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All the ideas for 'Thinking About Mathematics', 'The Question of Realism' and 'fragments/reports'

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78 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Epicurus accepted God in his popular works, but not in his writings on nature [Epicurus, by Sext.Empiricus]
     Full Idea: Epicurus in his popular exposition allows the existence of God, but in expounding the real nature of things he does not allow it.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Sextus Empiricus - Against the Physicists (two books) I.58
     A reaction: Plato and Aristotle also distinguished their esoteric from their exoteric writings, but this is an indication that thei popular works may always have presented safer doctrines.
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Slavery to philosophy brings true freedom [Epicurus]
     Full Idea: To win true freedom you must be a slave to philosophy.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Seneca the Younger - Letters from a Stoic 008
     A reaction: A lovely idea. It is one thing to free the body, or to free one's social situation, but the challenge to 'free your mind' is either romantic nonsense or totally baffling, apart from the suggestion offered here. Reason is freedom. Very Kantian.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims at a happy life, through argument and discussion [Epicurus]
     Full Idea: Philosophy is an activity which secures the happy life by arguments and discussions.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Sextus Empiricus - Against the Ethicists (one book) VI.169
     A reaction: Presumably this aims at the happiness of the participant. Universal happiness would need to be much more political. If this is your aim then you can't just follow the winds of the argument, but must channel it towards happiness. No nasty truths?
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
We should come to philosophy free from any taint of culture [Epicurus]
     Full Idea: I congratulate you, sir, because you have come to philosophy free of any taint of culture.
     From: Epicurus (fragments/reports [c.289 BCE])
     A reaction: [source: Athenaeus, 'Deipnosophists' 13 588b] No one nowadays thinks such an aspiration remotely possible, not least because the culture is embedded in your native language, but I find the idea very appealing.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / f. Philosophy as healing
The aim of medicine is removal of sickness, and philosophy similarly removes our affections [Epicurus]
     Full Idea: Just as there is no benefit to medicine if it does not heal the sicknesses [nosos] of bodies, so too there is none to philosophy unless it expels that affections of the soul.
     From: Epicurus (fragments/reports [c.289 BCE], fr 221), quoted by James Allen - Soul's Virtue and the Health of the Body p.78
     A reaction: This sounds rather Buddhist, if the only route to happiness is to suppress the emotions. Epicurus probably refers to the more extreme desires, which only lead to harm. Galen quotes Chrysippus as endorsing this idea (see footnote 5).
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K]
     Full Idea: If there is no way of settling metaphysical questions, then who cares whether or not they make sense?
     From: Kit Fine (The Question of Realism [2001], 4 n20)
     A reaction: This footnote is aimed at logical positivists, who seemed to worry about whether metaphysics made sense, and also dismissed its prospects even if it did make sense.
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K]
     Full Idea: The 'quietist' view of metaphysics says that realist metaphysics should be abandoned, not because its questions cannot be framed, but because their answers cannot be found. The real world of metaphysics is akin to Kant's noumenal world.
     From: Kit Fine (The Question of Realism [2001], 4)
     A reaction: [He cites Blackburn, Dworkin, A.Fine, and Putnam-1987 as quietists] Fine aims to clarify the concepts of factuality and of ground, in order to show that metaphysics is possible.
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
We should say nothing of the whole if our contact is with the parts [Epicurus, by Plutarch]
     Full Idea: We should make no assertion about the whole when our contact is with the parts.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109e
2. Reason / C. Styles of Reason / 1. Dialectic
Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero]
     Full Idea: Epicurus despises and laughs at the whole of dialectic.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - Academica II.30.97
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero]
     Full Idea: Epicurus said that not every proposition is either true or false. ...Epicurus was afraid that if he admits that every proposition is true or false he will also have to admit that all events are caused by fate (if they are so from all eternity).
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.21
     A reaction: Epicurus proposed his 'swerve' in the movements of atoms to avoid this fatalism. Epicurus is agreeing with Aristotle, who did not accept excluded middle for a future contingent sea-fight.
