Combining Texts

All the ideas for 'talk', 'Presupposition' and 'What Required for Foundation for Maths?'

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


77 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
For the truth you need Prodicus's fifty-drachma course, not his one-drachma course [Socrates]
     Full Idea: Socrates: If I'd attended Prodicus's fifty-drachma course, I could tell you the truth about names straightway, but as I've only heard the one-drachma course, I don't know the truth about it.
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Cratylus 384b
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
A philosopher is one who cares about what other people care about [Socrates, by Foucault]
     Full Idea: Socrates asks people 'Are you caring for yourself?' He is the man who cares about the care of others; this is the particular position of the philosopher.
     From: report of Socrates (reports of career [c.420 BCE]) by Michel Foucault - Ethics of the Concern for Self as Freedom p.287
     A reaction: Priests, politicians and psychiatrists also care quite intensely about the concerns of other people. Someone who was intensely self-absorbed with the critical task of getting their own beliefs right would count for me as a philosopher.
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Socrates opened philosophy to all, but Plato confined moral enquiry to a tiny elite [Vlastos on Socrates]
     Full Idea: To confine, as Plato does in 'Republic' IV-VII, moral inquiry to a tiny elite, is to obliterate the Socratic vision which opens up the philosophic life to all.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.18
     A reaction: This doesn't mean that Plato is necessarily 'elitist'. It isn't elitist to point out that an activity is very difficult.
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Philosophical discussion involves dividing subject-matter into categories [Socrates, by Xenophon]
     Full Idea: Self-discipline and avoidance of pleasure makes people most capable of philosophical discussion, which is called 'discussion' (dialegesthai - sort out) because people divide their subject-matter into categories.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 4.5.12
     A reaction: This could be the original slogan for analytical philosophy, as far as I am concerned. I don't think philosophy aims at complete and successful analysis (cf. Idea 2958), but at revealing the structure and interconnection of ideas. This is wisdom.
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Socrates began the quest for something universal with his definitions, but he didn't make them separate [Socrates, by Aristotle]
     Full Idea: Socrates began the quest for something universal in addition to the radical flux of perceptible particulars, with his definitions. But he rightly understood that universals cannot be separated from particulars.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1086b
2. Reason / C. Styles of Reason / 1. Dialectic
It is legitimate to play the devil's advocate [Socrates]
     Full Idea: It is legitimate to play the devil's advocate.
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Phaedrus 272c
2. Reason / C. Styles of Reason / 2. Elenchus
In Socratic dialogue you must say what you believe, so unasserted premises are not debated [Vlastos on Socrates]
     Full Idea: Socrates' rule of "say only what you believe"….excluded debate on unasserted premises, thereby distinguishing Socratic from Zenonian and earlier dialectics.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.14
Socrates was pleased if his mistakes were proved wrong [Socrates]
     Full Idea: Socrates: I'm happy to have a mistaken idea of mine proved wrong.
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Gorgias 458a
The method of Socrates shows the student is discovering the truth within himself [Socrates, by Carlisle]
     Full Idea: Socrates tended to prefer the method of questioning, for this made it clear that the student was discovering the truth within himself.
     From: report of Socrates (reports of career [c.420 BCE]) by Clare Carlisle - Kierkegaard: a guide for the perplexed 7
     A reaction: Sounds like it will only facilitate conceptual analysis, and excludes empirical knowledge. Can you say to Socrates 'I'll just google that'?
Socrates always proceeded in argument by general agreement at each stage [Socrates, by Xenophon]
     Full Idea: When Socrates was setting out a detailed argument, he used to proceed by such stages as were generally agreed, because he thought that this was the infallible method of argument.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 4.6.16
     A reaction: This sounds right, and shows how strongly Socrates perceived philosophy to be a group activity, of which I approve. It seems to me that philosophy is clearly a spoken subject before it is a written one. The lonely speculator comes much later.
2. Reason / D. Definition / 2. Aims of Definition
Definitions make our intuitions mathematically useful [Mayberry]
     Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1)
2. Reason / D. Definition / 6. Definition by Essence
Socrates sought essences, which are the basis of formal logic [Socrates, by Aristotle]
     Full Idea: It is not surprising that Socrates sought essences. His project was to establish formal reasoning, of whose syllogisms essences are the foundations.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1078b22
     A reaction: This seems to reinforce the definitional view of essences, since definitions seem to be at the centre of most of Socrates's quests.
