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All the ideas for 'Theaetetus', 'Phil of Mathematics: why nothing works' and 'works'

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92 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Leibniz aims to give coherent rational support for empiricism [Leibniz, by Perkins]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophers are always switching direction to something more interesting [Plato]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is a science of the intelligible nature of being [Leibniz, by Cover/O'Leary-Hawthorne]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Leibniz tried to combine mechanistic physics with scholastic metaphysics [Leibniz, by Pasnau]
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
Understanding mainly involves knowing the elements, not their combinations [Plato]
Either a syllable is its letters (making parts as knowable as whole) or it isn't (meaning it has no parts) [Plato]
2. Reason / A. Nature of Reason / 1. On Reason
Reason is the faculty for grasping apriori necessary truths [Leibniz, by Burge]
2. Reason / A. Nature of Reason / 4. Aims of Reason
For Leibniz rationality is based on non-contradiction and the principle of sufficient reason [Leibniz, by Benardete,JA]
2. Reason / A. Nature of Reason / 6. Coherence
A rational account is essentially a weaving together of things with names [Plato]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical [Leibniz, by Benardete,JA]
2. Reason / C. Styles of Reason / 3. Eristic
Eristic discussion is aggressive, but dialectic aims to help one's companions in discussion [Plato]
2. Reason / D. Definition / 4. Real Definition
A primary element has only a name, and no logos, but complexes have an account, by weaving the names [Plato]
2. Reason / E. Argument / 6. Conclusive Proof
Leibniz is inclined to regard all truths as provable [Leibniz, by Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Nature uses the infinite everywhere [Leibniz]
A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We master arithmetic by knowing all the numbers in our soul [Plato]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
How can you contemplate Platonic entities without causal transactions with them? [Putnam]
7. Existence / B. Change in Existence / 1. Nature of Change
There seem to be two sorts of change: alteration and motion [Plato]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity [Leibniz, by Jolley]
8. Modes of Existence / A. Relations / 1. Nature of Relations
If relations can be reduced to, or supervene on, monadic properties of relata, they are not real [Leibniz, by Swoyer]
Relations aren't in any monad, so they are distributed, so they are not real [Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
Forms have sensation and appetite, the latter being the ability to act on other bodies [Leibniz, by Garber]
The essence of a thing is its real possibilities [Leibniz, by Cover/O'Leary-Hawthorne]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Leibniz moved from individuation by whole entity to individuation by substantial form [Leibniz, by Garber]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
The laws-of-the-series plays a haecceitist role [Leibniz, by Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Identity of a substance is the law of its persistence [Leibniz]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
Leibniz bases pure primitive entities on conjunctions of qualitative properties [Leibniz, by Adams,RM]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Leibnizian substances add concept, law, force, form and soul [Leibniz, by Cover/O'Leary-Hawthorne]
Substances are essentially active [Leibniz, by Jolley]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
Leibniz strengthened hylomorphism by connecting it to force in physics [Leibniz, by Garber]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
If a word has no parts and has a single identity, it turns out to be the same kind of thing as a letter [Plato]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A sum is that from which nothing is lacking, which is a whole [Plato]
The whole can't be the parts, because it would be all of the parts, which is the whole [Plato]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Leibniz's view (that all properties are essential) is extreme essentialism, not its denial [Leibniz, by Mackie,P]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Leibniz was not an essentialist [Leibniz, by Wiggins]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz]
9. Objects / F. Identity among Objects / 9. Sameness
Things are the same if one can be substituted for the other without loss of truth [Leibniz]
10. Modality / A. Necessity / 2. Nature of Necessity
Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking]
10. Modality / B. Possibility / 1. Possibility
How can things be incompatible, if all positive terms seem to be compatible? [Leibniz]
10. Modality / B. Possibility / 5. Contingency
A reason must be given why contingent beings should exist rather than not exist [Leibniz]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility [Leibniz, by Harré]
Each monad expresses all its compatible monads; a possible world is the resulting equivalence class [Leibniz, by Rumfitt]
Leibniz proposed possible worlds, because they might be evil, where God would not create evil things [Leibniz, by Stewart,M]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Leibniz has a counterpart view of de re counterfactuals [Leibniz, by Cover/O'Leary-Hawthorne]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Things are only knowable if a rational account (logos) is possible [Plato]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Expertise is knowledge of the whole by means of the parts [Plato]
For Leibniz, divine understanding grasps every conceivable possibility [Leibniz, by Perkins]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
It is impossible to believe something which is held to be false [Plato]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
How can a belief exist if its object doesn't exist? [Plato]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Leibniz said dualism of mind and body is illusion, and there is only mind [Leibniz, by Martin/Barresi]
Leibniz is an idealist insofar as the basic components of his universe are all mental [Leibniz, by Jolley]
12. Knowledge Sources / B. Perception / 1. Perception
Perception is infallible, suggesting that it is knowledge [Plato]
Our senses could have been separate, but they converge on one mind [Plato]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
With what physical faculty do we perceive pairs of opposed abstract qualities? [Plato]
Thought must grasp being itself before truth becomes possible [Plato]
You might mistake eleven for twelve in your senses, but not in your mind [Plato]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
An inadequate rational account would still not justify knowledge [Plato]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Parts and wholes are either equally knowable or equally unknowable [Plato]
Without distinguishing marks, how do I know what my beliefs are about? [Plato]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
A rational account might be seeing an image of one's belief, like a reflection in a mirror [Plato]
A rational account involves giving an image, or analysis, or giving a differentiating mark [Plato]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Maybe primary elements can be named, but not receive a rational account [Plato]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
A rational account of a wagon would mean knowledge of its hundred parts [Plato]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
What evidence can be brought to show whether we are dreaming or not? [Plato]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
If you claim that all beliefs are true, that includes beliefs opposed to your own [Plato]
Clearly some people are superior to others when it comes to medicine [Plato]
How can a relativist form opinions about what will happen in the future? [Plato]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
The essence of substance is the law of its changes, as in the series of numbers [Leibniz]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Leibniz introduced the idea of degrees of consciousness, essential for his monads [Leibniz, by Perkins]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
We think we are free because the causes of the will are unknown; determinism is a false problem [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Leibniz has a panpsychist view that physical points are spiritual [Leibniz, by Martin/Barresi]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Occasionalism give a false view of natural laws, miracles, and substances [Leibniz, by Jolley]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
Concepts are ordered, and show eternal possibilities, deriving from God [Leibniz, by Arthur,R]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size) [Leibniz, by Hart,WD]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad [Leibniz, by Perkins]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Leibniz identified beauty with intellectual perfection [Leibniz, by Gardner]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Humans are moral, and capable of reward and punishment, because of memory and self-consciousness [Leibniz, by Jolley]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials [Leibniz, by Jolley]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Leibniz rejected atoms, because they must be elastic, and hence have parts [Leibniz, by Garber]
Microscopes and the continuum suggest that matter is endlessly divisible [Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Leibniz struggled to reconcile bodies with a reality of purely soul-like entities [Jolley on Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
Leibniz eventually said resistance, rather than extension, was the essence of body [Leibniz, by Pasnau]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Leibniz wanted to explain motion and its laws by the nature of body [Leibniz, by Garber]
The law within something fixes its persistence, and accords with general laws of nature [Leibniz]
26. Natural Theory / D. Laws of Nature / 10. Closure of Physics
Leibniz had an unusual commitment to the causal completeness of physics [Leibniz, by Papineau]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Leibniz uses 'force' to mean both activity and potential [Leibniz]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
God must be the epitome of goodness, and we can only approach a divine state by being as good as possible [Plato]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
God's existence is either necessary or impossible [Leibniz, by Scruton]
28. God / C. Attitudes to God / 5. Atheism
Leibniz was closer than Spinoza to atheism [Leibniz, by Stewart,M]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
There must always be some force of evil ranged against good [Plato]