21 ideas
| 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) |
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| Full Idea: Normal propositional modal logics derive from the minimal system K: wffs of PC are axioms; □(p⊃q)⊃(□p⊃□q); uniform substitution; modus ponens; necessitation (α→□α). | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1) |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| Full Idea: If a frame contains any dead end or blind world, then D is not valid on that frame, ...but D is valid on every serial frame. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.1) |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| Full Idea: In S4 there are exactly 14 distinct modalities, and any modality may be reduced to one containing no more than three modal operators in sequence. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: The significance of this may be unclear, but it illustrates one of the rewards of using formal systems to think about modal problems. There is at least an appearance of precision, even if it is only conditional precision. |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| Full Idea: S5 contains the four main reduction laws, so the first of any pair of operators may be deleted. Hence all but the last modal operator may be deleted. This leaves six modalities: p, ◊p, □p, and their negations. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |
| Full Idea: If one wants the quantifiers in each world to range only over the things that exist in that world, and one doesn't believe that the same things exist in every world, one would probably not want the Barcan formula. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.2) | |
| A reaction: I haven't quite got this, but it sounds to me like I should reject the Barcan formula (but Idea 9449!). I like a metaphysics to rest on the actual world (with modal properties). I assume different things could have existed, but don't. |
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 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) |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| Full Idea: A relation is 'Euclidean' if aRb and aRc imply bRc. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: If a thing has a relation to two separate things, then those two things will also have that relation between them. If I am in the same family as Jim and as Jill, then Jim and Jill are in the same family. |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| Full Idea: A de dicto necessary truth says that something is φ, that this proposition is a necessary truth, i.e. that in every accessible world something (but not necessarily the same thing in each world) is φ. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.1) | |
| A reaction: At last, a really clear and illuminating account of this term! The question is then invited of what is the truthmaker for a de dicto truth, assuming that the objects themselves are truthmakers for de re truths. |