28 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. |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 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'. |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 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) |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 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) |