14 ideas
| 22752 | Reasoning is impossible without a preconception [Sext.Empiricus] |
| Full Idea: It is not possible either to seek or to doubt without a preconception. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.22) | |
| A reaction: [Sextus quotes this from 'the sapient Epicurus'] I think this may be a message across the centuries to Hegel, who attempted this impossible feat. My picture of philosophy is a continual shift of the preconceptions, to explore thoroughly. |
| 11970 | Logicians like their entities to exhibit a maximum degree of purity [Kaplan] |
| Full Idea: Logicians like their entities to exhibit a maximum degree of purity. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.97) | |
| A reaction: An important observation, which explains why the modern obsession with logic has often led us down the metaphysical primrose path to ontological hell. |
| 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. |
| 11969 | Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan] |
| Full Idea: The use of models is so natural to logicians ...that they sometimes take seriously what are only artefacts of the model, and adopt a bare particular metaphysics. Why? Because the model so nicely separates the bare particular from its clothing. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.97) | |
| A reaction: See also Idea 11970. I think this observation is correct, and incredibly important. We need to keep quite separate the notion of identity in conceptual space from our notion of identity in the actual world. The first is bare, the second fat. |
| 11971 | The simplest solution to transworld identification is to adopt bare particulars [Kaplan] |
| Full Idea: If we adopt the bare particular metaphysical view, we have a simple solution to the transworld identification problem: we identify by bare particulars. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.98) | |
| A reaction: See Ideas 11969 and 11970 on this idea. The problem with bare particulars is that they can change their properties utterly, so that Aristotle in the actual world can be a poached egg in some possible world. We need essences. |
| 11973 | Unusual people may have no counterparts, or several [Kaplan] |
| Full Idea: An extremely vivid person might have no counterparts, and Da Vinci seems to me to have more than one essence. Bertrand Russell is clearly the counterpart of at least three distinct persons in some more plausible world. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.100) | |
| A reaction: Lewis prefers the notion that there is at most one counterpart, the 'closest' entity is some world. I think he also claims there is at least one counterpart. I like Kaplan's relaxed attitude to these things, which has more explanatory power. |
| 11972 | Essence is a transworld heir line, rather than a collection of properties [Kaplan] |
| Full Idea: I prefer to think of essence as a transworld heir line, rather than as the more familiar collection of properties, because the latter too much suggests the idea of a fixed and final essential description. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.100) | |
| A reaction: He is sympathetic to the counterpart idea, and close to Lewis's view of essences, as the intersection of counterparts. I like his rebellion against fixed and final descriptions, but am a bit doubtful about his basic idea. Causation should be involved. |
| 11967 | Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan] |
| Full Idea: Among the proposals for conditions under which two sentences have the same ordinary sense, the most liberal (Carnap and Church) is that they be logically equivalent, and the most restrictive (Benson Mates) is that they never have the same sense. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.89) | |
| A reaction: Personally I would move the discussion to the level of the propositions being expressed before I attempted a solution. |
| 22754 | Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus] |
| Full Idea: Asserting that the good is 'the useful', or 'what is choiceworthy for its own sake', or 'that which contributes to happiness', does not teach us what good is but states its accidental property. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.35) | |
| A reaction: This seems to be a pretty accurate statement of Moore's famous Open Question argument. I read it in an Aristotelian way - that that quest is always for the essential nature of the thing itself, not for its role or function or use. |
| 22755 | Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus] |
| Full Idea: Just as fire which is warmth-giving by nature warms all men, and does not chill some of them, so what is good by nature ought to be good for all, and not good for some but not good for others. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.69) | |
| A reaction: This is going to confine the naturally good to the basics of life, which we all share. Is a love of chess a natural good? It seems to capture an aspect of human nature, without appealing to everyone. Sextus says nothing is good for everyone. |
| 22756 | If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus] |
| Full Idea: If the desire for wealth or health is desirable, we ought not to purse wealth or health, lest by acquiring them we cease to desire them any longer. | |
| From: Sextus Empiricus (Against the Ethicists (one book) [c.180], II.81) | |
| A reaction: He is investigating whether desires can be desirable, and if so which ones. Roots of this are in Plato's 'Gorgias' on drinking water. Similar to 'if compassion is the highest good then we need lots of suffering'. Desire must be a means, not an end. |