40 ideas
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| Full Idea: It doesn't follow from the fact that a given sentence is being used to implicitly define one of its ingredient terms, that it is not a factual statement. 'This stick is a meter long at t' may define an ingredient terms and express something factual. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This looks like a rather good point, but it is tied in with a difficulty about definition, which is deciding which sentences are using a term, and which ones are defining it. If I say 'this stick in Paris is a meter long', I'm not defining it. |
| 5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
| Full Idea: We call a belief true when it is belief in a true proposition, ..but it is to propositions that the primary formal meanings of 'truth' and 'falsehood' apply. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: I think this is wrong. A proposition such as 'it is raining' would need a date-and-time stamp to be a candidate for truth, and an indexical statement such as 'I am ill' would need to be asserted by a person. Of course, books can contain unread truths. |
| 5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
| Full Idea: I take it as evident that the truth or falsehood of a belief depends upon a fact to which the belief 'refers'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: A nice bold commitment to a controversial idea. The traditional objection is to ask how you are going to formulate the 'facts' except in terms of more beliefs, so you ending up comparing beliefs. Facts are a metaphysical commitment, not an acquaintance. |
| 5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
| Full Idea: The correspondence of proposition and fact grows increasingly complicated as we pass to more complicated types of propositions: existence-propositions, general propositions, disjunctive and hypothetical propositions, and so on. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: An important point. Truth must not just work for 'it is raining', but also for maths, logic, tautologies, laws etc. This is why so many modern philosophers have retreated to deflationary and minimal accounts of truth, which will cover all cases. |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
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Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| Full Idea: Conventualism is a factualist view: it presupposes that sentences of logic have truth values. It differs from a realist view in its conception of the source of those truth values, not on their existence. I call the denial of truths Non-Factualism. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: It barely seems to count as truth is we say 'p is true because we say so'. It is a truth about an agreement, not a truth about logic. Driving on the left isn't a truth about which side of the road is best. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 5780 | The three questions about belief are its contents, its success, and its character [Russell] |
| Full Idea: There are three issues about belief: 1) the content which is believed, 2) the relation of the content to its 'objective' - the fact which makes it true or false, and 3) the element which is belief, as opposed to consideration or doubt or desire. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: The correct answers to the questions (trust me) are that propositions are the contents, the relation aimed at is truth, which is a 'metaphysical ideal' of correspondence to facts, and belief itself is an indefinable feeling. See Hume, Idea 2208. |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts. |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| Full Idea: The central impetus behind the analytic explanation of the a priori is a desire to explain the possibility of a priori knowledge without having to postulate a special evidence-gathering faculty of intuition. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: I don't see at all why one has to postulate a 'faculty' in order to talk about intuition. I take an intuition to be an apprehension of a probable truth, combined with an inability to articulate how the conclusion was arrived at. |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| Full Idea: The analytic theory of the apriority of logic arose indirectly, as a by-product of the attempt to explain in what a grasp of the meaning of the logical constants consists. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: Preumably he is referring to Wittgenstein's anguish over the meaning of the word 'not' in his World War I notebooks. He first defined the constants by truth tables, then asserted that they were purely conventional - so logic is conventional. |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| Full Idea: If there is no sentence I must hold true if it is to mean what it does, then there is no basis on which to argue that I am entitled to hold it true without evidence. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: He is exploring Quine's view. Truth by convention depends on agreeing which part of the usage of a term constitutes its defining sentence(s), and that may be rather tricky. Boghossian says this slides into the 'dreaded indeterminacy of meaning'. |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| Full Idea: It is consistent with a belief's being a priori in the strong sense that we should have pragmatic reasons for dropping it from our best overall theory. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], n 6) | |