2. Reason / E. Argument / 6. Conclusive Proof
Proof shows that it is true, but also why it must be true [Mayberry]
     Full Idea: When you have proved something you know not only that it is true, but why it must be true.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2)
     A reaction: Note the word 'must'. Presumably both the grounding and the necessitation of the truth are revealed.
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle]
     Full Idea: Socrates aimed to establish formal logic, of whose syllogisms essences are the foundations. He developed inductive arguments and also general definitions.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1078b
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Logic would be more natural if negation only referred to predicates [Dummett]
     Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates.
     From: Michael Dummett (Presupposition [1960], p.27)
     A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry]
     Full Idea: Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2)
     A reaction: This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive.
There is a semi-categorical axiomatisation of set-theory [Mayberry]
     Full Idea: We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2)
     A reaction: I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry]
     Full Idea: The (misnamed!) Axiom of Infinity expresses Cantor's fundamental assumption that the species of natural numbers is finite in size.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
     Full Idea: The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2)
     A reaction: Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of size is part of the very conception of a set [Mayberry]
     Full Idea: Our very notion of a set is that of an extensional plurality limited in size.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2)
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
     Full Idea: In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-1)
     A reaction: [The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'.
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic only has its main theorems because it is so weak [Mayberry]
     Full Idea: First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.411-2)
     A reaction: He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1).
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
     Full Idea: Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Natural language 'not' doesn't apply to sentences [Dummett]
     Full Idea: Natural language does not possess a sentential negation-operator.
     From: Michael Dummett (Presupposition [1960], p.27)
     A reaction: This is a criticism of Strawson, who criticises logic for not following natural language, but does it himself with negation. In the question of how language and logic connect, this idea seems important. Term Logic aims to get closer to natural language.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
     Full Idea: The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-2)
     A reaction: Modal logic displays both approaches, with different systems for global and local domains.
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
     Full Idea: No logic which can axiomatize real analysis can have the Löwenheim-Skolem property.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
     Full Idea: The purpose of a 'classificatory' axiomatic theory is to single out an otherwise disparate species of structures by fixing certain features of morphology. ...The aim is to single out common features.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2)
Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
     Full Idea: The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2)
     A reaction: Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system.
'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
     Full Idea: The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-1)
     A reaction: A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares?
5. Theory of Logic / K. Features of Logics / 6. Compactness
No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
     Full Idea: No logic which can axiomatise arithmetic can be compact or complete.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
     A reaction: I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness).
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]
     Full Idea: We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2)
     A reaction: Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
     Full Idea: Quantities for Greeks were concrete things - lines, surfaces, solids, times, weights. At the centre of their science of quantity was the beautiful theory of ratio and proportion (...in which the notion of number does not appear!).
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2)
     A reaction: [He credits Eudoxus, and cites Book V of Euclid]
Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]
     Full Idea: The abstract objects of modern mathematics, the real numbers, were invented by the mathematicians of the seventeenth century in order to simplify and to generalize the Greek science of quantity.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
     Full Idea: In Cantor's new vision, the infinite, the genuine infinite, does not disappear, but presents itself in the guise of the absolute, as manifested in the species of all sets or the species of all ordinal numbers.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2)
Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
     Full Idea: We may describe Cantor's achievement by saying, not that he tamed the infinite, but that he extended the finite.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2)
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
If proof and definition are central, then mathematics needs and possesses foundations [Mayberry]
     Full Idea: If we grant, as surely we must, the central importance of proof and definition, then we must also grant that mathematics not only needs, but in fact has, foundations.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1)
The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry]
     Full Idea: The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1)
     A reaction: This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well.
Foundations need concepts, definition rules, premises, and proof rules [Mayberry]
     Full Idea: An account of the foundations of mathematics must specify four things: the primitive concepts for use in definitions, the rules governing definitions, the ultimate premises of proofs, and rules allowing advance from premises to conclusions.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2)
Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry]
     Full Idea: No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry]
     Full Idea: The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry]
     Full Idea: If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry]
     Full Idea: The idea that set theory must simply be identified with first-order Zermelo-Fraenkel is surprisingly widespread. ...The first-order axiomatic theory of sets is clearly inadequate as a foundation of mathematics.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-2)
     A reaction: [He is agreeing with a quotation from Skolem].
We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry]
     Full Idea: One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-1)
     A reaction: Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order.
