Combining Texts

All the ideas for 'World and Essence', 'First-Order Logic' and 'Evil and Omnipotence'

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21 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
9. Objects / A. Existence of Objects / 4. Impossible objects
16435 Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
14655 The 'identity criteria' of a name are a group of essential and established facts [Plantinga]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
14658 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga]
9. Objects / D. Essence of Objects / 2. Types of Essence
14656 Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14654 Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga]
14653 X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga]
14660 If a property is ever essential, can it only ever be an essential property? [Plantinga]
14661 Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga]
9. Objects / F. Identity among Objects / 5. Self-Identity
14657 Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga]
10. Modality / A. Necessity / 4. De re / De dicto modality
14652 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
14659 We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
1473 Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG]
1472 The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG]