Combining Texts

All the ideas for 'poems', 'Platonistic Theories of Universals' and 'First-order Logic, 2nd-order, Completeness'

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15 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor

8964	Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz]

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 / 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]

8. Modes of Existence / D. Universals / 4. Uninstantiated Universals

8962	'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz]

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism

8961	Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz]

10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds

8963	Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention

6017	Nomos is king [Pindar]