36 ideas
| 11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
| Full Idea: My assimilation of essence to definition ...may not provide us with an analysis of the concept, but it does provide us with a good model of how the concept works. | |
| From: Kit Fine (Essence and Modality [1994], p. 3) | |
| A reaction: An example of the modern shift in analytic philosophy, away from the dream of given a complete analysis of a concept, towards giving an account of the concepts relationships. Compare Shoemaker in Idea 8559. |
| 11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
| Full Idea: In modern analytic philosophy we find that, as a result of sustained empiricist critique, the idea of real definition has been more or less given up (unless it be taken to be vestigially present in the notion of a sortal). | |
| From: Kit Fine (Essence and Modality [1994], p. 3) | |
| A reaction: The account of essences as falling under sortals (roughly, categorising terms) is associated with David Wiggins. Kit Fine is in the business of reviving Aristotelian real definitions, as are fans of scientific essentialism (see under 'Nature'). |
| 11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K] |
| Full Idea: There is an analogy between defining a term and giving the essence of an object. ..However, I am inclined to think that the two cases are not merely parallel but are, at bottom, the same. | |
| From: Kit Fine (Essence and Modality [1994], p.13) | |
| A reaction: The proposal is something like the meaning of a concept being the essence of the concept. And essence is definition. The parallel is that they both lead to necessities, either derived from objects or from concepts. Sounds good to me. |
| 13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
| Full Idea: Axiom of Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y). That is, a set is determined by its members. If every z in one set is also in the other set, then the two sets are the same. | |
| From: Kenneth Kunen (Set Theory [1980], §1.5) |
| 13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
| Full Idea: Axiom of Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z). Any pair of entities must form a set. | |
| From: Kenneth Kunen (Set Theory [1980], §1.6) | |
| A reaction: Repeated applications of this can build the hierarchy of sets. |
| 13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
| Full Idea: Axiom of Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A). That is, the union of a set (all the members of the members of the set) must also be a set. | |
| From: Kenneth Kunen (Set Theory [1980], §1.6) |
| 13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
| Full Idea: Axiom of Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x). That is, there is a set which contains zero and all of its successors, hence all the natural numbers. The principal of induction rests on this axiom. | |
| From: Kenneth Kunen (Set Theory [1980], §1.7) |
| 13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
| Full Idea: Power Set Axiom: ∀x ∃y ∀z(z ⊂ x → z ∈ y). That is, there is a set y which contains all of the subsets of a given set. Hence we define P(x) = {z : z ⊂ x}. | |
| From: Kenneth Kunen (Set Theory [1980], §1.10) |
| 13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
| Full Idea: Axiom of Replacement Scheme: ∀x ∈ A ∃!y φ(x,y) → ∃Y ∀X ∈ A ∃y ∈ Y φ(x,y). That is, any function from a set A will produce another set Y. | |
| From: Kenneth Kunen (Set Theory [1980], §1.6) |
| 13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
| Full Idea: Axiom of Foundation: ∀x (∃y(y ∈ x) → ∃y(y ∈ x ∧ ¬∃z(z ∈ x ∧ z ∈ y))). Aka the 'Axiom of Regularity'. Combined with Choice, it means there are no downward infinite chains. | |
| From: Kenneth Kunen (Set Theory [1980], §3.4) |
| 13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
| Full Idea: Axiom of Choice: ∀A ∃R (R well-orders A). That is, for every set, there must exist another set which imposes a well-ordering on it. There are many equivalent versions. It is not needed in elementary parts of set theory. | |
| From: Kenneth Kunen (Set Theory [1980], §1.6) |
| 13029 | Set Existence: ∃x (x = x) [Kunen] |
| Full Idea: Axiom of Set Existence: ∃x (x = x). This says our universe is non-void. Under most developments of formal logic, this is derivable from the logical axioms and thus redundant, but we do so for emphasis. | |
| From: Kenneth Kunen (Set Theory [1980], §1.5) |
| 13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
| Full Idea: Comprehension Scheme: for each formula φ without y free, the universal closure of this is an axiom: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ). That is, there must be a set y if it can be defined by the formula φ. | |
| From: Kenneth Kunen (Set Theory [1980], §1.5) | |
| A reaction: Unrestricted comprehension leads to Russell's paradox, so restricting it in some way (e.g. by the Axiom of Specification) is essential. |
| 13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
| Full Idea: Axiom of Constructability: this is the statement V = L (i.e. ∀x ∃α(x ∈ L(α)). That is, the universe of well-founded von Neumann sets is the same as the universe of sets which are actually constructible. A possible axiom. | |
| From: Kenneth Kunen (Set Theory [1980], §6.3) |
| 11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
| Full Idea: One object depends upon another (in one sense of the term) if its essence prevents it from existing without the other object. | |
| From: Kit Fine (Essence and Modality [1994], p. 2) | |
| A reaction: I take the interest of this to be that essences are usually thought to be intrinsic, but this seems to involve the object in necessary external relations. |
