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All the ideas for 'Frege philosophy of mathematics', 'The Scientific Image' and 'Phaedrus'

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56 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Can we understand an individual soul without knowing the soul in general? [Plato]
     Full Idea: Do you think it possible to form an adequate conception of the nature of an individual soul without considering the nature of soul in general?
     From: Plato (Phaedrus [c.366 BCE], 270c)
     A reaction: Do animals understand anything (as opposed to simply being aware of things)?
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato]
     Full Idea: When I believe that I have found in anyone the ability to discuss unity and plurality as they exist in the nature of things, I follow his footsteps as if he was a god.
     From: Plato (Phaedrus [c.366 BCE], 266b)
     A reaction: This sounds like the problem of identity, which is at the heart of modern metaphysics.
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
A speaker should be able to divide a subject, right down to the limits of divisibility [Plato]
     Full Idea: A speaker must be able to define a subject generically, and then to divide it into its various specific kinds until he reaches the limits of divisibility.
     From: Plato (Phaedrus [c.366 BCE], 277b)
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
     Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11)
     A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
     Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
     Full Idea: A prime number is one which is measured by a unit alone.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11)
     A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
     Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
     Full Idea: A number is a multitude composed of units.
     From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2)
     A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
     Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
     Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that.
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
     Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)
     A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
     Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
     Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't.
7. Existence / D. Theories of Reality / 2. Realism
Reasoning needs to cut nature accurately at the joints [Plato]
     Full Idea: In our reasoning we need a clear view of the ability to divide a genus into species, observing the natural joints, not mangling any of the parts, like an unskilful butcher.
     From: Plato (Phaedrus [c.366 BCE], 265d)
     A reaction: In modern times this Platonic idea has become the standard metaphor for realism. I endorse it. I think nature has joints, and we should hunt for them. There are natural sets. The joints may exist in abstract concepts, as well as in objects.
Realism is just the application of two-valued semantics to sentences [Dummett]
     Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist.
7. Existence / E. Categories / 2. Categorisation
I revere anyone who can discern a single thing that encompasses many things [Plato]
     Full Idea: If I believe that someone is capable of discerning a single thing that is also by nature capable of encompassing many, I follow 'straight behind, in his footsteps, as if he were a god'.
     From: Plato (Phaedrus [c.366 BCE], 266b)
     A reaction: [Plato quote Odyssey 2.406] This is the sort of simple but profound general observation which only the early philosophers bothered to make, and no one comments on now. Encompassing many under one is the very essence of thinking.
8. Modes of Existence / D. Universals / 2. Need for Universals
It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato]
     Full Idea: It takes a man to understand by the use of universals, and to collect out of the multiplicity of sense-impressions a unity arrived at by a process of reason.
     From: Plato (Phaedrus [c.366 BCE], 249b)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato]
     Full Idea: What overpowering love knowledge would inspire if it could bring a clear image of itself before our sight, and the same may be said of the other forms.
     From: Plato (Phaedrus [c.366 BCE], 250d)
     A reaction: the motivation in Plato's theory
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
     Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts.
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
     Full Idea: The existence of abstract objects is a pseudo-problem.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18)
     A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought.
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
     Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'.
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
     Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object.
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
     Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15)
     A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology.
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
     Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta?
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
     Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12
     A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable.
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
     Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10)
     A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria.
10. Modality / A. Necessity / 11. Denial of Necessity
Empiricists deny what is unobservable, and reject objective modality [Fraassen]
     Full Idea: To be an empiricist is to withhold belief in anything that goes beyond the actual, observable phenomena, and to recognise no objective modality in nature.
     From: Bas C. van Fraassen (The Scientific Image [1980], p.202), quoted by J Ladyman / D Ross - Every Thing Must Go 2.3.1
     A reaction: To only believe in what is actually observable strikes me as ridiculous. It might be, though, that we observe modality, in observing dispositions. If you pull back a bowstring, you feel the possibilities.
