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All the ideas for 'works', 'fragments/reports' and 'Frege philosophy of mathematics'

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69 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
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]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
No perceptible object is truly straight or curved [Protagoras]
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]
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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
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]
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]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
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]
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]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
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]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Everything that exists consists in being perceived [Protagoras]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Man is the measure of all things - of things that are, and of things that are not [Protagoras]
There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras]
You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
God is "the measure of all things", more than any man [Plato on Protagoras]
Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras]
Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras]
14. Science / B. Scientific Theories / 1. Scientific Theory
Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
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]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
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]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / E. Analyticity / 2. Analytic Truths
The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD]
23. Ethics / B. Contract Ethics / 1. Contractarianism
For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Successful education must go deep into the soul [Protagoras]
It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
25. Social Practice / E. Policies / 5. Education / b. Education principles
He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily]
Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
28. God / C. Attitudes to God / 5. Atheism
He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]