27 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 18365 | If truths are just identical with facts, then truths will make themselves true [David] |
| Full Idea: According to the identity theory of truth, a proposition is true if and only if it is identical with a fact. ...This leads to the unacceptable claim that every true proposition makes itself true (because it is identical to its fact). | |
| From: Marian David (Truth-making and Correspondence [2009], n 14) |
| 18362 | Examples show that truth-making is just non-symmetric, not asymmetric [David] |
| Full Idea: That 'there is at least one proposition' ...is a case where something makes itself true, which generates a counterexample to the natural assumption that truth-making is asymmetric; truth-making, it seems, is merely non-symmetric. | |
| From: Marian David (Truth-making and Correspondence [2009], 4) |
| 18360 | It is assumed that a proposition is necessarily true if its truth-maker exists [David] |
| Full Idea: Friends of the truth-maker principle usually hold that the following states a crucial necessary condition on truth-making: if x makes y true, then, necessarily, if x exists then y is true. | |
| From: Marian David (Truth-making and Correspondence [2009], 2) | |
| A reaction: My objection is that the proposition y is taken to pre-exist, primly awaiting the facts that will award it 'truth'. An ontology that contains an infinity of propositions, most of which so far lack a truth-value, is incoherent. You can have x, but no y! |
| 18358 | Two different propositions can have the same fact as truth-maker [David] |
| Full Idea: Two different propositions can have the same fact as truth-maker. For example, 'L is happy or L is hungry', and 'L is happy or L is thirsty', which are both made true by the fact that L is happy. | |
| From: Marian David (Truth-making and Correspondence [2009], 1) |
| 18355 | What matters is truth-making (not truth-makers) [David] |
| Full Idea: The term 'truthmaker' just labels whatever stands in the truth-making relation to a truth. The truth-making relation is crucial. It would have been just as well to refer to the truth-'maker' principle as the truth-'making' principle. | |
| From: Marian David (Truth-making and Correspondence [2009], 1) | |
| A reaction: This is well said. The commitment of this theory is to something which makes each proposition true. There is no initial commitment to any theories about what sorts of things do the job. |
| 18354 | Correspondence is symmetric, while truth-making is taken to be asymmetric [David] |
| Full Idea: Correspondence appears to be a symmetric relation while truth-making appears to be, or is supposed to be, an asymmetric relation. | |
| From: Marian David (Truth-making and Correspondence [2009], Intro) |
| 18356 | Correspondence is an over-ambitious attempt to explain truth-making [David] |
| Full Idea: Truth-maker theory says that the attempt by correspondence to fill in the generic truth-maker principle with something more informative fails. It is too ambitious, offering a whole zoo of funny facts that are not needed. | |
| From: Marian David (Truth-making and Correspondence [2009], 1) | |
| A reaction: A typical funny fact is a disjunctive fact, which makes 'he is hungry or thirsty' true (when it can just be made true by the simple fact that he is thirsty). |
| 18363 | Correspondence theorists see facts as the only truth-makers [David] |
| Full Idea: Correspondence theorists are committed to the view that, since truth is correspondence with a fact, only facts can make true propositions true. | |
| From: Marian David (Truth-making and Correspondence [2009], 4) |
| 18364 | Correspondence theory likes ideal languages, that reveal the structure of propositions [David] |
| Full Idea: Correspondence theorists tend to promote ideal languages, ...which is intended to mirror perfectly the structure of the propositions it expresses. | |
| From: Marian David (Truth-making and Correspondence [2009], n 03) |
| 18357 | What makes a disjunction true is simpler than the disjunctive fact it names [David] |
| Full Idea: The proposition that 'L is happy or hungry' can be made true by the fact that L is happy. This does not have the same complexity or constituent structure as the proposition it makes true. | |
| From: Marian David (Truth-making and Correspondence [2009], 1) |
| 18359 | One proposition can be made true by many different facts [David] |
| Full Idea: One proposition can be made true by many different facts (such as 'there are some happy dogs'). | |
| From: Marian David (Truth-making and Correspondence [2009], 1) |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 18361 | A reflexive relation entails that the relation can't be asymmetric [David] |
| Full Idea: An asymmetric relation must be irreflexive: any case of aRa will yield a reductio of the assumption that R is asymmetric. | |
| From: Marian David (Truth-making and Correspondence [2009], 4) |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |