Combining Philosophers

All the ideas for Hermarchus, B Hale / C Wright and Anaxagoras

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47 ideas

2. Reason / F. Fallacies / 1. Fallacy
It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Singular terms refer if they make certain atomic statements true [Hale/Wright]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Things get smaller without end [Anaxagoras]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Nothing is created or destroyed; there is only mixing and separation [Anaxagoras]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus]
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
8. Modes of Existence / B. Properties / 3. Types of Properties
Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Objects just are what singular terms refer to [Hale/Wright]
12. Knowledge Sources / B. Perception / 1. Perception
Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The senses are too feeble to determine the truth [Anaxagoras]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato]
16. Persons / F. Free Will / 1. Nature of Free Will
Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
Reference needs truth as well as sense [Hale/Wright]
19. Language / E. Analyticity / 2. Analytic Truths
Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Mind creates the world from a mixture of pure substances [Anaxagoras, by ]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle]
The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle]
26. Natural Theory / C. Causation / 1. Causation
Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato]
27. Natural Reality / G. Biology / 1. Biology
Germs contain microscopic organs, which become visible as they grow [Anaxagoras]
28. God / A. Divine Nature / 1. God
When things were unified, Mind set them in order [Anaxagoras]
Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras]
28. God / C. Attitudes to God / 5. Atheism
Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch]
Anaxagoras was the first recorded atheist [Anaxagoras, by Watson]