10 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). |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
| From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
| A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
| 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. |
| 20948 | Human cultures are organisms which grow, and then fade and die [Spengler, by Bowie] |
| Full Idea: Spengler relies upon the idea of human cultures as organisms which grow and then inevitably die, having lost their vitality. | |
| From: report of Oswald Spengler (The Decline of the West [1918]) by Andrew Bowie - Introduction to German Philosophy 2 'Herder' | |
| A reaction: He should have thought more about technology. If the 'West' collapses and is replaced by China (say), the new Chinese culture will be barely distinguishable from the West, because they will pursue similar technologies. |