Combining Texts

All the ideas for 'What are Sets and What are they For?', 'Modern Philosophy:introduction and survey' and 'Commentary on the Metaphysics'

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43 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
Philosophy aims to provide a theory of everything [Scruton]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Understanding begins with the notion of being and essence [Avicenna]
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
If p entails q, then p is sufficient for q, and q is necessary for p [Scruton]
2. Reason / E. Argument / 4. Open Question
We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton]
3. Truth / A. Truth Problems / 1. Truth
A true proposition is consistent with every other true proposition [Scruton]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
The pragmatist does not really have a theory of truth [Scruton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton]
8. Modes of Existence / B. Properties / 12. Denial of Properties
If possible worlds are needed to define properties, maybe we should abandon properties [Scruton]
9. Objects / A. Existence of Objects / 5. Simples
The simple's whatness is its very self [Avicenna]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The ultimate material of things has the unity of total formlessness [Avicenna]
9. Objects / D. Essence of Objects / 2. Types of Essence
An essence can either be universal (in the mind) or singular (in concrete particulars) [Avicenna, by Panaccio]
10. Modality / A. Necessity / 11. Denial of Necessity
Hume assumes that necessity can only be de dicto, not de re [Scruton]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Epistemology is about the justification of belief, not the definition of knowledge [Scruton]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
In the Cogito argument consciousness develops into self-consciousness [Scruton]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Maybe our knowledge of truth and causation is synthetic a priori [Scruton]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
Touch only seems to reveal primary qualities [Scruton]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
We only conceive of primary qualities as attached to secondary qualities [Scruton]
If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton]
12. Knowledge Sources / B. Perception / 3. Representation
The representational theory says perceptual states are intentional states [Scruton]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Why should you believe someone who says there are no truths? [Scruton]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Every event having a cause, and every event being determined by its cause, are not the same [Scruton]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton]
19. Language / F. Communication / 4. Private Language
Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton]
23. Ethics / B. Contract Ethics / 5. Free Rider
Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton]
23. Ethics / D. Deontological Ethics / 2. Duty
Membership is the greatest source of obligation [Scruton]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton]
26. Natural Theory / C. Causation / 1. Causation
'Cause' used to just mean any valid explanation [Scruton]
27. Natural Reality / C. Space / 4. Substantival Space
Measuring space requires no movement while I do it [Scruton]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton]