21 ideas
| 18915 | 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. |
| 18919 | 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. |
| 18913 | 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. |
| 18907 | 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) |
| 18912 | 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? |
| 18922 | 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. |
| 18905 | 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. |
| 18908 | 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) |
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics. |
| 18917 | 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'. |
| 18916 | 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. |
| 18921 | 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. |
| 16643 | Accidents always remain suited to a subject [Bonaventura] |
| Full Idea: An accident's aptitudinal relationship to a subject is essential, and this is never taken away from accidents….for it is true to say that they are suited to a subject. | |
| From: Bonaventura (Commentary on Sentences [1252], IV.12.1.1.1c) | |
| A reaction: This is the compromise view that allows accidents to be separated, for Transubstantiation, while acknowledging that we identify them with their subjects. |
| 16696 | Successive things reduce to permanent things [Bonaventura] |
| Full Idea: Everything successive reduces to something permanent. | |
| From: Bonaventura (Commentary on Sentences [1252], II.2.1.1.3 ad 5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.2 | |
| A reaction: Avicenna first took successive entities seriously, but Bonaventure and Aquinas seem to have rejected them, or given reductive accounts of them. It resembles modern actualists versus modal realists. |
| 18918 | 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) |
| 18920 | '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. |
| 18906 | 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. |