Set theory is not just another axiomatised part of mathematics [Mayberry]
     Full Idea: The fons et origo of all confusion is the view that set theory is just another axiomatic theory and the universe of sets just another mathematical structure. ...The universe of sets ...is the world that all mathematical structures inhabit.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.416-1)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Socrates did not consider universals or definitions as having separate existence, but Plato made Forms of them [Socrates, by Aristotle]
     Full Idea: Socrates did not regard the universals or the objects of definitions as separate existents, while Plato did separate them, and called this sort of entity ideas/forms.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1078b30
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry]
     Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields.
     From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2)
     A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things).
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
For Socrates our soul, though hard to define, is our self [Vlastos on Socrates]
     Full Idea: For Socrates our soul is our self - whatever that might turn out to be.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.55
     A reaction: The problem with any broad claim like this is that we seem to be able to distinguish between essential and non-essential aspects of the self or of the soul.
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Socrates first proposed that we are run by mind or reason [Socrates, by Frede,M]
     Full Idea: It would seem that historically the decisive step was taken by Socrates in conceiving of human beings as being run by a mind or reason.. …He postulated an entity whose precision nature and function then was a matter of considerable debate.
     From: report of Socrates (reports of career [c.420 BCE]) by Michael Frede - Intro to 'Rationality in Greek Thought' p.19
     A reaction: This is, for me, a rather revelatory idea. I am keen on the fact the animals make judgements which are true and false, and also that we exhibit rationality when walking across uneven ground. So pure rationality is a cultural construct!
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
No one willingly commits an evil or base act [Socrates]
     Full Idea: I am fairly certain that no wise man believes anyone sins willingly or willingly perpetrates any evil or base act.
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Protagoras 345e
Socrates did not accept the tripartite soul (which permits akrasia) [Vlastos on Socrates]
     Full Idea: Xenophon indirectly indicates that he does not associate Socrates in any way with the tripartite psychology of the 'Republic', for within that theory akrasia would be all too possible.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.102
People do what they think they should do, and only ever do what they think they should do [Socrates, by Xenophon]
     Full Idea: There is no one who knows what they ought to do, but thinks that they ought not to do it, and no one does anything other than what they think they ought to do.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 4.6.6
     A reaction: This is Socrates' well-known rejection of the possibility of weakness of will (akrasia - lit. 'lack of control'). Aristotle disagreed, and so does almost everyone else. Modern smokers seem to exhibit akrasia. I have some sympathy with Socrates.
Socrates was shocked by the idea of akrasia, but observation shows that it happens [Aristotle on Socrates]
     Full Idea: Socrates thought it a shocking idea that when a man actually has knowledge in him something else should overmaster it, ..but this is glaringly inconsistent with the observed facts.
     From: comment on Socrates (reports of career [c.420 BCE]) by Aristotle - Nicomachean Ethics 1145b24
     A reaction: Aristotle seems very confident, but it is not at all clear (even to the agent) what is going on when apparent weakness of will occurs (e.g. breaking a diet). What exactly does the agent believe at the moment of weakness?
The common belief is that people can know the best without acting on it [Socrates]
     Full Idea: Most people think there are many who recognise the best but are unwilling to act on it.
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Protagoras 352d
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
For Socrates, wisdom and prudence were the same thing [Socrates, by Xenophon]
     Full Idea: Socrates did not distinguish wisdom from prudence, but judged that the man who recognises and puts into practice what is truly good, and the man who knows and guards against what is disgraceful, are both wise and prudent.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 3.9.3
     A reaction: Compare Aristotle, who separates them, claiming that prudence is essential for moral virtue, but wisdom is pursued at a different level, closer to the gods than to society.
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
For Socrates, virtues are forms of knowledge, so knowing justice produces justice [Socrates, by Aristotle]
     Full Idea: Socrates thought that the virtues were all forms of knowledge, and therefore once a man knew justice, he would be a just man.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Eudemian Ethics 1216b07
     A reaction: The clearest possible statement of Socrates' intellectualism. Aristotle rejected the Socrates view, but I find it sympathetic. Smokers who don't want to die seem to be in denial. To see the victims is to condemn the crime.
Socrates was the first to base ethics upon reason, and use reason to explain it [Taylor,R on Socrates]
     Full Idea: Socrates was the first significant thinker to try basing ethics upon reason, and to try uncovering its natural principles solely by the use of reason.
