15 ideas
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 9212 | Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K] |
| Full Idea: Possible states of affairs have often been taken to be propositions, but this cannot be correct, since any possible state of affairs is possibly a state of affairs, but no proposition is possibly a state of affairs. | |
| From: Kit Fine (The Problem of Possibilia [2003], 2) | |
| A reaction: The point is, presumably, that the state of affairs cannot be the proposition itself, but (at least) what the proposition refers to. I can't see any objection to that. |
| 9213 | The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K] |
| Full Idea: A possible world can't be defined (by Stalnaker and Plantinga) as a way the world might have been, because a possible world is possibly the world, yet no way the world might have been is possibly the world. | |
| From: Kit Fine (The Problem of Possibilia [2003], 2) | |
| A reaction: His point is that any definition of a possible world must cover the actual world, because that is one of them. 'Might have been' is not applicable to the actual world. It seems a fairly important starting point for discussion of possible worlds. |
| 5901 | Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham] |
| Full Idea: Bentham has not made up his mind whether he thinks that 'right' means 'productive of the general happiness', or that being productive of the general happiness is what makes acts right (and he would have thought the difference unimportant). | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by W. David Ross - The Right and the Good §I | |
| A reaction: The issue is whether rightness exists as a concept separate from happiness. I take it Bentham would vote for the first reading, as he has no interest in what is right, apart from increasing happiness. |
| 5934 | Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham] |
| Full Idea: Most of Bentham's 'dimensions' of pleasure refer to further pleasures, or are irrelevant to the pleasure; we are left with intensity and duration as the characteristics on which depend the value of a pleasure qua pleasure, and there is nothing to add. | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by W. David Ross - The Right and the Good §VI | |
| A reaction: I agree. When Bentham produces his list he seems to be trying to add a bogus enrichment to what is really a rather crude and basic notion of the aim of life. Your simple hedonist appears to only desire high intensity and long duration. |
| 3777 | Pleasure and pain control all human desires and duties [Bentham] |
| Full Idea: Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], I.1) | |
| A reaction: Ridiculous. Both halves are false. We pursue things for other reasons, and to deny this makes his idea a tautology. Deep ecology has nothing to do with human pleasure or pain. |
| 3554 | Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham] |
| Full Idea: It is easy to fall into Bentham's mindless assumption that happiness must be a specific state of feeling good about something, but it is mysterious why anyone would think morality a good strategy for achieving this. | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by Julia Annas - The Morality of Happiness 2.7 |
| 3781 | The value of pleasures and pains is their force [Bentham] |
| Full Idea: It behoves the legislator to understand the force of pleasures and pains, which is their value. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], IV.1) |
| 3778 | The community's interest is a sum of individual interests [Bentham] |
| Full Idea: The interest of the community is the sum of the interests of the several members who compose it. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], I.4) |
| 20280 | Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham] |
| Full Idea: A full-grown horse or dog is beyond comparison a more rational animal than an infant of a day, or even a month, old. But suppose they be otherwise, what would it avail? The question is not, Can they reason? nor Can they talk? but, Can they suffer? | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], XVIII 1 n), quoted by Peter Singer - Practical Ethics 03 | |
| A reaction: This is certainly an inspiring, and even shocking question, which never seems to have been so directly asked before in the entire history of European thought. Awesome. |
| 3779 | Unnatural, when it means anything, means infrequent [Bentham] |
| Full Idea: Unnatural, when it means anything, means unfrequent. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], II.14 n8.9) |
| 3780 | We must judge a thing morally to know if it conforms to God's will [Bentham] |
| Full Idea: It is necessary to know first whether a thing is right in order to know from thence whether it be conformable to the will of God. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], II.18) |