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

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77 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]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Slavery to philosophy brings true freedom [Epicurus]
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]
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]
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]
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]
2. Reason / C. Styles of Reason / 1. Dialectic
Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
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 / D. Assumptions for Logic / 2. Excluded Middle
Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero]
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]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
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 / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
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 / 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]
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]
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]
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]
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]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus]
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]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Bath water is too hot for some, too cold for others [Epicurus, by Plutarch]
If two people disagree over taste, who is right? [Epicurus, by Plutarch]
When entering a dark room it is colourless, but colour gradually appears [Epicurus]
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]
Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius]
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]
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.]
16. Persons / F. Free Will / 4. For Free Will
There is no necessity to live with necessity [Epicurus]
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]
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]
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]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Fine things are worthless if they give no pleasure [Epicurus]
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]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius]
Pleasures only differ in their duration and the part of the body affected [Epicurus]
The end for Epicurus is static pleasure [Epicurus, by Annas]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Justice has no independent existence, but arises entirely from keeping contracts [Epicurus]
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]
23. Ethics / C. Virtue Theory / 4. External Goods / a. External goods
A wise man would be happy even under torture [Epicurus, by Diog. Laertius]
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]
25. Social Practice / F. Life Issues / 4. Suicide
Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius]
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]
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]
Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus]
What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
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]
28. God / A. Divine Nature / 2. Divine Nature
For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero]
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]
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]
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]