     From: comment on Socrates (reports of career [c.420 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.7
     A reaction: Interesting. It seems to me that Socrates overemphasised reason, presumably because it was a novelty. Hence his view that akrasia is impossible, and that virtue is simply knowledge. Maybe action is not just rational, but moral action is.
All human virtues are increased by study and practice [Socrates, by Xenophon]
     Full Idea: If you consider the virtues that are recognised among human beings, you will find that they are all increased by study and practice.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 2.6.41
     A reaction: 'Study' is the intellectualist part of this remark; the reference to 'practice' fits with Aristotle view that virtue is largely a matter of good habits. The next question would be how theoretical the studies should be. Philosophy, or newspapers?
The wise perform good actions, and people fail to be good without wisdom [Socrates, by Xenophon]
     Full Idea: It is the wise who perform truly good actions, and those who are not wise cannot, and, if they try to, fail.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 3.9.6
     A reaction: The essence of Socrates' intellectualism, with which Aristotle firmly disagreed (when he assert that only practical reason was needed for virtuous actions, rather than wisdom or theory). Personally I side more with Socrates than with Aristotle on this.
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Socrates despised good looks [Socrates, by Plato]
     Full Idea: Socrates despises good looks to an almost inconceivable extent.
     From: report of Socrates (reports of career [c.420 BCE]) by Plato - The Symposium 216e
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Socrates conservatively assumed that Athenian conventions were natural and true [Taylor,R on Socrates]
     Full Idea: Socrates' moral philosophy was essentially conservative. He assumed that the principles the Athenians honoured were true and natural, so there was little possibility of conflict between nature and convention in his thinking.
     From: comment on Socrates (reports of career [c.420 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8
     A reaction: Taylor contrasts Socrates with Callicles, who claims that conventions oppose nature. This fits with Nietzsche's discontent with Socrates, as the person who endorses conventional good and evil, thus constraining the possibilities of human nature.
22. Metaethics / B. Value / 2. Values / b. Successful function
A well-made dung basket is fine, and a badly-made gold shield is base, because of function [Socrates, by Xenophon]
     Full Idea: A dung-basket is fine, and a golden shield contemptible, if the one is finely and the other badly constructed for carrying out its function.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 3.8.6
     A reaction: This is the basis of a key idea in Aristotle, that virtue (or excellence) arises directly from function. I think it is the most important idea in virtue theory, and seems to have struck most Greeks as being self-evident.
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Things are both good and fine by the same standard [Socrates, by Xenophon]
     Full Idea: Things are always both good and fine by the same standard.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 3.8.5
     A reaction: This begs many questions, but perhaps it leads to what we call intuitionism, which is an instant ability is perceive a fine action (even in an enemy). This leads to the rather decadent view that the aim of life is the production of beauty.
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
The only good is knowledge, and the only evil is ignorance [Socrates, by Diog. Laertius]
     Full Idea: There is only one good, namely knowledge, and there is only one evil, namely ignorance.
     From: report of Socrates (reports of career [c.420 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.4.14
     A reaction: Ignorance of how to commit evil sounds quite good.
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Socrates was the first to put 'eudaimonia' at the centre of ethics [Socrates, by Vlastos]
     Full Idea: Socrates' true place in the development of Greek thought is that he is the first to establish the eudaimonist foundation of ethical theory, which became the foundation of the schools which sprang up around him.
     From: report of Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.10
     A reaction: I suspect that he was the first to fully articulate a widely held Greek belief. The only ethical question that they asked was about the nature of a good human life.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
By 'areté' Socrates means just what we mean by moral virtue [Vlastos on Socrates]
     Full Idea: Socrates uses the word 'areté' to mean precisely what we mean by moral virtue.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.200
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Socrates is torn between intellectual virtue, which is united and teachable, and natural virtue, which isn't [PG on Socrates]
     Full Idea: Socrates worries about the unity and teachability of virtue because he is torn between virtue as intellectual (unified and teachable) and virtue as natural (plural and unteachable).
     From: comment on Socrates (reports of career [c.420 BCE]) by PG - Db (ideas)
     A reaction: Admittedly virtue could be natural but still unified and teachable, but Socrates clearly had a dilemma, and this seems to make sense of it.
Socrates agrees that virtue is teachable, but then denies that there are teachers [Socrates, by MacIntyre]
     Full Idea: Socrates' great point of agreement with the sophists is his acceptance of the thesis that areté is teachable. But paradoxically he denies that there are teachers.
