Combining Texts

All the ideas for 'In Defense of Essentialism', 'Introduction to Zermelo's 1930 paper' and 'On 'The Beginning of Philosophy''

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14 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

19456	Philosophy is distinguished from other sciences by its complete lack of presuppositions [Feuerbach]
	Full Idea: Philosophy does not presuppose anything. It is precisely in this fact of non-presupposition that its beginning lies - a beginning by virtue of which it is set apart from all the other sciences.
	From: Ludwig Feuerbach (On 'The Beginning of Philosophy' [1841], p.135)
	A reaction: Most modern philosophers seem to laugh at such an idea, because everything is theory-laden, culture-laden, language-laden etc. As an aspiration I love it, and think good philosophers get quite close to the goal (which, I admit, is not fully attainable).

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17833	The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
	Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical.
	From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213)

17834	Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
	Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets.
	From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215)
	A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets).

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

17837	Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
	Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory.
	From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17836	The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
	Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself.
	From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217)

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 / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds

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.