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
     Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero]
     Full Idea: Epicureans make the impudent assertion that disjunctions consisting of contrary propositions are true, but that the statements contained in the propositions are neither of them true.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 16.36
     A reaction: Is that 'it is definitely one or the other, but we haven't a clue which one'? Seems to fit speculations about Goldbach's Conjecture. It doesn't sound terribly impudent to me. Or is it the crazy 'It's definitely one of them, but it's neither of them'?
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
     Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
     Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4)
     A reaction: The sequence is 'Cauchy' if N exists.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
     Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7)
     A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
     Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2)
     A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
     Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate.
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
     Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1)
     A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
     Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1)
     A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
     Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names?
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1)
     A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up.
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
     Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2)
     A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare.
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
     Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2)
     A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
     Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1)
     A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
     Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1)
     A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
     Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
     A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise.
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K]
     Full Idea: My main objection to Fine's notion of grounding as fundamental is that it violates 'purity' - that fundamental truths should involve only fundamental notions.
     From: comment on Kit Fine (The Question of Realism [2001]) by Theodore Sider - Writing the Book of the World 08.2
     A reaction: [p.106 of Sider for 'purity'] The point here is that to define a grounding relation you have to mention the 'higher' levels of the relationship (as in a 'city' being grounded in physical stuff), which doesn't seem fundamental enough.
Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider]
     Full Idea: When p 'grounds' q then q holds in virtue of p's holding; q's holding is nothing beyond p's holding; the truth of p explains the truth of q in a particularly tight sense (explanation of q by p in this sense requires that p necessitates q).
     From: report of Kit Fine (The Question of Realism [2001], 15-16) by Theodore Sider - Writing the Book of the World 08.1
     A reaction: This proposal has become a hot topic in current metaphysics, as attempts are made to employ 'grounding' in various logical, epistemological and ontological contexts. I'm a fan - it is at the heart of metaphysics as structure of reality.
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
Grounding relations are best expressed as relations between sentences [Fine,K]
     Full Idea: I recommend that a statement of ground be cast in the following 'canonical' form: Its being the case that S consists in nothing more than its being the case that T, U... (where S, T, U... are particular sentences).
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: The point here is that grounding is to be undestood in terms of sentences (and 'its being the case that...'), rather than in terms of objects, properties or relations. Fine thus makes grounding a human activity, rather than a natural activity.
7. Existence / C. Structure of Existence / 2. Reduction
Reduction might be producing a sentence which gets closer to the logical form [Fine,K]
     Full Idea: One line of reduction is logical analysis. To say one sentence reduces to another is to say that they express the same proposition (or fact), but the grammatical form of the second is closer to the logical form than the grammatical form of the first.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: Fine objects that S-and-T reduces to S and T, which is two propositions. He also objects that this approach misses the de re ingredient in reduction (that it is about the things themselves, not the sentences). It also overemphasises logical form.
Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K]
     Full Idea: A second line of reduction is semantic, and holds in virtue of the meaning of the sentences. It should then be possible to acquire an understanding of the reduced sentence on the basis of understanding the sentences to which it reduces.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: Fine says this avoids the first objection to the grammatical approach (see Reaction to Idea 15050), but still can't handle the de re aspect of reduction. Fine also doubts whether this understanding qualifies as 'reduction'.
Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K]
     Full Idea: The third, more recent, approach to reduction is a modal matter. A class of propositions will reduce to - or supervene upon - another if, necessarily, any truth from the one is entailed by truths from the other.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: [He cites Armstrong, Chalmers and Jackson for this approach] Fine notes that some people reject supervenience as a sort of reduction. He objects that this reduction doesn't necessarily lead to something more basic.
The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K]
     Full Idea: The notion of ground should be distinguished from the strict notion of reduction. A statement of reduction implies the unreality of what is reduced, but a statement of ground does not.