| 11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
| Full Idea: Essence has been conceived either on the model of definition, involving the 'real' as opposed to 'nominal' definitions, or it is elucidated in modal terms, located in de re cases of modal attributions (an object being necessarily a certain way). | |
| From: Kit Fine (Essence and Modality [1994], p. 2) | |
| A reaction: [compressed] Fine sets out to defend the definitional view, which derives from Aristotle, his line being that necessity depends on essence, and so cannot be used to define it. I think I agree. |
| 11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
| Full Idea: We have an informal way of saying an object essentially has a property, as 'the object must have the property if it is to be the object that it is', and this form of words manages to convey what we wish to convey. | |
| From: Kit Fine (Essence and Modality [1994], p. 4) | |
| A reaction: The importance of this claim is that it makes no mention of 'necessity'. Fine's view is plausible, but hard to evaluate once he has said. We seem to then divide an object's properties into identity properties, causal properties and peripheral properties. |
| 11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
| Full Idea: The simplest form of the modal account takes an object to have a property essentially just in case it is necessary that the object has the property. | |
| From: Kit Fine (Essence and Modality [1994], p. 3) | |
| A reaction: Fine wants to reverse the account, explaining necessities in terms of prior essences. |
| 11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
| Full Idea: With the advent of quantified modal logic, philosophers have been in a better position to formulate essentialist claims. | |
| From: Kit Fine (Essence and Modality [1994], p. 3) | |
| A reaction: A nice illustration of the role which logic plays in modern analytic philosophy. It is not an unreasonable assumption that we will understand a theoretical problem more clearly if we can articulate it more accurately. |
| 11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
| Full Idea: Far from viewing essence as a special case of metaphysical necessity, we should view metaphysical necessity as a special case of essence. | |
| From: Kit Fine (Essence and Modality [1994], p. 9) | |
| A reaction: This strikes me as one of the most powerful proposals in modern philosophy (even if it is a reiteration of Aristotle!). |
| 16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
| Full Idea: If an essence is a sum of essential properties (had in all possible worlds where it exists), Fine points out that it seems grossly to overgenerate essential properties ('S is either a man or a mouse', or 'S is such that 2+2=4'). | |
| From: report of Kit Fine (Essence and Modality [1994]) by E.J. Lowe - What is the Source of Knowledge of Modal Truths? 6 | |
| A reaction: To me this is the sort of mess you get into when you accept that 'being such that p' is a property. Defenders of the modal approach always have to eliminate 'trivial' properties from essences, but non-trivial is a defining feature of an essence. |
| 11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
| Full Idea: Can we not recognise a sense of 'what an object is', according to which it lies in the nature of a singleton to have Socrates as a member, even though it does not lie in the nature of Socrates to belong to the singleton? | |
| From: Kit Fine (Essence and Modality [1994], p. 5) | |
| A reaction: Important and persuasive. It echoes the example in Idea 11162, that the necessary relation is not part of the essence. Socrates is necessarily in {Socrates}, but that is because of the set, not because of Socrates. Essences causes necessities. |
| 11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
| Full Idea: Necessarily any necessary truth will hold if Socrates exists. But it is no part of Socrates' essence that there be infinitely many prime numbers, ..or that objects like the Eiffel Tower have their own necessary essence. | |
| From: Kit Fine (Essence and Modality [1994], p. 5-6) | |
| A reaction: This and the 'singleton Socrates' example (Idea 11165) are the twin prongs of Fine's attack on the modal account of essentialism. I think they constitute one of the best single pages in the whole of recent philosophy. Bravo. |
| 10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
| Full Idea: Fine's view is that the notion of an essential property of a thing should be bound up with the notion of what it is to be that thing (unlike, for example, Socrates being such that there are infinitely many primes). | |
| From: report of Kit Fine (Essence and Modality [1994]) by Adolph Rami - Essential vs Accidental Properties §2 | |
| A reaction: I would think that Fine is so obviously right that it was hardly worth saying, but philosophers are a funny lot, and are quite likely to claim that features of prime numbers are part of the essence of a long-dead philosopher. |
| 10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
| Full Idea: According to Fine's definitional characterization of essential properties, they are those of an object's properties that are part of the object's 'definition'. | |
| From: report of Kit Fine (Essence and Modality [1994]) by Adolph Rami - Essential vs Accidental Properties §2 | |
| A reaction: This demands not just an account of what a definition is, but also the notion that there is only one fixed and correct definition (since the object presumably only has one essence) - but there seems to be something relative about a good definition. |
| 11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
