Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'The Epistemology of Essence (draft)' and 'Trees, Terms and Truth'

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19 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
If facts are the truthmakers, they are not in the world [Engelbretsen]
     Full Idea: If there are such things as truthmakers (facts), they are not to be found in the world. As Strawson would say to Austin: there is the cat, there is the mat, but where in the world is the fact that the cat is on the mat?
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
     A reaction: He cites Strawson, Quine and Davidson for this point.
There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
     Full Idea: A false proposition is not made false by anything like a 'falsifying' fact. A false proposition simply fails to be made true by any fact.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
     A reaction: Sounds good. In truthmaker theory, one truth-value (T) is 'made', but the other one is not, so there is no symmetry between the two. Better to talk of T and not-T? See ideas on Excluded Middle.
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Traditional term logic struggled to express relations [Engelbretsen]
     Full Idea: The greatest challenge for traditional term logicians was the proper formulation and treatment of relational expressions.
     From: George Engelbretsen (Trees, Terms and Truth [2005])
     A reaction: The modern term logic of Fred Sommers claims to have solved this problem.
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
     Full Idea: That terms can be negated, that such negation is distinguishable from denial, and that propositions can be construed syntactically as predicationally tied pairs of terms, are important for the tree theory of predication, and for term logic.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 2)
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
     Full Idea: Nineteenth century logicians debated whether logic should be treated simply as a branch of mathematics, and mathematics could be applied to it, or whether mathematics is a branch of logic, with no mathematics used in formulating logic.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 3)
     A reaction: He cites Boole, De Morgan and Peirce for the first view, and Frege and Russell (and their 'logicism') for the second. The logic for mathematics slowly emerged from doing it, long before it was formalised. Mathematics is the boss?
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical syntax is actually close to surface linguistic form [Engelbretsen]
     Full Idea: The underlying logical syntax of language is close to the surface syntax of ordinary language.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 5)
     A reaction: This is the boast of the Term logicians, in opposition to the strained and unnatural logical forms of predicate logic, which therefore don't give a good account of the way ordinary speakers reason. An attractive programme. 'Terms' are the key.
Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
     Full Idea: Sommers's 'tree theory' of predication assumes that propositions can be analysed as pairs of terms joined by some kind of predicational glue.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 2)
     A reaction: This is the basis of Sommers's upgraded Aristotelian logic, known as Term Logic. The idea of reasoning with 'terms', rather than with objects, predicates and quantifiers, seems to me very appealing. I think I reason more about facts than about objects.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
     Full Idea: Standard logic recognises only one kind of negation: sentential negation. Consequently, negation of a general term/predicate always amounts to negation of the entire sentence.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 3)
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'.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
     Full Idea: Existence and nonexistence are not primarily properties of individual objects (dogs, unicorns), but of totalities. To say that some object exists is just to say that it is a constituent of the world, which is a characteristic of the world, not the object.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
     A reaction: This has important implications for the problem of truthmakers for negative existential statements (like 'there are no unicorns'). It is obviously a relative of Armstrong's totality facts that do the job. Not sure about 'a characteristic of'.
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Facts are not in the world - they are properties of the world [Engelbretsen]
     Full Idea: Facts must be viewed as properties of the world - not as things in the world.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
     A reaction: Not sure I'm happy with either of these. Do animals grasp facts? If not, are they (as Strawson said) just the truths expressed by true sentences? That is not a clear idea either, given that facts are not the sentences themselves. Facts overlap.
7. Existence / E. Categories / 4. Category Realism
Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
     Full Idea: The natural categories of individuals are arranged in a hierarchy of inclusion relations that is isomorphic with the linguistic semantic structure.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 5)
     A reaction: This is the conclusion of a summary of modern Term Logic. The claim is that Sommers discerned this structure in our semantics (via the study of 'terms'), and was pleasantly surprised to find that it matched a plausible structure of natural categories.
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
If conceivability is a priori coherence, that implies possibility [Tahko]
     Full Idea: Maybe conceivability could be understood as a priori coherence, which implies possibility.
     From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 3.2)
     A reaction: I'm not quite sure why 'a priori' has to be there. Assessing conceivability just is assessing coherence. That couches it as a rational activity, rather than as a purely imaginary one. Trying to conceive a square circle isn't just daydreaming.
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Essences are used to explain natural kinds, modality, and causal powers [Tahko]
     Full Idea: Essences are supposed to do a lot of explanatory work: natural kinds can be identified in terms of their essences, metaphysical modality can be reduced to essence, the causal power of objects can be explained with the help of essence.
     From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 1)
     A reaction: Natural kinds and modality are OK with me, but I'm dubious about the third one. If an essence explains something's causal powers, I have no idea what an essence might be. Essence are largely characterised in terms of causal powers.
19. Language / B. Reference / 2. Denoting
Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
     Full Idea: In term logic, what a term denotes are the objects having the property it signifies. What a statement denotes is the world, that which has the constitutive property it signifies.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
19. Language / D. Propositions / 1. Propositions
'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
     Full Idea: Whereas 'Socrates is wise' denotes a sentence, 'that Socrates is wise' denotes a proposition.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 4)
     A reaction: In traditional parlance, 'reported speech' refers to the underlying proposition, because it does not commit to the actual words being used. As a lover of propositions (as mental events, not mysterious abstract objects), I like this.
19. Language / F. Communication / 3. Denial
Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
     Full Idea: There is a crucial distinction in term logic between affirming a negated predicate term of some subject and denying the unnegated version of that term of that same subject. We must distinguish 'X is non-P' from 'X is not P'.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 2)
     A reaction: The first one affirms something about X, but the second one just blocks off a possible description of X. 'X is non-harmful' and 'X is not harmful' - if X had ceased to exist, the second would be appropriate and the first wouldn't? I'm guessing.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko]
     Full Idea: The conception of essence taken for granted in much of the 'scientific essentialist' literature is that essence can be explained in terms of modality (rather than the other way round).
     From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 2.1)
     A reaction: [He cites Ellis and Bird] That is, presumably, that they are inclined to say that the essence of gold is a set of necessary properties. Maybe conceptual necessities dictate the properties of gold, and they in turn dictate metaphysical necessities?
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko]
     Full Idea: If essence is conceived in terms of modality and the laws of nature are metaphysically necessary, it seems that the laws of nature constitute essentialist knowledge, so the discovery of essences is mostly due to scientists.
     From: Tuomas E. Tahko (The Epistemology of Essence (draft) [2013], 2.1)
     A reaction: This seems muddled to me. The idea that the laws themselves are essences is way off target. No one thinks all knowledge of necessities is essentialist. Mumford, for example, doesn't even believe in laws.