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: That seems like a bit of a caricature of reduction. If you see a grey cloud and it reduces to a swarm of mosquitoes, you do not say that the cloud was 'unreal'. Fine is setting up a stall for 'ground' in the metaphysical market. We all seek structure.
7. Existence / D. Theories of Reality / 3. Reality
What is real can only be settled in terms of 'ground' [Fine,K]
     Full Idea: Questions of what is real are to be settled upon the basis of considerations of ground.
     From: Kit Fine (The Question of Realism [2001], Intro)
     A reaction: This looks like being one of Fine's most important ideas, which is shifting the whole basis of contemporary metaphysics. Only Parmenides and Heidegger thought Being was the target. Aristotle aims at identity. What grounds what is a third alternative.
In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K]
     Full Idea: The first main approach says metaphysical reality is to be identified with what is 'objective' or 'factual'. ...According to the second conception, metaphysical reality is to be identified with what is 'irreducible' or 'fundamental'.
     From: Kit Fine (The Question of Realism [2001], 1)
     A reaction: Fine is defending the 'fundamental' approach, via the 'grounding' relation. The whole structure, though, seems to be reality. In particular, a complete story must include the relations which facilitate more than mere fundamentals.
Why should what is explanatorily basic be therefore more real? [Fine,K]
     Full Idea: We may grant that some things are explanatorily more basic than others, but why should that make them more real?
     From: Kit Fine (The Question of Realism [2001], 8)
     A reaction: This is the question asked by the 'quietist'. Fine's answer is that our whole conception of Reality, with its intrinsic structure, is what lies at the basis, and this is primitive.
Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K]
     Full Idea: I conclude that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms.
     From: Kit Fine (The Question of Realism [2001], Intro)
     A reaction: Fine offers arguments to support his claim, but it seems hard to disagree with. The only alternative I can see is to understand reality in terms of our experiences, and this is the road to metaphysical hell.
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius]
     Full Idea: We could not seek for anything if we had not some notion of it.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius]
     Full Idea: We could not give names to things, if we had not a preliminary notion of what the things were.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch]
     Full Idea: Epicurus says that colours are not intrinsic to bodies but a result of certain arrangements and positions relative to the eye, which implies that body is no more colourless than coloured.
     From: report of Epicurus (fragments/reports [c.289 BCE], Fr 30) by Plutarch - 74: Reply to Colotes §1110
     A reaction: This seems to me such a self-evident truth that I am puzzled as to why anyone would claim that colours are real features of bodies. Epicurus points out that entering a dark room we see no colour, but then colour appears after a while.
Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K]
     Full Idea: As long as colour terms pick out fundamental physical properties, I would be willing to countenance their use in the description of Reality in itself, ..even if they are based on a peculiar form of sensory awareness.
     From: Kit Fine (The Question of Realism [2001], 8)
     A reaction: This seems to explain why metaphysicians are so fond of using colour as their example of a property, when it seems rather subjective. There seem to be good reasons for rejecting Fine's view.
12. Knowledge Sources / B. Perception / 5. Interpretation
Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius]
     Full Idea: Sensation is out of reach of control, because one sensation cannot judge another which resembles itself, as they have equal value, and different sensations have different objects.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20
     A reaction: Scepticism about the possibility of purely empirical knowledge; an interesting comment on the question of whether perceptions contain any intrinsic knowledge.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius]
     Full Idea: The criteria of truth are the senses, the preconceptions, and the passions.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius]
     Full Idea: Reason cannot judge the senses, because it is based on them.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus]
     Full Idea: Epicurus denied the possibility of knowledge in order to retain moral (or hedonistic) values as the highest values.
     From: comment on Epicurus (fragments/reports [c.289 BCE]) by Friedrich Nietzsche - The Will to Power (notebooks) §578
     A reaction: The history of philosophy suggests that this dichotomy is unnecessary. Dogmatist place a high value on multitudes of things.
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
Epicurus says if one of a man's senses ever lies, none of his senses should ever be believed [Epicurus, by Cicero]
     Full Idea: Epicurus says that if one sense has told a lie once in a man's life, no sense must ever be believed.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - Academica II.25.79
13. Knowledge Criteria / E. Relativism / 1. Relativism
When entering a dark room it is colourless, but colour gradually appears [Epicurus]
     Full Idea: On entering a dark room we see no colour, but do so after waiting a short time.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Plutarch - 74: Reply to Colotes 1110d
Bath water is too hot for some, too cold for others [Epicurus, by Plutarch]
     Full Idea: In the very same bath some treat the water as too hot, others as too cold.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109b
If two people disagree over taste, who is right? [Epicurus, by Plutarch]
     Full Idea: If one person says the wine is dry and the other that it is sweet, and neither errs in his sensation, how is the wine any more dry than sweet?
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Plutarch - 74: Reply to Colotes 1109b
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K]
     Full Idea: The main sources of evidence for judgments of ground are intuitive and explanatory. The relationship of ground is a form of explanation, ..explaining what makes a proposition true, which needs simplicity, breadth, coherence, non-circularity and strength.
     From: Kit Fine (The Question of Realism [2001], 7)
     A reaction: My thought is that not only must grounding explain, and therefore be a good explanation, but that the needs of explanation drive our decisions about what are the grounds. It is a bit indeterminate which is tail and which is dog.
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K]
     Full Idea: We take ground to be an explanatory relation: if the truth that P is grounded in other truths, then they account for its truth; P's being the case holds in virtue of the other truths' being the case. ...It is the ultimate form of explanation.
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: To be 'ultimate' that which grounds would have to be something which thwarted all further explanation. Popper, for example, got quite angry at the suggestion that we should put a block on further investigation in this way.
15. Nature of Minds / A. Nature of Mind / 2. Psuche
The rational soul is in the chest, and the non-rational soul is spread through the body [Epicurus]
     Full Idea: Democritus and Epicurus say the soul has two parts, one which is rational and is situated in the chest area, and the other which is non-rational and is spread throughout the entire compound of the body
     From: Epicurus (fragments/reports [c.289 BCE])
     A reaction: [source Aetius 4.4.6]
Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius]
     Full Idea: Epicurus says the soul is a blend of fiery stuff (for bodily warmth), airy stuff (rest), breath (motion), and a nameless stuff (sense-perception).
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Aetius - fragments/reports 4.3.11
     A reaction: Obviously Epicurus thought the four stuffs were different combinations of atoms, rather than being elements. Is there no stuff which gives reason? Reason must reduce to motion, presumably.
16. Persons / F. Free Will / 1. Nature of Free Will
Epicurus was the first to see the free will problem, and he was a libertarian [Epicurus, by Long/Sedley]
     Full Idea: By posing the problem of determinism, Epicurus became arguably the first philosopher to recognise the philosophical centrality of what we call the Free Will Question. His strongly libertarian approach is strongly contrasted with Stoic determinism.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by AA Long / DN Sedley - Hellenic Philosophers commentary
     A reaction: Epicurus introduced the rather dubious 'swerve' of the atoms to make room for free will. It seems to me more consistent to stick with the determinism of Democritus. Zeno became a determinist in reaction to Epicurus.
16. Persons / F. Free Will / 2. Sources of Free Will
Epicurus showed that the swerve can give free motion in the atoms [Epicurus, by Diogenes of Oen.]
     Full Idea: There is a free motion in the atoms, which Democritus did not discover, but which Epicurus brought to light, and which consists in a swerve, as he demonstrated on the basis of what is seen to be the case?
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes (Oen) - Wall inscription 54.II-III
     A reaction: I presume the last bit means that we see that we have freedom of choice, and infer the swerve in the atoms as the only possible explanation. The worry for libertarians is, of course, who is in charge of the swerve.
