12 ideas
| 8463 | Maths can be reduced to logic and set theory [Quine] |
| Full Idea: Researches in the foundations of mathematics have made it clear that all of (interpreted) mathematics can be got down to logic and set theory, and the objects needed for mathematics can be got down to the category of classes (and classes of classes..). | |
| From: Willard Quine (The Scope and Language of Science [1954], §VI) | |
| A reaction: This I take to be a retreat from pure logicism, presumably influenced by Gödel. So can set theory be reduced to logic? Crispin Wright is the one the study. |
| 8461 | The category of objects incorporates the old distinction of substances and their modes [Quine] |
| Full Idea: The category of objects embraces indiscriminately what would anciently have been distinguished as substances and as modes or states of substances. | |
| From: Willard Quine (The Scope and Language of Science [1954], §6) | |
| A reaction: This nicely captures Quine's elimination of properties, by presenting them as inseparable from their objects/substances. Armstrong calls this 'Ostrich Nominalism' (for refusing to address the universals problem) but Quineans are unshaken. |
| 11976 | Aristotelian essentialism says essences are not relative to specification [Lewis] |
| Full Idea: So-called 'Aristotelian essentialism' is the doctrine of essences not relative to specifications. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
| A reaction: In other words, they are so-called 'real essences', understood as de re. Quine says essences are all de dicto, and relative to some specification. I vote for Aristotle. |
| 11978 | Causal necessities hold in all worlds compatible with the laws of nature [Lewis] |
| Full Idea: Just as a sentence is necessary if it holds in all worlds, so it is causally necessary if it holds in all worlds compatible with the laws of nature. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], V) | |
| A reaction: I don't believe in the so-called 'laws of nature', so I'm not buying that. Is there no distinction in Lewis's view between those sentences which must hold, and those which happen to hold universally? |
| 11979 | It doesn't take the whole of a possible Humphrey to win the election [Lewis] |
| Full Idea: Even if Humphrey is a modal continuant, it doesn't take the whole of him to do such things as winning. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], Post B) | |
| A reaction: This responds to Kripke's famous example, that people only care about what happens to themselves, and not to some 'counterpart' of themselves. |
| 16994 | Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis] |
| Full Idea: Probably Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus Lewis's view seems even more bizarre that the usual transworld identification it replaces. | |
| From: comment on David Lewis (Counterpart theory and Quant. Modal Logic [1968]) by Saul A. Kripke - Naming and Necessity notes and addenda note 13 | |
| A reaction: I begin to see this as a devastating reply to a theory I previously found quite congenial. |
| 11974 | Counterparts are not the original thing, but resemble it more than other things do [Lewis] |
| Full Idea: Your counterparts resemble you closely in content and context in important respects. They resemble you more closely than do the other things in their worlds. But they are not really you. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
| A reaction: It is a dilemma. If my counterpart were exactly me, I couldn't contemplate possibly losing a leg, or my sanity. But if my counterpart isn't exactly me, then I don't have much interest in its fate. Only essences can save us here. Cf. me tomorrow. |
| 11975 | If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis] |
| Full Idea: If whatever thing in world w6 it is that resembles you more closely than anything else in w6 is nevertheless quite unlike you; nothing in w6 resembles you at all closely. If so, you have no counterpart in w6. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
| A reaction: This is the nub, because the whole theory rests on deciding whether two things resemble sufficiently 'closely'. But then we need a criterion of closeness, so we must start talking about which properties matter. Essences loom. |
| 11977 | Essential attributes are those shared with all the counterparts [Lewis] |
| Full Idea: An essential attribute of something is an attribute it shares with all its counterparts. | |
| From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
| A reaction: I don't like this. It ties essence entirely to identity, but I think essence precedes identity. Essence is a nexus of causal and explanatory powers which bestows an identity on each thing. But essence might be unstable, and identity with it. |
| 20945 | Belief is no more rational than is tasting and smelling [Hamann] |
| Full Idea: Belief happens as little in terms of reasons as tasting and smelling. | |
| From: J.G. Hamann (works [1770], v2:74), quoted by Andrew Bowie - Introduction to German Philosophy | |
| A reaction: That is one idea definitively expressed! I take it as only a partial truth. Beliefs happen as a result of observation and experience. But someone can draw our attention to something (and we can hunt it out ourselves), which is giving a reason for belief. |
| 8462 | A hallucination can, like an ague, be identified with its host; the ontology is physical, the idiom mental [Quine] |
| Full Idea: A physical ontology has a place for states of mind. An inspiration or a hallucination can, like the fit of ague, be identified with its host for the duration. It leaves our mentalistic idioms fairly intact, but reconciles them with a physical ontology. | |
| From: Willard Quine (The Scope and Language of Science [1954], §VI) | |
| A reaction: Quine is employing the same strategy that he uses for substances and properties (Idea 8461): take the predication as basic, rather than reifying the thing being predicated. The ague analogy suggests that Quine is an incipient functionalist. |
| 7666 | God is not a mathematician, but a poet [Hamann, by Berlin] |
| Full Idea: Hamann's fundamental doctrine was that God was not a geometer, not a mathematician, but a poet. | |
| From: report of J.G. Hamann (works [1770]) by Isaiah Berlin - The Roots of Romanticism Ch.3 | |
| A reaction: [This idea is wonderfully expressed by D.H.Lawrence in his poem 'Red Geranium and Godly Mignonette]. The idea becomes attractive when you ask whether God would need to do mathematics. |