Combining Texts

All the ideas for 'Protagoras', 'Letters to Des Bosses' and 'Plurals and Complexes'

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47 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
We can grasp the wisdom of God a priori [Leibniz]
2. Reason / B. Laws of Thought / 4. Contraries
Only one thing can be contrary to something [Plato]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice is a non-logical principle of set-theory [Hossack]
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Extensional mereology needs two definitions and two axioms [Hossack]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural reference will refer to complex facts without postulating complex things [Hossack]
Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
A plural comprehension principle says there are some things one of which meets some condition [Hossack]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
The theory of the transfinite needs the ordinal numbers [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I take the real numbers to be just lengths [Hossack]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
Set theory is the science of infinity [Hossack]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz]
Monads do not make a unity unless a substantial chain is added to them [Leibniz]
Monads control nothing outside of themselves [Leibniz]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
There is active and passive power in the substantial chain and in the essence of a composite [Leibniz]
Primitive force is what gives a composite its reality [Leibniz]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
If asked whether justice itself is just or unjust, you would have to say that it is just [Plato]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Things seem to be unified if we see duration, position, interaction and connection [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Every substance is alive [Leibniz]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Complex particulars are either masses, or composites, or sets [Hossack]
The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz]
9. Objects / D. Essence of Objects / 12. Essential Parts
A composite substance is a mere aggregate if its essence is just its parts [Leibniz]
10. Modality / B. Possibility / 1. Possibility
There is a reason why not every possible thing exists [Leibniz]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
The most important things in life are wisdom and knowledge [Plato]
The only real evil is loss of knowledge [Plato]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
Truth is mutually agreed perception [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
Everything resembles everything else up to a point [Plato]
18. Thought / A. Modes of Thought / 1. Thought
A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Courage is knowing what should or shouldn't be feared [Plato]
22. Metaethics / B. Value / 2. Values / j. Evil
No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Some pleasures are not good, and some pains are not evil [Plato]
People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Socrates did not believe that virtue could be taught [Plato]
Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
Allow no more miracles than are necessary [Leibniz]