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All the ideas for 'works', 'Nature and Meaning of Numbers' and 'Putnam's Paradox'

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58 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
For Plato true wisdom is supernatural [Plato, by Weil]
     Full Idea: It is evident that Plato regards true wisdom as something supernatural.
     From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.61
     A reaction: Taken literally, I assume this is wrong, but we can empathise with the thought. Wisdom has the feeling of rising above the level of mere knowledge, to achieve the overview I associate with philosophy.
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius]
     Full Idea: Plato, who mentions nearly all the ancient philosophers, nowhere speaks of Democritus; he wished to burn all of his books, but was persuaded that it was futile.
     From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.7.8
2. Reason / C. Styles of Reason / 1. Dialectic
Two contradictories force us to find a relation which will correlate them [Plato, by Weil]
     Full Idea: Where contradictions appear there is a correlation of contraries, which is relation. If a contradiction is imposed on the intelligence, it is forced to think of a relation to transform the contradiction into a correlation, which draws the soul higher.
     From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.70
     A reaction: A much better account of the dialectic than anything I have yet seen in Hegel. For the first time I see some sense in it. A contradiction is not a falsehood, and it must be addressed rather than side-stepped. A kink in the system, that needs ironing.
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
     Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv'
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
     Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7
     A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is!
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
     Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb'
     A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective.
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
     Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1
     A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology.
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
     Full Idea: A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.
     From: David Lewis (Putnam's Paradox [1984], 'Why Model')
     A reaction: This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
     Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref)
     A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
     Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
     Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
     Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4
     A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
     Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243
     A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
     Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII
     A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind.
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
     Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4
     A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
     Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref)
     A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
     Full Idea: A system S is said to be infinite when it is similar to a proper part of itself.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
     Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5
     A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
     Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
     Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers.
     From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1
     A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
     Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
     Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered
     A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
     Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6
     A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis.
7. Existence / D. Theories of Reality / 4. Anti-realism
Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis]
     Full Idea: Anti-realists say the only world is imaginary, or only has the parts or classes or relations we divide it into, or doubt that reference to the world is possible, or doubt that our interpretations can achieve truth.
     From: David Lewis (Putnam's Paradox [1984], 'Why Anti-R')
     A reaction: [compression of a paragraph on anti-realism] Lewis is a thoroughgoing realist. A nice example of the rhetorical device of ridiculing an opponent by suggesting that they don't even know what they themselves believe.
8. Modes of Existence / A. Relations / 3. Structural Relations
Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki]
     Full Idea: 'Structure' tends to be characterized by Plato as something that is mathematically expressed.
     From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects V.3 iv
     A reaction: [Koslicki is drawing on Verity Harte here]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas]
     Full Idea: Plato's theory of Forms allowed him to claim that the sophists and other opponents were trapped in the world of appearance. What they therefore taught was only apparent wisdom and virtue.
     From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.118
Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle]
     Full Idea: The Platonists, on the basis of purely logical arguments, posit the existence of an indivisible 'triangle in itself'.
     From: report of Plato (works [c.375 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 316a15
     A reaction: A helpful confirmation that geometrical figures really are among the Forms (bearing in mind that numbers are not, because they contain one another). What shape is the Form of the triangle?
When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius]
     Full Idea: When Diogenes told Plato he saw tables and cups, but not 'tableness' and 'cupness', Plato replied that this was because Diogenes had eyes but no intellect.
     From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.2.6
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato]
     Full Idea: If there is the same Form for the Forms and for their participants, then they must have something in common.
     From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato]
     Full Idea: We say there is the form of man, horse and health, but nothing else, making the same mistake as those who say that there are gods but that they are in the form of men. They just posit eternal men, and here we are not positing forms but eternal sensibles.
     From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 997b
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato]
     Full Idea: A Form is a cause of things only in the way that white mixed with white is a cause.
     From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a
The Forms cannot be changeless if they are in changing things [Aristotle on Plato]
     Full Idea: The Forms could not be changeless if they were in changing things.
