25 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. |
| 23449 | Interpreting a text is representing it as making sense [Morris,M] |
| Full Idea: Interpreting a text is a matter of making sense of it. And to make sense of a text is to represent it as making sense. | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.2) | |
| A reaction: 'Making sense' is obviously not a very precise or determinate concept. It is probably better to say that the process is 'trying' to make sense of the text, because most texts don't totally make sense. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 23484 | Bipolarity adds to Bivalence the capacity for both truth values [Morris,M] |
| Full Idea: According to the Principle of Bipolarity, every meaningful sentence must be capable both of being true and of being false. It is not enough merely that every sentence must be either true or false (which is Bivalence). | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 3D) | |
| A reaction: It is said that early Wittgenstein endorses this. That is, in addition to being true, the sentence must be capable of falsehood (and vice versa). This seems to be flirting with the verification principle. I presume it is 'affirmative' sentences. |
| 23494 | Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M] |
| Full Idea: There are two problems with defining the quantifiers in terms of conjunction and disjunction. The general statements are unspecific, and do not say which things have the properties, and also they can't range over infinite objects. | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 5C) | |
| A reaction: That is, the universal quantifier is lots of ands, and the existential is lots of ors. If there only existed finite objects, then naming them all would be universal, and the infinite wouldn't be needed. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 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'. |
| 23451 | Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M] |
| Full Idea: Just distinguishing things is not enough for counting (and hence arithmetic). We need the crucial extra notion of the successor in a series of some kind. | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.5) | |
| A reaction: This is a step towards the Peano Axioms of arithmetic. The successors could be fingers and toes, taken in a conventional order, and matched one-to-one to the objects. 'My right big toe of cows' means 16 cows (but non-verbally). |
| 23460 | To count, we must distinguish things, and have a series with successors in it [Morris,M] |
| Full Idea: Distinguishing between things is not enough for counting. …We need the crucial extra notion of a successor in a series of a certain kind. | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro) | |
| A reaction: This is the thinking that led to the Dedekind-Peano axioms for arithmetic. E.g. each series member can only have one successor. There is an unformalisable assumption that the series can then be applied to the things. |
| 23452 | Discriminating things for counting implies concepts of identity and distinctness [Morris,M] |
| Full Idea: The discrimination of things for counting needs to bring with it the notion of identity (and, correlatively, distinctness). | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.5) | |
| A reaction: Morris is exploring how practices like counting might reveal necessary truths about the world. |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 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) |
| 23491 | There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M] |
| Full Idea: The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of the proposition is: Such and such is the case. | |
| From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 4.5) | |
| A reaction: [last bit in Ogden translation] LW eventually expresses this symbolically. We could just say a proposition is an assertion. This strikes as either a rather empty claim, or an unfounded one. |
| 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) |