     From: report of Socrates (reports of career [c.420 BCE]) by Alasdair MacIntyre - A Short History of Ethics Ch.3
     A reaction: This is part of Socrates's presentation of himself as 'not worthy'. Virtue would be teachable, if only anyone knew what it was. He's wrong. Lots of people have a pretty good idea of virtue, and could teach it. The problem is in the pupils.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We should ask what sort of people we want to be [Socrates]
     Full Idea: Socrates: What sort of person should one be?
     From: Socrates (reports of career [c.420 BCE]), quoted by Plato - Gorgias 487e
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
Socrates believed that basically there is only one virtue, the power of right judgement [Socrates, by Williams,B]
     Full Idea: Socrates believed that basically there is only one virtue, the power of right judgement.
     From: report of Socrates (reports of career [c.420 BCE]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.1
     A reaction: Which links with Aristotle's high place for 'phronesis' (prudence?). The essence of Socrates' intellectualism. Robots and saints make very different judgements, though.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Socrates made the civic values of justice and friendship paramount [Socrates, by Grayling]
     Full Idea: In Socrates' thought, the expressly civic values of justice and friendship became paramount.
     From: report of Socrates (reports of career [c.420 BCE]) by A.C. Grayling - What is Good? Ch.2
     A reaction: This is the key move in ancient ethics, away from heroism, and towards the standard Aristotelian social virtues. I say this is the essence of what we call morality, and the only one which can be given a decent foundational justification (social health).
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Courage is scientific knowledge [Socrates, by Aristotle]
     Full Idea: Socrates thought that courage is scientific knowledge.
     From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Eudemian Ethics 1230a06
     A reaction: Aristotle himself says that reason produces courage, but he also says it arises from natural youthful spirits. I favour the view that there is a strong rational component in true courage.
23. Ethics / F. Existentialism / 1. Existentialism
Socrates emphasises that the knower is an existing individual, with existence his main task [Socrates, by Kierkegaard]
     Full Idea: The infinite merit of the Socratic position was precisely to accentuate the fact that the knower is an existing individual, and that the task of existing is his essential task.
     From: report of Socrates (reports of career [c.420 BCE]) by Søren Kierkegaard - Concluding Unscientific Postscript 'Inwardness'
     A reaction: Always claim Socrates as the first spokesman for your movement! It is true that Socrates is always demanding the views of his interlocutors, and not just abstract theories. See Idea 1647.
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Obedience to the law gives the best life, and success in war [Socrates, by Xenophon]
     Full Idea: A city in which the people are most obedient to the laws has the best life in time of peace and is irresistible in war.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Memorabilia of Socrates 4.4.15
     A reaction: This is a conservative view, with the obvious problem case of bad laws, but in general it seems to me clearly right. This is why it is so vital that nothing should be done to bring the law into disrepute, such as petty legislation or prosecution.
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Socrates was the first to grasp that a cruelty is not justified by another cruelty [Vlastos on Socrates]
     Full Idea: Socrates was the first Greek to grasp the truth that if someone has done a nasty thing to me, this does not give the slightest moral justification for doing anything nasty to him.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.190
25. Social Practice / F. Life Issues / 5. Sexual Morality
A lover using force is a villain, but a seducer is much worse, because he corrupts character [Socrates, by Xenophon]
     Full Idea: The fact that a lover uses not force but persuasion makes him more detestable, because a lover who uses force proves himself a villain, but one who uses persuasion ruins the character of the one who consents.
     From: report of Socrates (reports of career [c.420 BCE]) by Xenophon - Symposium 8.20
     A reaction: A footnote says that this distinction was enshrined in Athenian law, where seduction was worse than rape. This is a startling and interest contrast to the modern view, which enshrines rights and freedoms, and says seduction is usually no crime at all.
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Socrates holds that right reason entails virtue, and this must also apply to the gods [Vlastos on Socrates]
     Full Idea: It is essential to Socrates' rationalist programme in theology to assume that the entailment of virtue by wisdom binds gods no less than men. He would not tolerate one moral standard for me and another for gods.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.164
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
A new concept of God as unswerving goodness emerges from Socrates' commitment to virtue [Vlastos on Socrates]
     Full Idea: Undeviating beneficent goodness guides Socrates' thought so deeply that he applies it even to the deity; he projects a new concept of god as a being that can cause only good, never evil.
     From: comment on Socrates (reports of career [c.420 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.197