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). |
| 19722 | We could know the evidence for our belief without knowing why it is such evidence [Mittag] |
| Full Idea: While one might understand the proposition entailed by one's evidence, one might have no idea how or why one's evidence entails it. This seems to imply one is not justified in believing the proposition on the basis of one's evidence. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidential') | |
| A reaction: An example might be seen if a layman tours a physics lab. This looks like a serious problem for evidentialism. Once you see why the evidence entails the proposition, you are getting closer to understanding than to knowledge. Explanation. |
| 19723 | Evidentialism can't explain that we accept knowledge claims if the evidence is forgotten [Mittag] |
| Full Idea: If one came to believe p with good evidence, but has since forgotten that evidence, we might think one can continue to believe justifiably, but evidentialism appears unable to account for this. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Forgotten') | |
| A reaction: We would still think that the evidence was important, and we would need to trust the knower's claim that the forgotten evidence was good. So it doesn't seem to destroy the evidentialist thesis. |
| 19720 | Evidentialism concerns the evidence for the proposition, not for someone to believe it [Mittag] |
| Full Idea: Evidentialism is not a theory about when one's believing is justified; it is a theory about what makes one justified in believing a proposition. It is a thesis regarding 'propositional justification', not 'doxastic justification'. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Preliminary') | |
| A reaction: Thus it is entirely about whether the evidence supports the proposition, and has no interest in who believes it or why. Knowledge is when you believe a true proposition which has good support. This could be internalist or externalist? |
| 19721 | Coherence theories struggle with the role of experience [Mittag] |
| Full Idea: Traditional coherence theories seem unable to account for the role experience plays in justification. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidence') | |
| A reaction: I'm inclined to say that experience only becomes a justification when it has taken propositional (though not necessarily lingistic) form. That is, when you see it 'as' something. Uninterpreted shape and colour can justify virtually nothing. |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |