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All the ideas for 'works', 'The Nature of Mathematical Knowledge' and 'Quaestiones de Potentia Dei'

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63 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.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
     Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
     Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets).
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2
     A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist.
Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
     Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts).
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3)
     A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means.
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
     Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3)
     A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means.
The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
     Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4)
     A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
     Full Idea: The real numbers stand to measurement as the natural numbers stand to counting.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
     Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A one-operation is the segregation of a single object [Kitcher]
     Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3)
     A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The old view is that mathematics is useful in the world because it describes the world [Kitcher]
     Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
     Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2)
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
     Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2)
Mathematical intuition is not the type platonism needs [Kitcher]
     Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3)
     A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'.
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
     Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1)
     A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematical knowledge arises from basic perception [Kitcher]
     Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to.
My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
     Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction.
We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
     Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2)
     A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction.
The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
     Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
     Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I)
     A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Arithmetic is an idealizing theory [Kitcher]
     Full Idea: I construe arithmetic as an idealizing theory.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'.
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
     Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics.
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
     Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory.
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
     Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
     Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1)
     A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them?
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
     Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6)
     A reaction: Nice question! He's a fan of getting at the explanatory in mathematics.
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
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
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?
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
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
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
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 / 2. Abstract Objects / b. Need for abstracta
Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
     Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing.
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 / 1. Unifying an Object / b. Unifying aggregates
'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas]
     Full Idea: There are two sorts of one. There is the one which is convertible with being, which adds nothing to being except being undivided; and this deprives of multitude. Then there is the principle of number, which to the notion of being adds measurement.
     From: Thomas Aquinas (Quaestiones de Potentia Dei [1269], q3 a16 ad 3-um)
     A reaction: [From a lecture handout] I'm not sure I understand this. We might say, I suppose, that insofar as water is water, it is all one, but you can't count it. Perhaps being 'unified' and being a 'unity' are different?
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 / 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
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
     Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4)
     A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
In long mathematical proofs we can't remember the original a priori basis [Kitcher]
     Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2)
     A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2.
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
     Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3)
     A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view.
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
     Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6)
     A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
     Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2)
     A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]
     Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence.
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3
     A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation
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]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
     Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man.
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.
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