13 ideas
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid? |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true. | |
| From: Vann McGee (Logical Consequence [2014], 2) |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory. |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: A helpful link between logical truths and analytic truths, which had not struck me before. |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish. | |
| From: Vann McGee (Logical Consequence [2014], 5) | |
| A reaction: [He cites Quine 1935] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation). |
| 13437 | A CAR and its major PART can become identical, yet seem to have different properties [Gallois] |
| Full Idea: At t1 there is a whole CAR, and a PART of it, which is everything except the right front wheel. At t2 the wheel is removed, leaving just PART, so that CAR is now PART. But PART was a proper part of CAR, and CAR had the front wheel. Different properties! | |
| From: André Gallois (Occasions of Identity [1998], 1.II) | |
| A reaction: [compressed summary] The problem is generated by appealing to Leibniz's Law. My immediate reaction is that this is the sort of trouble you get into if you include such temporal truths about things as 'properties'. |
| 16233 | Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois] |
| Full Idea: A problem for Gallois is that he leaves us no way to talk about questions of genuine identity through time, and thus undercuts one motivation for his own position. | |
| From: comment on André Gallois (Occasions of Identity [1998]) by Katherine Hawley - How Things Persist 5.8 | |
| A reaction: Gallois seems to need a second theory of identity to support his Occasional Identity theory. Two things need an identity each, before we can say that the two identities coincide. (Time to read Gallois!) |
| 14755 | Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider] |
| Full Idea: Gallois's core claim is that the identity relation holds with respect to times, ...and he must claim that there is no such thing as the relation of identity simpliciter. | |
| From: report of André Gallois (Occasions of Identity [1998]) by Theodore Sider - Four Dimensionalism 5.5 | |
| A reaction: Gallois is essentially responding to the statue and clay problem, but it seems a bit drastic to entirely change our concept of two things being identical, such as Hesperus and Phosphorus. 'Identity' seems to have several meanings; let's sort them out. |
| 16231 | Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley] |
| Full Idea: Gallois' Occasional Identity Thesis is that objects can be identical at one time without being identical at all times. | |
| From: report of André Gallois (Occasions of Identity [1998]) by Katherine Hawley - How Things Persist 5.4 | |
| A reaction: The analogy is presumably with two crossing roads being identical at one place but not at others. It is a major misunderstanding to infer from Special Relativity that time is just like space. |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'. | |
| From: Vann McGee (Logical Consequence [2014], 8) | |
| A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |