Combining Texts

All the ideas for 'poems', 'The Sophist' and 'Plurals and Complexes'

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38 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
We must fight fiercely for knowledge, understanding and intelligence [Plato]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
The desire to split everything into its parts is unpleasant and unphilosophical [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
Good analysis involves dividing things into appropriate forms without confusion [Plato]
Dialectic should only be taught to those who already philosophise well [Plato]
2. Reason / C. Styles of Reason / 2. Elenchus
In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [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 / A. Nature of Existence / 3. Being / d. Non-being
What does 'that which is not' refer to? [Plato]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
If statements about non-existence are logically puzzling, so are statements about existence [Plato]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
To be is to have a capacity, to act on other things, or to receive actions [Plato]
7. Existence / D. Theories of Reality / 6. Physicalism
Some alarming thinkers think that only things which you can touch exist [Plato]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Whenever there's speech it has to be about something [Plato]
We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Good thinkers spot forms spread through things, or included within some larger form [Plato]
The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
If we see everything as separate, we can then give no account of it [Plato]
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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
A soul without understanding is ugly [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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Nomos is king [Pindar]
23. Ethics / A. Egoism / 1. Ethical Egoism
Wickedness is an illness of the soul [Plato]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Didactic education is hard work and achieves little [Plato]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]