     From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 998a
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato]
     Full Idea: The greatest discovery in the history of human thought is Plato's discovery of abstract objects.
     From: comment on Plato (works [c.375 BCE]) by James Robert Brown - Philosophy of Mathematics Ch. 2
     A reaction: Compare Idea 2860! Given the diametrically opposed views, it is clearly likely that Plato's central view is the most important idea in the history of human thought, even if it is wrong.
9. Objects / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
     Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1)
     A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology.
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki]
     Full Idea: Due to the mathematical nature of structure and the teleological cause underlying the creation of Platonic wholes, these wholes are intelligible, and are in fact the proper objects of science.
     From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3
     A reaction: I like this idea, because it pays attention to the connection between how we conceive objects to be, and how we are able to think about objects. Only examining these two together enables us to grasp metaphysics.
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki]
     Full Idea: The 'structure' of an object tends to be characterised by Plato as something that is mathematically expressible.
     From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3
     A reaction: This seems to be pure Pythagoreanism (see Idea 644). Plato is pursuing Pythagoras's research programme, of trying to find mathematics buried in every aspect of reality.
Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki]
     Full Idea: Plato was less concerned than Aristotle with the project of how to account, in completely general terms, for the source of unity within a mereologically complex object.
     From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.5
     A reaction: Plato seems to have simply asserted that some sort of harmony held things together. Aristotles puts the forms [eidos] within objects, rather than external, so he has to give a fuller account of what is going on in an object. He never managed it!
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle]
     Full Idea: Plato's doctrine was that the Forms and mathematicals are two substances and that the third substance is that of perceptible bodies.
     From: report of Plato (works [c.375 BCE]) by Aristotle - Metaphysics 1028b
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
     Full Idea: The mereological sum of the coffee in my cup, the ink in this sentence, a nearby sparrow, and my left shoe is a miscellaneous mess of an object, yet its boundaries are by no means unrelated to the joints of nature.
     From: David Lewis (Putnam's Paradox [1984], 'What Might')
     A reaction: In that case they do, but if there are no atoms at the root of physics then presumably their could also be thoroughly jointless assemblages, involving probability distributions etc. Even random scattered atoms seem rather short of joints.
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki]
     Full Idea: Plato considers a 'container' model for wholes (which are disjoint from their parts) [Parm 144e3-], and a 'nihilist' model, in which only wholes are mereological atoms, and a 'bare pluralities' view, in which wholes are not really one at all.
     From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.2
     A reaction: [She cites Verity Harte for this analysis of Plato] The fourth, and best, seems to be that wholes are parts which fall under some unifying force or structure or principle.
9. Objects / D. Essence of Objects / 2. Types of Essence
Only universals have essence [Plato, by Politis]
     Full Idea: Plato argues that only universals have essence.
     From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Plato and Aristotle take essence to make a thing what it is [Plato, by Politis]
     Full Idea: Plato and Aristotle have a shared general conception of essence: the essence of a thing is what that thing is simply in virtue of itself and in virtue of being the very thing it is. It answers the question 'What is this very thing?'
     From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben]
     Full Idea: For Plato, an acceptable explanation is one such that there is no possibility of there being the opposite explanation at all, and he thought that only explanations in terms of the Forms, but never physical explanations, could meet this requirement.
     From: report of Plato (works [c.375 BCE]) by David-Hillel Ruben - Explaining Explanation Ch 2
     A reaction: [Republic 436c is cited]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Plato wanted to somehow control and purify the passions [Vlastos on Plato]
     Full Idea: Plato put high on his agenda a project which did not figure in Socrates' programme at all: the hygienic conditioning of the passions. This cannot be an intellectual process, as argument cannot touch them.
     From: comment on Plato (works [c.375 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.88
     A reaction: This is the standard traditional view of any thinker who exaggerates the importance and potential of reason in our lives.
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
     Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics
     A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven?
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
     Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind.
     From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73)
     A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
     Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not.
     From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV
     A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic.
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Causal theories of reference make errors in reference easy [Lewis]
     Full Idea: Whatever happens in special cases, causal theories usually make it easy to be wrong about the thing we refer to.
