Combining Texts

All the ideas for 'First-order Logic, 2nd-order, Completeness', 'Guide to Ground' and 'The Iliad or the Poem of Force'

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33 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]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
17286 Logical consequence is verification by a possible world within a truth-set [Fine,K]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
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]
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]
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]
24. Political Theory / C. Ruling a State / 1. Social Power
23812 Force is what turns man into a thing, and ultimately into a corpse [Weil]
25. Social Practice / D. Justice / 1. Basis of justice
23813 Only people who understand force, and don't respect it, are capable of justice [Weil]