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All the ideas for 'Frege's Theory of Numbers', 'works' and 'Truth-makers'

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15 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
Part-whole is the key relation among truth-makers [Mulligan/Simons/Smith]
     Full Idea: The most important (ontological) relations holding among truth-makers are the part and whole relations.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §6)
     A reaction: Hence Peter Simons goes off and writes the best known book on mereology. Looks very promising to me.
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
Truth-makers cannot be the designata of the sentences they make true [Mulligan/Simons/Smith]
     Full Idea: Truth-makers cannot be the designata of the sentences they make true, because sentences with more than one truth-maker would then be ambiguous, and 'a' and 'a exists' would have the same designatum.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §3)
Moments (objects which cannot exist alone) may serve as truth-makers [Mulligan/Simons/Smith]
     Full Idea: A 'moment' is an existentially dependent or non-self-sufficient object, that is, an object which is of such a nature that it cannot exist alone, ....... and we suggest that moments could serve as truth-makers.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §2)
     A reaction: [These three writers invented the term 'truth-maker']
The truth-maker for a sentence may not be unique, or may be a combination, or several separate items [Mulligan/Simons/Smith]
     Full Idea: A proposition may have a minimal truth-maker which is not unique, or a sentence may be made true by no single truth-maker but only by several jointly, or again only by several separately.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §3)
Despite negative propositions, truthmakers are not logical complexes, but ordinary experiences [Mulligan/Simons/Smith]
     Full Idea: Because of negative propositions, investigators of truth-makers have said that they are special non-objectual entities with a logical complexity, but we think a theory is possible in which the truth relation is tied to ordinary and scientific experience.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §6)
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence has to invoke facts or states of affairs, just to serve as truth-makers [Mulligan/Simons/Smith]
     Full Idea: The correspondence theory of truth invokes a special category of non-objectual entities - facts, states of affairs, or whatever - simply to serve as truth-makers.
     From: Mulligan/Simons/Smith (Truth-makers [1984], §3)
4. Formal Logic / G. Formal Mereology / 1. Mereology
Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P]
     Full Idea: Abelard's theory of substantial integral wholes is not a pure mereology in the modern sense, since he holds that there are privileged divisions; ..the division of a whole must be into its principal parts. Some wholes have a natural division.
     From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2
     A reaction: This is a mereology that cuts nature at the joints, rather than Lewis's 'unrestricted composition', so I find Abelard rather appealing.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P]
     Full Idea: Abelard argued that if the universal 'animal' were completely present in both Socrates and an ass, making each wholly an animal, then the same thing, animal, will be simultaneously rational and irrational, with contraries present in the whole thing.
     From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2
     A reaction: If we have universals for rationality and irrationality, they can distinguish the two. But we must also say that rationality is not an aspect of animal, which seems to mean that mind isn't either. What is the essence of an animal? Not reason?
Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P]
     Full Idea: Abelard was an irrealist about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. The concrete individual is enough to populate the world.
     From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2
     A reaction: If a Nominalist claims that 'only particulars exist', this makes him an extreme nominalist, and remarkably materialistic for his time (though he accepted the soul, as well as God).
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio]
     Full Idea: Abelard concluded that only words can be 'predicated of many'. A universal is nothing but a general linguistic predicate, and its universality depends not on its mode of being, but on its mode of signifying.
     From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter'
     A reaction: Abelard seems to be the originator of what is now called Predicate Nominalism, with Nelson Goodman as his modern representative. If it is just words, is there no fact of two things having the 'same' property?
10. Modality / A. Necessity / 4. De re / De dicto modality
The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein]
     Full Idea: The de dicto-de re modality distinction dates back to Abelard.
     From: report of Peter Abelard (works [1135]) by Alex Orenstein - W.V. Quine Ch.7
     A reaction: Most modern philosophers couldn't (apparently) care less where a concept originated, but one of the principles of this database is that such things do matter. I'm not sure why, but if we want the whole picture, we need the historical picture.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard]
     Full Idea: Abelard's problem is that it is not clear how singular forms could do the job they are supposed to do - to account for abstraction, namely - if they were purely singular aspects.
     From: comment on Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter'
     A reaction: A very nice question! If we say that abstracta are just acquired by ignoring all but that feature in some objects, how do we identify 'that' feature in order to select it? The instances must share something in common to be abstracted.
19. Language / C. Assigning Meanings / 3. Predicates
Nothing external can truly be predicated of an object [Abelard, by Panaccio]
     Full Idea: Abelard argued from the commonly accepted definition of a universal as 'what can be predicated of man', that no external thing can ever be predicated of anything.
     From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter'
     A reaction: It sounds to me as if Abelard is confusing predicates with properties! Maybe no external can be a property of anything, but I take predicates to just be part of what you can say about anything, and that had better included external facts.
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P]
     Full Idea: In Abelard's view a natural kind is a well-defined collection of things that have the same features, so that natural kinds have no special status, being no more than discrete integral wholes whose principle of membership is similarity.
     From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2
     A reaction: I take a natural kind to be a completely stable and invariant class of things. Presumably this invariance has an underlying explanation, but Abelard seems to take the Humean line that we cannot penetrate beyond the experienced surface.