     From: David Lewis (Putnam's Paradox [1984], 'What Is')
     A reaction: I suppose the point of this is that there are no checks and balances to keep reference in focus, but just a requirement to keep connected to an increasingly attenuated causal chain.
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis]
     Full Idea: Description theories of reference are supposed to have been well and truly refuted. I think not: ..it is still tenable with my seven points, and part of the truth of reference [7: rigidity, egocentric, tokens, causal, imperfect, indeterminate, families].
     From: David Lewis (Putnam's Paradox [1984], 'Glob Desc')
     A reaction: (The bit at the end refers to his seven points, on p.59). He calls his basic proposal 'causal descriptivism', incorporating his seven slight modifications of traditional descriptivism about reference.
19. Language / F. Communication / 1. Rhetoric
Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato]
     Full Idea: Plato is liable to the charge of having been duped by a figure of speech, albeit the most profound of all, the trope of reification.
     From: comment on Plato (works [c.375 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.12
     A reaction: That might be a plausible account if his view was ridiculous, but given how many powerful friends Plato has, especially in the philosophy of mathematics, we should assume he was cleverer than that.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
Plato never refers to examining the conscience [Plato, by Foucault]
     Full Idea: Plato never speaks of the examination of conscience - never!
     From: report of Plato (works [c.375 BCE]) by Michel Foucault - On the Genealogy of Ethics p.276
     A reaction: Plato does imply some sort of self-evident direct knowledge about that nature of a healthy soul. Presumably the full-blown concept of conscience is something given from outside, from God. In 'Euthyphro', Plato asserts the primacy of morality (Idea 337).
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato]
     Full Idea: Once gods and fate and social expectation were no longer there, Plato felt it necessary to discover ethics inside human nature, not just as ethical knowledge (Socrates' view), but in the structure of the soul.
     From: comment on Plato (works [c.375 BCE]) by Bernard Williams - Shame and Necessity II - p.43
     A reaction: anti Charles Taylor
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray]
     Full Idea: Plato's legacy to European thought was a trio of capital letters - the Good, the Beautiful and the True.
     From: report of Plato (works [c.375 BCE]) by John Gray - Straw Dogs 2.8
     A reaction: It seems to have been Baumgarten who turned this into a slogan (Idea 8117). Gray says these ideals are lethal, but I identify with them very strongly, and am quite happy to see the good life as an attempt to find the right balance between them.
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle]
     Full Idea: Plato says the life of pleasure is more desirable with the addition of intelligence, and if the combination is better, pleasure is not the good.
     From: report of Plato (works [c.375 BCE]) by Aristotle - Nicomachean Ethics 1172b27
     A reaction: It is obvious why we like pleasure, but not why intelligence makes it 'better'. Maybe it is just because we enjoy intelligence?
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas]
     Full Idea: Plato came to the conclusion that virtue and happiness consist in the life of philosophy itself.
     From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.117
     A reaction: This view is obviously ridiculous, because it largely excludes almost the entire human race, which sees philosophy as a cul-de-sac, even if it is good. But virtue and happiness need some serious thought.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut]
     Full Idea: Two virtues that are ordinarily kept distinct - theoretical and practical wisdom - are joined by Plato; he thinks that neither one can be fully possessed unless it is combined with the other.
     From: report of Plato (works [c.375 BCE]) by Richard Kraut - Plato
     A reaction: I get the impression that this doctrine comes from Socrates, whose position is widely reported as 'intellectualist'. Aristotle certainly held the opposite view.
23. Ethics / F. Existentialism / 4. Boredom
Plato is boring [Nietzsche on Plato]
     Full Idea: Plato is boring.
     From: comment on Plato (works [c.375 BCE]) by Friedrich Nietzsche - Twilight of the Idols 9.2
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle]
     Full Idea: With a single exception (Plato) everyone agrees about time - that it is not generated. Democritus says time is an obvious example of something not generated.
     From: report of Plato (works [c.375 BCE]) by Aristotle - Physics 251b14