21 ideas
| 1922 | Spiritual qualities only become advantageous with the growth of wisdom [Plato] |
| Full Idea: If virtue is a beneficial attribute of spirit, it must be wisdom; for spiritual qualities are not in themselves advantageous, but become so with wisdom…..Hence men cannot be good by nature. | |
| From: Plato (Meno [c.385 BCE], 88c) | |
| A reaction: Personally I haven't got any 'spiritual qualities', so I don't really understand this. |
| 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] |
| 11259 | How can you seek knowledge of something if you don't know it? [Plato] |
| Full Idea: How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know? | |
| From: Plato (Meno [c.385 BCE], 80d05) | |
| A reaction: Vasilis Politis cites this as a nice example of the 'aporiai' (puzzles) which Aristotle said were the foundation of enquiry. Nowadays the problem is called the 'paradox of enquiry'. |
| 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). |
| 20219 | True opinions only become really valuable when they are tied down by reasons [Plato] |
| Full Idea: True opinions are a fine thing and all they do is good, …but they escape from a man's mind, so they are not worth much until one ties them down by (giving) an account of the reason why. | |
| From: Plato (Meno [c.385 BCE], 98a3) | |
| A reaction: This gives justification the role of guarantee, stabilising and securing true beliefs (rather than triggering some new thing called 'knowledge'). |
| 5985 | Seeking and learning are just recollection [Plato] |
| Full Idea: Seeking and learning are in fact nothing but recollection. | |
| From: Plato (Meno [c.385 BCE], 81d) | |
| A reaction: This is a prelude to the famous conversation with the slave boy about geometry. You don't have to follow Plato into the doctrine of reincarnation; this remark is a key slogan for all rationalists. As pupils in maths lessons, we pull knowledge from within. |
| 5986 | The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato] |
| Full Idea: The slave boy's knowledge of geometry will not come from teaching but from questioning; he will recover it for himself, and the spontaneous recovery of knowledge that is in him is recollection. | |
| From: Plato (Meno [c.385 BCE], 85d) | |
| A reaction: Of course, if maths and geometry are huge tautological axiom systems, we would expect to be able to derive them (with hints from a teacher) entirely from their axioms. It is not clear why we might be able to derive the truths of all nature a priori. |
| 1923 | As a guide to action, true opinion is as good as knowledge [Plato] |
| Full Idea: True opinion is as good a guide as knowledge for the purpose of acting rightly. | |
| From: Plato (Meno [c.385 BCE], 97b) | |
| A reaction: This is the germ of Peirce's epistemology - that knowledge is an interesting theoretical concept, but opinion/belief is what matters, and most needs explanation. |
| 1919 | You don't need to learn what you know, and how do you seek for what you don't know? [Plato] |
| Full Idea: You could argue that a man cannot discover what he does know or what he doesn't. The first needs no discovery, and how do you begin looking for the second? | |
| From: Plato (Meno [c.385 BCE], 80e) |
| 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. |
| 1913 | Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato] |
| Full Idea: Is virtue something that can be taught, or does it come by practice, or is it a natural aptitude, or something else? | |
| From: Plato (Meno [c.385 BCE], 70a) |
| 1921 | If virtue is a type of knowledge then it ought to be taught [Plato] |
| Full Idea: If virtue is some sort of knowledge, then clearly it could be taught. | |
| From: Plato (Meno [c.385 BCE], 87c) |
| 1927 | It seems that virtue is neither natural nor taught, but is a divine gift [Plato] |
| Full Idea: If our discussion is right, virtue is acquired neither by nature nor by teaching. Whoever has it gets it by divine dispensation, without taking thought. | |
| From: Plato (Meno [c.385 BCE], 99e) |
| 1918 | How can you know part of virtue without knowing the whole? [Plato] |
| Full Idea: Does anyone know what a part of virtue is without knowing the whole? | |
| From: Plato (Meno [c.385 BCE], 79c) |
| 1916 | Even if virtues are many and various, they must have something in common to make them virtues [Plato] |
| Full Idea: Even if virtues are many and various, at least they all have some common character which makes them all virtues. | |
| From: Plato (Meno [c.385 BCE], 72c) |
| 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'). |