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird]
     Full Idea: To 'accept' a theory is not to believe it, but is instead to believe it to be empirically adequate.
     From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Alexander Bird - Philosophy of Science Ch.4
     A reaction: The second half of this doesn't avoid the word 'belief'. Nevertheless the suggestion is that we never believe (i.e. commit to truth) ever again. So you avoid an on-coming bus because the threat appears to be 'empirically adequate'. Hm.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
True knowledge is of the reality behind sense experience [Plato]
     Full Idea: True knowledge is concerned with the abode of true reality, without colour or shape, intangible but utterly real, apprehensible only to the intellect.
     From: Plato (Phaedrus [c.366 BCE], 247c)
14. Science / A. Basis of Science / 5. Anomalies
If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato]
     Full Idea: There are some occasions when both prosecution and defence should positively suppress the facts in favour of probability, if the facts are improbable.
     From: Plato (Phaedrus [c.366 BCE], 272e)
14. Science / B. Scientific Theories / 2. Aim of Science
To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen]
     Full Idea: Science aims to give us theories which are empirically adequate; and acceptance of a theory involves as belief only that it is empiricially adequate.
     From: Bas C. van Fraassen (The Scientific Image [1980], p.12), quoted by J Ladyman / D Ross - Every Thing Must Go 2.3.1
     A reaction: This won't tell us what to do if there is a tie between two theories, and we will want to know the criteria for 'adequate'. Presumably there are theories which are empirically quite good, but not yet acceptable. Theories commit beyond experience.
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird]
     Full Idea: Van Fraassen asks why we should think that the actual explanation of the evidence should be found among the theories we are considering, when there must be an infinity of theories which are also potential explanations of the evidence?
     From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Alexander Bird - Philosophy of Science Ch.4
     A reaction: This has become one of the leading modern anti-realist arguments. We must introduce an element of faith here; presumably evolution makes us experts on immediate puzzles, competent on intermediate ones, and hopeful on remote ones.
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
An explanation is just descriptive information answering a particular question [Fraassen, by Salmon]
     Full Idea: On van Fraassen's theory an explanation is simply an answer to a why-question; it is nothing other than descriptive information that, in a given context, answers a particular type of question.
     From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Wesley Salmon - Four Decades of Scientific Explanation 4.3
     A reaction: Presumably we would need some sort of criterion for a 'good' explanation, and it seems to me that a very good explanation might be given which was nevertheless beyond the grasp of the questioner.
15. Nature of Minds / A. Nature of Mind / 2. Psuche
The soul is self-motion [Plato]
     Full Idea: Self-motion is of the very nature of the soul.
     From: Plato (Phaedrus [c.366 BCE], 245e)
     A reaction: This culminates a length discussion of the soul. He gives an implausible argument that the soul is immortal, because it could never cease its self-motion. Why are we so unimpressed by motion, when the Greeks were amazed by it?
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie]
     Full Idea: Plato had a conception of the emotions and our bodily appetites as being like wild horses, to be harnassed and controlled by reason.
     From: report of Plato (Phaedrus [c.366 BCE]) by Peter Goldie - The Emotions 4 'Education'
     A reaction: This seems to make Plato the patriarch of puritanism. See Symposium, as well as Phaedrus. But bringing up children can often seem like taming wild beasts.
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
     Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help!
An argument for conceptual priority is greater simplicity in explanation [Dummett]
     Full Idea: An argument for conceptual priority is greater simplicity in explanation.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12)
     A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?).
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
     Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16)
     A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
     Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'.
     From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14
     A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981.
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
     Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14)
     A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction...
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
     Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'.
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
     Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects.
     From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)
     A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc.
19. Language / F. Communication / 1. Rhetoric
Only a good philosopher can be a good speaker [Plato]
     Full Idea: Unless a man becomes an adequate philosopher he will never be an adequate speaker on any subject.
     From: Plato (Phaedrus [c.366 BCE], 261a)
     A reaction: Depends. Hitler showed little sign of clear philosophical thinking, but the addition of lights and uniforms seemed to sweep reasonably intelligent people along with him.
