12 ideas
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
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. |
3916 | Hopi consistently prefers verbs and events to nouns and things [Whorf] |
Full Idea: Hopi, with its preference for verbs, as contrasted to our own liking for nouns, perpetually turns our propositions about things into propositions about events. | |
From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.63) | |
A reaction: This should provoke careful thought about ontology - without concluding that it is entirely relative to language. |
3917 | Scientific thought is essentially a specialised part of Indo-European languages [Whorf] |
Full Idea: What we call "scientific thought" is a specialisation of the western Indo-European type of language. | |
From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.246) | |
A reaction: This is the beginnings of an absurd extreme relativist view of science, based on a confusion about meaning and thought. |
3915 | The Hopi have no concept of time as something flowing from past to future [Whorf] |
Full Idea: A Hopi has no general notion or intuition of time as a smooth flowing continuum in which everything in the universe proceeds at an equal rate, out of a future, through a present, into a past. | |
From: Benjamin Lee Whorf (An American Indian model of the Universe [1936], p.57) | |
A reaction: If true, this would not so much support relativism of language as the view that that conception of time is actually false. |