16. Persons / F. Free Will / 4. For Free Will
There is no necessity to live with necessity [Epicurus]
     Full Idea: Necessity is a bad thing, but there is no necessity to live with necessity.
     From: Epicurus (fragments/reports [c.289 BCE], 9)
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
How can pleasure or judgement occur in a heap of atoms? [Sext.Empiricus on Epicurus]
     Full Idea: If Epicurus makes the end consist in pleasure and asserts that the soul, like all else, is composed of atoms, it is impossible to explain how in a heap of atoms there can come about pleasure, or judgement of the good.
     From: comment on Epicurus (fragments/reports [c.289 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism III.187
     A reaction: This is a nice statement of the mind-body problem. Ontologically, physics still seems to present reality as a 'heap of particles', which gives no basis for the emergence of anything as strange as consciousness. But then magnetism is pretty strange.
19. Language / D. Propositions / 5. Unity of Propositions
A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K]
     Full Idea: A proposition essentially contains a given constituent if its replacement by some other constituent induces a shift in truth value. Thus Socrates is essential to the proposition that Socrates is a philosopher, but not to Socrates is self-identical.
     From: Kit Fine (The Question of Realism [2001], 6)
     A reaction: In this view the replacement of 'is' by 'isn't' would make 'is' (or affirmation) part of the essence of most propositions. This is about linguistic essence, rather than real essence. It has the potential to be trivial. Replace 'slightly' by 'fairly'?
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling]
     Full Idea: Epicurus was responsible for the innovatory recognition that the question of the will's freedom is central to ethics.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by A.C. Grayling - What is Good? Ch.3
     A reaction: Compare Ideas 7672 and 6018. Obviously ethical action needs freedom, but the idea of a 'free will' is quite different. It is a fiction, created to give some sort of arrogant ultimate responsibility to our actions, like God.
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Fine things are worthless if they give no pleasure [Epicurus]
     Full Idea: I spit on the fine and those who emptily admire it, when it doesn't make any pleasure.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Julia Annas - The Morality of Happiness Ch.16
     A reaction: in Athenaeus
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pleasure is the chief good because it is the most natural, especially for animals [Epicurus, by Diog. Laertius]
     Full Idea: Pleasure is the chief good, because all animals from the moment of their birth are delighted with pleasure and offended by pain by their natural instinct, without the employment of reason.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.29
     A reaction: The highest pleasure of predators is likely to be the killing of weaker animals. What all animals do isn't much of a criterion for the natural chief good. They also breathe.
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
The end for Epicurus is static pleasure [Epicurus, by Annas]
     Full Idea: Epicurus identifies our final end with what he calls tranquillity or 'ataraxia', which is static pleasure.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Julia Annas - The Morality of Happiness Ch.7
     A reaction: I don't recall any Greek ever spotting that boredom is a problem. But then they didn't have privacy, so other people always hold their attention. Maybe this is a dream of privacy.
Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius]
     Full Idea: The pains of the soul are worst, for the flesh is only sensible of present affliction, but the soul feels the past, present and future.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.29
     A reaction: I don't think feeling extended across time is very relevant. What matters is that pains of the soul usually endure far longer than physical suffering.
Pleasures only differ in their duration and the part of the body affected [Epicurus]
     Full Idea: If every pleasure lasted long, and affected the whole body, then there would be no difference between one pleasure and another
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.08
     A reaction: This seems to miss out on intensity, which is of great importance to most pleasure seekers. Also it is a pleasure to be alive, which is lifelong, but we barely notice it.