'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato]
     Full Idea: The purpose of the 'Phaedrus' is to pioneer the notion of philosophical rhetoric.
     From: comment on Plato (Phaedrus [c.366 BCE], Ch.10) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment
     A reaction: This is a wonderfully challenging view of what Plato was up to. One might connect it with Rorty's claim that philosophy should move away from epistemology and analysis, towards hermeneutics, which sounds to me like rhetoric. 'Phaedrus' is beautiful.
An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato]
     Full Idea: If a speech is to be classed as excellent, does that not presuppose knowledge of the truth about the subject of the speech in the mind of the speaker.
     From: Plato (Phaedrus [c.366 BCE], 259e)
     A reaction: I like the thought that Plato's main interest was rhetoric, but with the view that the only good rhetoric is truth-speaking. It would be hard to admire a speech if you disagreed with it.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is the clearest and most lovely of the Forms [Plato]
     Full Idea: Only beauty has the privilege of being the most clearly discerned and the most lovely of the forms.
     From: Plato (Phaedrus [c.366 BCE], 250e)
     A reaction: the motivation in Plato's theory
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato]
     Full Idea: In each one of us there are two ruling and impelling principles: a desire for pleasure, which is innate, and an acquired conviction which causes us to aim at excellence.
     From: Plato (Phaedrus [c.366 BCE], 237d)
     A reaction: This division is too neat and simple. An obsession with pleasure I would take to be acquired. If you set out to do something, I think there is an innate desire to do it well.
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Most pleasure is release from pain, and is therefore not worthwhile [Plato]
     Full Idea: Life is not worth living for pleasures whose enjoyment entirely depends on previous sensation of pain, like almost all physical pleasures.
     From: Plato (Phaedrus [c.366 BCE], 258e)
     A reaction: Eating exotic food which is hard to obtain? (Pay someone to obtain it). Rock climbing. Training for sport.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Reason impels us towards excellence, which teaches us self-control [Plato]
     Full Idea: The conviction which impels us towards excellence is rational, and the power by which it masters us we call self-control.
     From: Plato (Phaedrus [c.366 BCE], 237e)
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Bad people are never really friends with one another [Plato]
     Full Idea: It is not ordained that bad men should be friends with one another.
     From: Plato (Phaedrus [c.366 BCE], 255b)
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
     Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval?
     From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit')
27. Natural Reality / E. Cosmology / 3. The Beginning
If the prime origin is destroyed, it will not come into being again out of anything [Plato]
     Full Idea: If the prime origin is destroyed, it will not come into being again out of anything.
     From: Plato (Phaedrus [c.366 BCE], 245d)
     A reaction: This is the essence of Aquinas's Third Way of proving God's existence.
28. God / A. Divine Nature / 3. Divine Perfections
The mind of God is fully satisfied and happy with a vision of reality and truth [Plato]
     Full Idea: The mind of a god, sustained by pure intelligence and knowledge, is satisfied with the vision of reality, and nourished and made happy by the vision of truth.
     From: Plato (Phaedrus [c.366 BCE], 247d)
28. God / C. Attitudes to God / 4. God Reflects Humanity
We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato]
     Full Idea: Because we have never seen or formed an adequate idea of a god, we picture him to ourselves as a being of the same kind as ourselves but immortal.
     From: Plato (Phaedrus [c.366 BCE], 246d)
28. God / C. Attitudes to God / 5. Atheism
There isn't a single reason for positing the existence of immortal beings [Plato]
     Full Idea: There is not a single sound reason for positing the existence of such a being who is immortal
     From: Plato (Phaedrus [c.366 BCE], 246d)
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Soul is always in motion, so it must be self-moving and immortal [Plato]
     Full Idea: All soul is immortal, for what is always in motion is immortal. Only that which moves itself never ceases to be in motion.
     From: Plato (Phaedrus [c.366 BCE], 245c)