37 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. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 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. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 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. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 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). |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |