Set theory | Mathematical principles | Philosophy of mathematics

Hume's principle

Hume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in systems of second-order logic. Hume's principle is named for the Scottish philosopher David Hume and was coined by George Boolos. HP plays a central role in Gottlob Frege's philosophy of mathematics. Frege shows that HP and suitable definitions of arithmetical notions entail all axioms of what we now call second-order arithmetic. This result is known as Frege's theorem, which is the foundation for a philosophy of mathematics known as neo-logicism. (Wikipedia).

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PHILOSOPHY - David Hume

David Hume is one of Scotland’s greatest philosophers (Adam Smith is another, about whom we also have a film https://www.youtube.com/watch?v=ejJRhn53X2M). His claim to greatness lies in his appreciation of ordinary experience, his descriptions of consciousness and his humane, tolerant appr

From playlist WESTERN PHILOSOPHY

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2 Reid & Common Sense Realism - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the second in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. Is it the case that every simple idea is a “copy” of a simple impression? Hume is but the latest to deny that we have direct access to the external world. The “ideal

From playlist Reid's Critique of Hume (Dan Robinson)

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Reasons and Understanding in Hume's Enquiry

In this lecture, Professor Helen Beebee (University of Manchester) explores Hume's explanation of how we come to know what (we think) we know, focusing in particular on Hume's distinction between 'relations of ideas' and 'matters of fact and experience'. As an empiricist, Hume can explain

From playlist Philosophy

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1 The "Representational" Theory of Knowledge - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the first in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. Hume defends the thesis according to which “ALL THE PERCEPTIONS OF THE HUMAN MIND RESOLVE THEMSELVES INTO…IMPRESSIONS AND IDEAS”. Accordingly, “We may prosecute this

From playlist Philosophy of Mind

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8 Reid on the Principle of Morals - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the final lecture in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. “Like all other sciences, morals must have first principles, and all moral reasoning is based on them... In all rational belief, the thing believed is either

From playlist Reid's Critique of Hume (Dan Robinson)

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4 Reid on Causation & Active Powers - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the fourth in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. “It is evident that a power is a quality, and therefore can’t exist without a subject to which it belongs…This (Humean) suggestion— There exists some power that cann

From playlist Reid's Critique of Hume (Dan Robinson)

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7 Hume’s “Sentimentalist” Theory of Morals - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the seventh in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. In his Enquiry Concerning the Principles of Morals [1751], Hume states: “The final sentence, it is probable, which pronounces characters and actions amiable or odio

From playlist Reid's Critique of Hume (Dan Robinson)

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5 David Hume on Personal Identity - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the fifth in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. “There are some philosophers who imagine we are every moment intimately conscious of what we call our self; that we feel its existence and its continuance in existenc

From playlist Reid's Critique of Hume (Dan Robinson)

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Oxford 4b The Argument Concerning Induction

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

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Oxford 5c Of the Ancient and Modern Philosophies

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

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Oxford 3b Space and Time

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

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Oxford 3a Hume's Theory of General or Abstract Ideas

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

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Oxford 1b The Theory of Ideas

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

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6 Reid on Personal Identity - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the sixth in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. In the third of his Essays on The Intellectual Powers of Man, Reid devotes the fourth chapter to the concept of 'identity', and the sixth chapter to Locke's theory of

From playlist Reid's Critique of Hume (Dan Robinson)

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Oxford 2 Hume's Theory of Relations

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

Related pages

Number | Proportionality (mathematics) | Quantity | Logical consequence | Euclid's Elements | Cardinal number | Transfinite number | Second-order logic | Geometry | Gottlob Frege | Frege's theorem | Logicism | Arithmetic | Second-order arithmetic | Ordinal number | Euclid | David Hume | George Boolos