23. Ethics / B. Contract Ethics / 1. Contractarianism
Justice has no independent existence, but arises entirely from keeping contracts [Epicurus]
     Full Idea: Justice has no independent existence; it results from mutual contracts, and establishes itself wherever there is a mutual engagement to guard against doing or sustaining mutual injury.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.35
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
We choose virtue because of pleasure, not for its own sake [Epicurus, by Diog. Laertius]
     Full Idea: We choose the virtues for the sake of pleasure, and not on their own account.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.30
23. Ethics / C. Virtue Theory / 4. External Goods / a. External goods
A wise man would be happy even under torture [Epicurus, by Diog. Laertius]
     Full Idea: Even if the wise man were put to the torture, he would still be happy.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.26
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Friendship is by far the most important ingredient of a complete and happy life [Epicurus]
     Full Idea: Of all the things which wisdom provides for the happiness of the whole life, by far the most important is the acquisition of friendship.
     From: Epicurus (fragments/reports [c.289 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.31.28
25. Social Practice / F. Life Issues / 4. Suicide
Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius]
     Full Idea: Even though he lose his eyes, a wise man should still partake of life.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.26
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
Only Epicurus denied purpose in nature, for the whole world, or for its parts [Epicurus, by Annas]
     Full Idea: Epicurus alone among the ancient schools denies that in nature we find any teleological explanations. Nothing in nature is for anything, neither the world as a whole nor anything in it.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Julia Annas - Ancient Philosophy: very short introduction
     A reaction: This may explain the controversial position that epicureanism held in the seventeenth century, as well as its incipient atheism.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Democritus says atoms have size and shape, and Epicurus added weight [Epicurus, by Ps-Plutarch]
     Full Idea: Democritus said that the properties of the atoms are in number two, magnitude and shape, but Epicurus added to these a third one, weight.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Pseudo-Plutarch - On the Doctrine of the Philosophers 1.3.18
     A reaction: The addition of Epicurus seems very sensible, and an odd omission by Democritus. He seems to think that atoms have a uniform density, so that volume indicates weight.
Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus]
     Full Idea: The swerve of Epicurus takes place without a cause; it does not take place in consequence of being struck by another atom, since how can that take place if they are indivisible bodies travelling perpendicularly in straight lines by the force of gravity?
     From: comment on Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 10.22
     A reaction: The swerve is the most ad hoc proposal in the history of theoretical physics. This is interesting for spelling out that the travel in vertical parallels. What's that all about, then?
What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus]
     Full Idea: What fresh cause exists in nature to make the atom swerve (or do the atoms cast lots among them which is to swerve and which not?), or to serve as the reason for making a very small swerve and not a large one, or one swerve, and not two or three swerves?
     From: comment on Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On Fate ('De fato') 20.46
     A reaction: This is an appeal to the Principle of Sufficient Reason, which seems to be the main ground for rejecting the swerve. The only reason to accept the swerve is reluctance to accept determinism or fatalism.
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Stoics say time is incorporeal and self-sufficient; Epicurus says it is a property of properties of things [Epicurus]
     Full Idea: Stoics posited that time is an incorporeal which is conceived of all by itself, while Epicurus thinks that it is an accident of certain things, ...and he called in a property of properties.
     From: Epicurus (fragments/reports [c.289 BCE])
     A reaction: [Source Sextus 'Adversus Mathematicos' 10.219-227]
28. God / A. Divine Nature / 2. Divine Nature
For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero]
     Full Idea: For Epicureans the gods are made of atoms, so in that case they are not eternal.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.68
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Epicurus saw that gods must exist, because nature has imprinted them on human minds [Epicurus, by Cicero]
     Full Idea: Epicurus alone saw that gods must exist because nature herself has imprinted an idea of them in the minds of all mankind.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.43
28. God / C. Attitudes to God / 5. Atheism
Some say Epicurus only pretended to believe in the gods, so as not to offend Athenians [Epicurus, by Cicero]
     Full Idea: Some believe that Epicurus gave lip-service only to the gods, so as not to offend the Athenians, but in fact did not believe in them.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.84
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus]
     Full Idea: If god acted in accordance with the prayers of men, all men would rather quickly be destroyed, since they constantly pray for many sufferings to befall each other.
     From: Epicurus (fragments/reports [c.289 BCE])
     A reaction: [source Maximus the Abbott 'Gnom.' 14]