| A reaction: Does 'dropping it' from the theory mean just ignoring it, or actually denying it? C.I. Lewis is the ancestor of this view. Could it be our 'best' theory, while conflicting with beliefs that were strongly a priori? Pragmatism can embrace falsehoods. |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| Full Idea: If we learn geometrical truths by intuition, how could this faculty have misled us for so long? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This refers to the development of non-Euclidean geometries, though the main misleading concerns parallels, which involves infinity. Boghossian cites 'distance' as a concept the Euclideans had misunderstood. Why shouldn't intuitions be wrong? |
| 5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
| Full Idea: If privacy is the main objection to introspective data, we shall have to include among such data all sensations; a toothache, for example, is essentially private; a dentist may see the bad condition of your tooth, but does not feel your ache. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: Russell was perhaps the first to see why eliminative behaviourism is a non-starter as a theory of mind. Mental states are clearly a cause of behaviour, so they can't be the same thing. We might 'eliminate' mental states by reducing them, though. |
| 5779 | There are distinct sets of psychological and physical causal laws [Russell] |
| Full Idea: There do seem to be psychological and physical causal laws which are distinct from each other. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: This sounds like the essence of 'property dualism'. Reductive physicalists (like myself) say there is no distinction. Davidson, usually considered a property dualist, claims there are no psycho-physical laws. Russell notes that reduction may be possible. |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| Full Idea: Conceptual Role Semantics must explain what properties an inference or sentence involving a logical constant must have, if that inference or sentence is to be constitutive of its meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This is my perennial request that if something is to be defined by its function (or role), we must try to explain what properties it has that make its function possible, and those properties will be the more basic explanation. |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| Full Idea: 'Conceptual role semantics' says the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not others, ..so some inferences and sentences are constitutive of an expression's meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: If the meaning of the terms derives from the sentences in which they figure, that seems to be meaning-as-use. The view that it depends on the inferences seems very different, and is a more interesting but more risky claim. |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| Full Idea: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §II) | |
| A reaction: He is discussing Quine's attack on synonymy, and his scepticism about meaning. Boghossian and I believe in propositions, so we have no trouble with two statements having the same meaning. Denial of propositions breeds trouble. |
| 5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
| Full Idea: The important beliefs, even if they are not the only ones, are those which, if rendered into explicit words, take the form of a proposition. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This assertion is close to the heart of the twentieth century linking of ontology and epistemology to language. It is open to challenges. Why is non-propositional belief unimportant? Do dogs have important beliefs? Can propositions exist non-verbally? |
| 5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
| Full Idea: I shall distinguish a proposition expressed in words as a 'word-proposition', and one consisting of images as an 'image-proposition'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This, I think, is good, though it raises the question of what exactly an 'image' is when it is non-visual, as when a dog believes its owner called. This distinction prevents us from regarding all knowledge and ontology as verbal in form. |
| 5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
| Full Idea: A proposition may be defined as: what we believe when we believe truly or falsely. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: If we define belief as 'commitment to truth', Russell's last six words become redundant. "Propositions are the contents of beliefs", it being beliefs which are candidates for truth, not propositions. (Russell agrees, on p.308!) |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| Full Idea: Boghossian distinguishes metaphysical analyticity (truth purely in virtue of meaning, debunked by Quine, he says) from epistemic analyticity (knowability purely in virtue of understanding - a notion in good standing). | |
| From: report of Paul Boghossian (Analyticity Reconsidered [1996]) by Carrie Jenkins - Grounding Concepts 2.4 | |
| A reaction: [compressed] This fits with Jenkins's claim that we have a priori knowledge just through understanding and relating our concepts. She, however, rejects that idea that a priori is analytic. |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
| Full Idea: The epistemological notion of analyticity: a statement is 'true by virtue of meaning' provided that grasp of its meaning alone suffices for justified belief in its truth; the metaphysical reading is that it owes its truth to its meaning, not to facts. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Kripke thinks it is neither, but is a purely semantic notion. How could grasp of meaning alone be a good justification if it wasn't meaning which was the sole cause of the statement's truth? I'm not convinced by his distinction. |