| Full Idea: If there is nothing in the nature of Socrates which demands that he exists, then presumably there is nothing in the nature of Socrates which demands that his parents exist. | |
| From: Kit Fine (Essence and Modality [1994], p. 6) | |
| A reaction: This sounds conclusive to me, against any claim that Socrates necessarily had those parents, if the claim is based on the identity or esssence of Socrates. |
| 11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
| Full Idea: We naturally suppose, if a subject-predicate proposition is necessary, that the subject of the proposition is the source of the necessity. But that singleton 2 contains 2 is necessary, whether the number or the set is the subject of the proposition. | |
| From: Kit Fine (Essence and Modality [1994], p. 9) | |
| A reaction: A very nice addition to his general attack on the idea that essence should be accounted for in terms of his necessity. He asks a beautifully simple question: for each necessity that we accept, what is the source of that necessity? |
| 11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
| Full Idea: Conceptual (and logical) necessities can be taken to be the propositions which are true in virtue of the nature of all concepts (or just the logical concepts). | |
| From: Kit Fine (Essence and Modality [1994], p. 9-10) | |
| A reaction: The idea that something might be true simply because of the nature of a concept sounds good, and a slightly better formulation than traditional accounts of analytic truth. |
| 11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
| Full Idea: It is necessary that Socrates and the Eiffel Tower be distinct. But it is not essential to Socrates that he be distinct from the Tower, for there is nothing in his nature which connects him in any special way to it. | |
| From: Kit Fine (Essence and Modality [1994], p. 5) | |
| A reaction: I find this simple argument very persuasive in separating out necessary facts about an object from the essence of that object. |
| 11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
| Full Idea: The metaphysically necessary truths can be identified with the propositions which are true in virtue of the nature of all objects whatever. | |
| From: Kit Fine (Essence and Modality [1994], p. 9) | |
| A reaction: This is part of Fine's proposal that necessities are derived from the essences or natures of things, which view I find very congenial. |
| 11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
| Full Idea: Just as a necessary truth may be true in virtue of the identity of certain objects as opposed to others, so an analytic truth may be true in virtue of the meanings of certain terms as opposed to others (such as 'bachelor' rather than 'unmarried'). | |
| From: Kit Fine (Essence and Modality [1994], p.10) | |
| A reaction: This is a beautifully simple observation, that the necessity of 'bachelors are unmarried men' derives from part of the proposition, not from the whole of it. So what is it about the part that generates the apparent necessity? The nature of the concept! |
| 11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |
| Full Idea: Strictly speaking it is irrelevant to the meaning of 'bachelor' that the phrase 'unmarried man' means what it does. | |
| From: Kit Fine (Essence and Modality [1994], p.13) | |
| A reaction: His point is that the necessary truth here derives from the meaning of 'bachelor', and not from the meaning of 'unmarried man'. But is also true that 'unmarried man' means 'bachelor' (for those familiar with the latter, but not the former). |
| 22693 | The works we value most are in sympathy with our own moral views [John,E] |
| Full Idea: The works we tend to value most highly are ones that are in sympathy with the moral views we actually accept. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], Intro) | |
| A reaction: I would have to endorse this. She admits that we may rate other works very highly, but they won't appear on our list of favourites. This fact may well distort philosophical discussions of morality and art. |
| 22694 | We should understand what is morally important in a story, without having to endorse it [John,E] |
| Full Idea: Our responses to literature should show that we grasp whatever counts as morally important within the narrative, but not necessarily that we judge and feel in the way deemed appropriate by the work. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], 'Accommodating') | |
| A reaction: She gives as an example a story by Hemingway which places a high value on the courageous hunting of big game. A second example is the total amorality of a Highsmith novel. This idea seems exactly right to me. |
| 22695 | We value morality in art because that is what we care about - but it is a contingent fact [John,E] |
| Full Idea: Moral value is valuable in art because people care about moral value. This runs deep, but it is a contingent matter, and the value of morality in art hinges on art's need to provide something precious to us. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], 'Contingency') | |
| A reaction: I think this is exactly right. Thrillers are written with very little moral concern, for a readership which cares about brave and exciting deeds. Even there, violence has its ethics. |
| 22692 | A work can be morally and artistically excellent, despite rejecting moral truth [John,E] |
| Full Idea: A work that rejects moral truth can be artistically excellent, in part because of its moral content. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], Intr) | |
| A reaction: She cites the film 'Trainspotting', about desperate drug addicts, because it gives an amoral insight into their world. |