Combining Texts

All the ideas for 'Higher-Order Logic', 'Quantum: Einstein and Bohr' and 'Guide to Ground'

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34 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
17275 Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
17282 Truths need not always have their source in what exists [Fine,K]
3. Truth / B. Truthmakers / 7. Making Modal Truths
17283 If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K]
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]
17286 Logical consequence is verification by a possible world within a truth-set [Fine,K]
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
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]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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 / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17272 2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K]
17276 If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K]
17284 An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K]
17285 'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K]
17288 We learn grounding from what is grounded, not what does the grounding [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17281 If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K]
17280 Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17290 Only metaphysical grounding must be explained by essence [Fine,K]
17274 Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K]
7. Existence / C. Structure of Existence / 1. Grounding / d. Grounding and reduction
17278 We can only explain how a reduction is possible if we accept the concept of ground [Fine,K]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
17287 Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / E. Objects over Time / 5. Temporal Parts
17279 Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
17273 Each basic modality has its 'own' explanatory relation [Fine,K]
17289 Every necessary truth is grounded in the nature of something [Fine,K]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17291 We explain by identity (what it is), or by truth (how things are) [Fine,K]
17271 Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
15710 Bohr explained the periodic table and chemical properties of elements, using the quantum atom [Kumar]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
17277 If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K]