11 ideas
| 4748 | Anselm of Canterbury identified truth with God [Anselm, by Engel] |
| Full Idea: Anselm of Canterbury identified truth with God. | |
| From: report of Anselm (De Veritate (On Truth) [1095]) by Pascal Engel - Truth §1.6 | |
| A reaction: An interesting claim, perhaps, depending on what it means. God decrees truth, God knows all truth, God makes truth possible, God connects us to the world, God is the world…? |
| 12766 | Logical space is abstracted from the actual world [Stalnaker] |
| Full Idea: Logical space is not given independently of the individuals that occupy it, but is abstracted from the world as we find it. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.85) | |
| A reaction: I very much like the second half of this idea, and am delighted to find Stalnaker endorsing it. I take the logical connectives to be descriptions of how things behave, at a high level of generality. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 12764 | For the bare particular view, properties must be features, not just groups of objects [Stalnaker] |
| Full Idea: If we are to make sense of the bare particular theory, a property must be not just a rule for grouping individuals, but a feature of individuals in virtue of which they may be grouped. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.76) | |
| A reaction: He is offering an objection to the thoroughly extensional account of properties that is found in standard possible worlds semantics. Quite right too. We can't give up on the common sense notion of a property. |
| 12761 | An essential property is one had in all the possible worlds where a thing exists [Stalnaker] |
| Full Idea: If necessity is explained in terms of possible worlds, ...then an essential property is a property that a thing has in all possible worlds in which it exists. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.71) | |
| A reaction: This seems to me to be a quite shocking confusion of necessary properties with essential properties. The point is that utterly trivial properties can be necessary, but in no way part of the real essence of something. |
| 12763 | Necessarily self-identical, or being what it is, or its world-indexed properties, aren't essential [Stalnaker] |
| Full Idea: We can remain anti-essentialist while allowing some necessary properties: those essential to everything (self-identity), relational properties (being what it is), and world-indexed properties (being snub-nosed-only-in-Kronos). | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.73) | |
| A reaction: [a summary] He defined essential properties as necessary properties (Idea 12761), and now backpeddles. World-indexed properties are an invention of Plantinga, as essential properties to don't limit individuals. But they are necessary, not essential! |
| 12762 | Bare particular anti-essentialism makes no sense within modal logic semantics [Stalnaker] |
| Full Idea: I argue that one cannot make semantical sense out of bare particular anti-essentialism within the framework of standard semantics for modal logic. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.71) | |
| A reaction: Stalnaker characterises the bare particular view as ANTI-essentialist, because he has defined essence in terms of necessary properties. The bare particular seems to allow the possibility of Aristotle being a poached egg. |
| 12765 | Why imagine that Babe Ruth might be a billiard ball; nothing useful could be said about the ball [Stalnaker] |
| Full Idea: I cannot think of any point in making the counterfactual supposition that Babe Ruth is a billiard ball; there is nothing I can say about him in that imagined state that I could not just as well say about billiard balls that are not him. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.79) | |
| A reaction: A bizarrely circumspect semanticists way of saying that Ruth couldn't possibly be a billiard ball! Would he say the same about a group of old men in wheelchairs, one of whom IS Babe Ruth? |