11 ideas
| 14650 | Maybe proper names involve essentialism [Plantinga] |
| Full Idea: Perhaps the notion of a proper name itself involves essentialism. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.43) | |
| A reaction: This is just before Kripke's announcement of 'rigid designation', which seems to have relaunched modern essentialism. The thought is that you can't name something, if you don't have a stable notion of what is (and isn't) being named. |
| 14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
| Full Idea: Can't I name all the real numbers in the interval (0,1) at once? Couldn't I name them all 'Charley', for example? | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.40) | |
| A reaction: Plantinga is nervous about such a sweeping move, but can't think of an objection. This addresses a big problem, I think - that you are supposed to accept the real numbers when we cannot possibly name them all. |
| 4242 | Pure supervenience explains nothing, and is a sign of something fundamental we don't know [Nagel] |
| Full Idea: Pure, unexplained supervenience is never a solution to a problem but a sign that there is something fundamental we don't know. | |
| From: Thomas Nagel (The Psychophysical Nexus [2000], §III) | |
| A reaction: This seems right. It is not a theory or an explanation, merely the observation of a correlation which will require explanation. Why are they correlated? |
| 14647 | Surely self-identity is essential to Socrates? [Plantinga] |
| Full Idea: If anything is essential to Socrates, surely self-identity is. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.37) | |
| A reaction: This is the modern move of Plantinga and Adams, to make 'is identical with Socrates' the one property which assures the identity of Socrates (his 'haecceity'). My view is that self-identity is not a property. Plantinga wonders about that on p.44. |
| 14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
| Full Idea: An object has a property essentially just in case it couldn't conceivably have lacked that property. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.35) | |
| A reaction: Making it depend on what we can conceive seems a bit dubious, for someone committed to real essences. The key issue is how narrowly or broadly you interpret the word 'property'. The word 'object' needs a bit of thought, too! |
| 14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
| Full Idea: Aquinas says if a 'de dicto' statement is true, the 'de re' version may be false. The opposite also applies: 'What I am thinking of [17] is essentially prime' is true, but 'The proposition "what I am thinking of is prime" is necessarily true' is false. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.27) | |
| A reaction: In his examples the first is 'de re' (about the number), and the second is 'de dicto' (about that proposition). |
| 14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
| Full Idea: To explain the 'de re' via the 'de dicto' is to provide a rule enabling us to find, for each de re proposition, an equivalent de dicto proposition. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.41) | |
| A reaction: Many 'de dicto' paraphrases will change the modality of a 'de re' statement, so the challenge is to find the right equivalent version. Plantinga takes up this challenge. The 'de dicto' statement says the object has the property, and must have it. |
| 14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
| Full Idea: Some statements predicate modality of another statement (modality 'de dicto'); but others predicate of an object the necessary or essential possession of a property; these latter express modality 'de re'. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.26) | |
| A reaction: The distinction seems to originate in Aquinas, concerning whether God knows the future (or, how he knows the future). 'De dicto' is straightforward, but possibly the result of convention. 'De re' is controversial, and implies deep metaphysics. |
| 14651 | What Socrates could have been, and could have become, are different? [Plantinga] |
| Full Idea: Is there a difference between what Socrates could have been, and what he could have become? | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.44) | |
| A reaction: That is, I take it, 1) how different might he have been in the past, given how he is now?, and 2) how different might he have been in the past, and now, if he had permanently diverged from how he is now? 1) has tight constraints on it. |
| 13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
| Full Idea: Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles. | |
| From: Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5 | |
| A reaction: A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction. |
| 9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |
| Full Idea: It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason. | |
| From: Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55 | |
| A reaction: The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths. |