Combining Texts

All the ideas for 'fragments/reports', 'Summa totius logicae' and 'First-order Logic, 2nd-order, Completeness'

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21 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9108 From an impossibility anything follows [William of Ockham]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
9107 A proposition is true if its subject and predicate stand for the same thing [William of Ockham]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
16300 Ockham had an early axiomatic account of truth [William of Ockham, by Halbach]
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 / G. Quantification / 1. Quantification
9106 The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham]
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]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9113 Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
9110 The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
15388 Universals are single things, and only universal in what they signify [William of Ockham]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
9109 If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham]
19. Language / D. Propositions / 4. Mental Propositions
9105 Some concepts for propositions exist only in the mind, and in no language [William of Ockham]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]