Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Real Essentialism' and 'The Philosophy of Mathematics'

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30 ideas

2. Reason / D. Definition / 5. Genus and Differentia
'Animal' is a genus and 'rational' is a specific difference [Oderberg]
Definition distinguishes one kind from another, and individuation picks out members of the kind [Oderberg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Being is substantial/accidental, complete/incomplete, necessary/contingent, possible, relative, intrinsic.. [Oderberg]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
If tropes are in space and time, in what sense are they abstract? [Oderberg]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
We need to distinguish the essential from the non-essential powers [Oderberg]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
Empiricists gave up 'substance', as unknowable substratum, or reducible to a bundle [Oderberg]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Essences are real, about being, knowable, definable and classifiable [Oderberg, by PG]
9. Objects / D. Essence of Objects / 3. Individual Essences
Nominalism is consistent with individual but not with universal essences [Oderberg]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Essentialism is the main account of the unity of objects [Oderberg]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Essence is not explanatory but constitutive [Oderberg]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Properties are not part of an essence, but they flow from it [Oderberg]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Could we replace essence with collections of powers? [Oderberg]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Leibniz's Law is an essentialist truth [Oderberg]
10. Modality / B. Possibility / 4. Potentiality
Bodies have act and potency, the latter explaining new kinds of existence [Oderberg]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Realism about possible worlds is circular, since it needs a criterion of 'possible' [Oderberg]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Necessity of identity seems trivial, because it leaves out the real essence [Oderberg]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
Rigid designation has at least three essentialist presuppositions [Oderberg]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Essence is the source of a thing's characteristic behaviour [Oderberg]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
What makes Parmenidean reality a One rather than a Many? [Oderberg]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
The real essentialist is not merely a scientist [Oderberg]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
The reductionism found in scientific essentialism is mistaken [Oderberg]