God #CloserToTruth #RobertKuhn

#RobertLawrenceKuhn - on the #Origin and #Significance of #Zero

https://www.youtube.com/watch?v=jPbf6-2s6Sk

#JohnLeslie #Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfScience #Science #Nothing #Nothingness #Existence #Physics #LawsOfPhysics #LawsOfNature #Consciousness #PhilosophyOfConsciousness #Emergence #Cosmology #PhilosophyOfCosmology #Existence #Universe #Infinity #Mind #God #CloserToTruth #RobertKuhn

#RobertLawrenceKuhn - on the #Origin and #Significance of #Zero

https://www.youtube.com/watch?v=jPbf6-2s6Sk

#JohnLeslie #Philosophy #PhilosophyOfMathematics #Math #Maths #PhilosophyOfScience #Science #Nothing #Nothingness #Existence #Physics #LawsOfPhysics #LawsOfNature #Consciousness #PhilosophyOfConsciousness #Emergence #Cosmology #PhilosophyOfCosmology #Existence #Universe #Infinity #Mind #God #CloserToTruth #RobertKuhn

Rovaniemellä syntynyt suomalainen matemaatikko Jouko Väänänen on päivittänyt SEP-entryään toisen asteen logiikasta, https://plato.stanford.edu/entries/logic-higher-order/

Jos ketä mietityttää, kuinka toisen asteen logiikka oikeastaan vertautuu vahvuuden puolesta ensimmäiseen asteeseen ja joukko-oppiin matematiikan perustana, eikä formaalikieli muutenkaan tyrki, niin tuossa olisi tarjolla jännittävää tarinaa ja juonen käänteitä (lapin) toviksi.

#matematiikka #mathematics #logiikka #logic #sep #philosophyOfMathematics #rovaniemi #lappi

Rovaniemellä syntynyt suomalainen matemaatikko Jouko Väänänen on päivittänyt SEP-entryään toisen asteen logiikasta, https://plato.stanford.edu/entries/logic-higher-order/

Jos ketä mietityttää, kuinka toisen asteen logiikka oikeastaan vertautuu vahvuuden puolesta ensimmäiseen asteeseen ja joukko-oppiin matematiikan perustana, eikä formaalikieli muutenkaan tyrki, niin tuossa olisi tarjolla jännittävää tarinaa ja juonen käänteitä (lapin) toviksi.

#matematiikka #mathematics #logiikka #logic #sep #philosophyOfMathematics #rovaniemi #lappi

Rovaniemellä syntynyt suomalainen matemaatikko Jouko Väänänen on päivittänyt SEP-entryään toisen asteen logiikasta, https://plato.stanford.edu/entries/logic-higher-order/

Jos ketä mietityttää, kuinka toisen asteen logiikka oikeastaan vertautuu vahvuuden puolesta ensimmäiseen asteeseen ja joukko-oppiin matematiikan perustana, eikä formaalikieli muutenkaan tyrki, niin tuossa olisi tarjolla jännittävää tarinaa ja juonen käänteitä (lapin) toviksi.

#matematiikka #mathematics #logiikka #logic #sep #philosophyOfMathematics #rovaniemi #lappi

Rovaniemellä syntynyt suomalainen matemaatikko Jouko Väänänen on päivittänyt SEP-entryään toisen asteen logiikasta, https://plato.stanford.edu/entries/logic-higher-order/

Jos ketä mietityttää, kuinka toisen asteen logiikka oikeastaan vertautuu vahvuuden puolesta ensimmäiseen asteeseen ja joukko-oppiin matematiikan perustana, eikä formaalikieli muutenkaan tyrki, niin tuossa olisi tarjolla jännittävää tarinaa ja juonen käänteitä (lapin) toviksi.

#matematiikka #mathematics #logiikka #logic #sep #philosophyOfMathematics #rovaniemi #lappi

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#Philosophy #PhilosophyOfMathematics #Math #Maths #Logic #Metaphysics #Science #PhilosophyOfScience #Abstraction #Geometry #Arithmetic #Theorem #Theorems #Axiom #Axioms #Axiomatic #AxiomSystem #AxiomSystems #Computation #Irreducibility #CloserToTruth #RobertKuhn

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#Philosophy #PhilosophyOfMathematics #Math #Maths #Logic #Metaphysics #Science #PhilosophyOfScience #Abstraction #Geometry #Arithmetic #Theorem #Theorems #Axiom #Axioms #Axiomatic #AxiomSystem #AxiomSystems #Computation #Irreducibility #CloserToTruth #RobertKuhn

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#Philosophy #PhilosophyOfMathematics #Math #Maths #Logic #Metaphysics #Science #PhilosophyOfScience #Abstraction #Geometry #Arithmetic #Theorem #Theorems #Axiom #Axioms #Axiomatic #AxiomSystem #AxiomSystems #Computation #Irreducibility #CloserToTruth #RobertKuhn

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#Philosophy #PhilosophyOfMathematics #Math #Maths #Logic #Metaphysics #Science #PhilosophyOfScience #Abstraction #Geometry #Arithmetic #Theorem #Theorems #Axiom #Axioms #Axiomatic #AxiomSystem #AxiomSystems #Computation #Irreducibility #CloserToTruth #RobertKuhn

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#Philosophy #PhilosophyOfMathematics #Math #Maths #Logic #Metaphysics #Science #PhilosophyOfScience #Abstraction #Geometry #Arithmetic #Theorem #Theorems #Axiom #Axioms #Axiomatic #AxiomSystem #AxiomSystems #Computation #Irreducibility #CloserToTruth #RobertKuhn

#MarkBalaguer - Is #Mathematics #Eternal?

https://www.youtube.com/watch?v=62BgnprT3f4

#Philosophy #PhilosophyOfMathematics #Maths #Math #Logic #Numbers #Primes #PrimeNumbers #Counting #Idealism #Realism #AntiRealism #Platonism #AbstractObjects #Transfinites #TransfiniteNumbers #Infinity #Physics #Science #CloserToTruth #RobertKuhn