Combining Texts

All the ideas for 'fragments/reports', 'Beauty: a very short introduction' and 'Plurals and Complexes'

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34 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton]
3. Truth / A. Truth Problems / 2. Defining Truth
Defining truth presupposes that there can be a true definition [Scruton]
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 / 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]
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
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
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]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
The pleasure taken in beauty also aims at understanding and valuing [Scruton]
Art gives us imaginary worlds which we can view impartially [Scruton]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton]
Beauty shows us what we should want in order to achieve human fulfilment [Scruton]
Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Natural beauty reassures us that the world is where we belong [Scruton]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]