Combining Texts

All the ideas for 'works', 'Higher-Order Logic' and 'Real Essentialism'

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36 ideas

2. Reason / D. Definition / 5. Genus and Differentia
12249 'Animal' is a genus and 'rational' is a specific difference [Oderberg]
12242 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
9565 Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]
3339 For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
12238 The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
12254 Being is substantial/accidental, complete/incomplete, necessary/contingent, possible, relative, intrinsic.. [Oderberg]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
12253 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
12256 We need to distinguish the essential from the non-essential powers [Oderberg]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
12252 Empiricists gave up 'substance', as unknowable substratum, or reducible to a bundle [Oderberg]
9. Objects / D. Essence of Objects / 1. Essences of Objects
12241 Essences are real, about being, knowable, definable and classifiable [Oderberg, by PG]
9. Objects / D. Essence of Objects / 3. Individual Essences
12244 Nominalism is consistent with individual but not with universal essences [Oderberg]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
12240 Essentialism is the main account of the unity of objects [Oderberg]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
12247 Essence is not explanatory but constitutive [Oderberg]
9. Objects / D. Essence of Objects / 9. Essence and Properties
12258 Properties are not part of an essence, but they flow from it [Oderberg]
9. Objects / D. Essence of Objects / 15. Against Essentialism
12257 Could we replace essence with collections of powers? [Oderberg]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
12236 Leibniz's Law is an essentialist truth [Oderberg]
10. Modality / B. Possibility / 4. Potentiality
12250 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
12234 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
12235 Necessity of identity seems trivial, because it leaves out the real essence [Oderberg]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
12237 Rigid designation has at least three essentialist presuppositions [Oderberg]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
12245 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
12246 What makes Parmenidean reality a One rather than a Many? [Oderberg]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12239 The real essentialist is not merely a scientist [Oderberg]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
12243 The reductionism found in scientific essentialism is mistaken [Oderberg]