Combining Texts

All the ideas for 'Particulars in Particular Clothing', 'Higher-Order Logic' and 'Truth-makers and dependence'

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22 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
17325 Truth-maker theory can't cope with non-causal dependence [Liggins]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
17318 Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins]
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
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
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 / 5. Reason for Existence
17320 Either p is true or not-p is true, so something is true, so something exists [Liggins]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17326 The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
17327 Non-causal dependence is at present only dimly understood [Liggins]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
17322 Necessities supervene on everything, but don't depend on everything [Liggins]
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 / a. Nature of tropes
18431 Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
14. Science / D. Explanation / 1. Explanation / a. Explanation
17324 'Because' can signal an inference rather than an explanation [Liggins]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17321 Value, constitution and realisation are non-causal dependences that explain [Liggins]
17323 If explanations track dependence, then 'determinative' explanations seem to exist [Liggins]