Combining Texts

All the ideas for 'works', 'The Architecture of Mathematics' and 'works'

unexpand these ideas     |    start again     |     specify just one area for these texts


42 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
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin]
     Full Idea: In Peirce's system, a super-ordinate discipline provides general laws or principles for subordinate disciplines, which in turn provide concrete examples of those general laws.
     From: report of Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 1 'System'
     A reaction: Does he really mean that subordinate disciplines have no principles or laws? That can't be right.
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.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak]
     Full Idea: In Peirce's naturalist view of truth, it is a catch-all for the particular local aims of enquiry - empirical adequacy, predictive power, coherence, simplicity, elegance, explanatory power, a reliable guide to action, fruitfulness, great understanding.
     From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 1
     A reaction: The aims I cited in my thesis on explanation. One given, for me, is that truth is an ideal, which may or may not be attainable, to varying degrees. It is just what thinking aims at. I suspect, though, that these listed items have one thing in common.
Peirce did not think a belief was true if it was useful [Peirce, by Misak]
     Full Idea: Peirce was not in the slightest bit tempted by the thought that a belief is true if it is useful.
     From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2
     A reaction: All students of the pragmatic theory of truth should start with this idea, because it rejects the caricature view of pragmatic truth, a view which is easily rebutted. James seems to have been guilty of this sin.
If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce]
     Full Idea: Two related worries about Peirce's account of truth are (from Royce) what are we to make of truth if enquiry never reaches an end, and (from Russell) what are we to make of truth if enquiry ends prematurely?
     From: comment on Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 3 'issues'
     A reaction: The defence of Peirce must be that the theory is not holistic - referring to the whole Truth about absolutely everything. The discovery of the periodic table seems to me to support Peirce. In many areas basic enquiry has reached an end.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce]
     Full Idea: The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care.
     From: Charles Sanders Peirce (works [1892], CP5.567), quoted by Albert Atkin - Peirce 3 'separation'
     A reaction: [Dated 1902] Maybe we should identify a huge branch of human learning as Hyptheticals. Professor of Hypotheticals at Cambridge University. The trouble is it would have to include computer games. So why does maths matter more than games?
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak]
     Full Idea: Peirce takes bivalence not to be a law of logic, but a regulative assumption of enquiry.
     From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2 n10
     A reaction: I like this. For most enquiries it's either true or not true, it's either there or it's not there. When you aren't faced with these simple dichotomies (in history, or quantum mechanics) you can relax, and allow truth value gaps etc.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
     Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
     From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
     A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.
7. Existence / D. Theories of Reality / 3. Reality
The real is the idea in which the community ultimately settles down [Peirce]
     Full Idea: The real is the idea in which the community ultimately settles down.
     From: Charles Sanders Peirce (works [1892]), quoted by Martin Kusch - Knowledge by Agreement Ch.16
     A reaction: If this is anti-realism, then I don't like it. If it is realist, then it is probably a bit on the optimistic side (if you think about cultures that are into witchcraft and voodoo).
8. Modes of Existence / A. Relations / 1. Nature of Relations
Peirce and others began the mapping out of relations [Peirce, by Hart,WD]
     Full Idea: It was Peirce and Schröder in the nineteenth century who began a systematic taxonomy of relations.
     From: report of Charles Sanders Peirce (works [1892], 4) by William D. Hart - The Evolution of Logic 4
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 / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin]
     Full Idea: The realism about possibilities, generalities, tendencies and habits that we find in Peirce's later maxim is something that the logical positivists would have been uncomfortable with.
     From: report of Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 2 'Concl'
     A reaction: Atkin examines the various later statements of the earlier maxim, given here in Idea 21490. Ryle and Quine express the empiricist and logical positivist approach to dispositions.
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 / 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 / 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
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
The possible can only be general, and the force of actuality is needed to produce a particular [Peirce]
     Full Idea: The possible is necessarily general…..It is only actuality, the force of existence, which bursts the fluidity of the general and produces a discrete unit.
     From: Charles Sanders Peirce (works [1892]), quoted by François Recanati - Mental Files 13.1
     A reaction: [Papers 4 1967:147] This was quoted by Prior, and is often cited. Recanati is interested in the notion of a singular thought being tied to actuality, by generating a mental file.
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce]
     Full Idea: Inquiry is not standing upon a bedrock of fact. It is walking up a bog, and can only say, this ground seems to hold for the present. Here I will stay until it begins to give way.
     From: Charles Sanders Peirce (works [1892], CP 5.589), quoted by Gottfried Leibniz - Letter to Newton 4
     A reaction: [I don't know which article this lovely quote comes from]
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.
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