Combining Texts

All the ideas for 'In Defense of Essentialism', 'Letters to Russell' and 'A Theory of Conditionals'

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14 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18253 I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
     Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.
     From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
     A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18166 The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
     Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish.
     From: Gottlob Frege (Letters to Russell [1902], 1902.06.22)
     A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air?
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
18269 Logical objects are extensions of concepts, or ranges of values of functions [Frege]
     Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there?
     From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr
     A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology.
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
14193 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA]
     Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation.
     From: L.A. Paul (In Defense of Essentialism [2006], §1)
     A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures.
14195 If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA]
     Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort.
     From: L.A. Paul (In Defense of Essentialism [2006], §1)
     A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary.
14196 Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA]
     Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue).
     From: L.A. Paul (In Defense of Essentialism [2006], §1)
     A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue.
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
14198 Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA]
     Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual.
     From: L.A. Paul (In Defense of Essentialism [2006], §5)
     A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness.
9. Objects / D. Essence of Objects / 2. Types of Essence
14190 Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA]
     Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones.
     From: L.A. Paul (In Defense of Essentialism [2006], Intro)
     A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial.
9. Objects / D. Essence of Objects / 6. Essence as Unifier
14191 Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA]
     Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures.
     From: L.A. Paul (In Defense of Essentialism [2006], Intro)
     A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers.
9. Objects / D. Essence of Objects / 15. Against Essentialism
14192 Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA]
     Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality.
     From: L.A. Paul (In Defense of Essentialism [2006], Intro)
     A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with.
14197 An object's modal properties don't determine its possibilities [Paul,LA]
     Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia.
     From: L.A. Paul (In Defense of Essentialism [2006], §3)
     A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world.
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
14286 In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker]
     Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14285 A possible world is the ontological analogue of hypothetical beliefs [Stalnaker]
     Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven!
14189 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA]
     Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta.
     From: L.A. Paul (In Defense of Essentialism [2006], Intro)
     A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world.