30 ideas
| 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. |
| 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) |
| 16657 | Substance, Quantity and Quality are real; other categories depend on those three [Henry of Ghent] |
| Full Idea: Among creatures there are only three 'res' belong to the three first categories: Substance, Quantity and Quality. All other are aspects [rationes] and intellectual concepts with respect to them, with reality only as grounded on the res of those three. | |
| From: Henry of Ghent (Quodlibeta [1284], VII:1-2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3 | |
| A reaction: Pasnau connects with the 'arrangement of being', giving an 'ontologically innocent' structure to reality. That seems to be what we all want, if only we could work out the ontologically guilty bit. |
| 16658 | The only reality in the category of Relation is things from another category [Henry of Ghent] |
| Full Idea: There is beyond a doubt nothing real in the category of Relation, except what is a thing from another category. | |
| From: Henry of Ghent (Quodlibeta [1284], VII:1-2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3 | |
| A reaction: This seems to have been the fairly orthodox scholastic view of relations. |
| 16645 | Accidents are diminished beings, because they are dispositions of substance (unqualified being) [Henry of Ghent] |
| Full Idea: Accidents are beings only in a qualified and diminished sense, because they are not called beings, nor are they beings, except because they are dispositions of an unqualified being, a substance. | |
| From: Henry of Ghent (Quodlibeta [1284], XV.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.4 | |
| A reaction: This is aimed to 'half' detach the accidents (as the Eucharist requires). Later scholastics detached them completely. Late scholastics seem to have drifted back to Henry's view. The equivocal use of 'being' here was challenged later. |
| 7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
| Full Idea: There is a convincing claim that we need to leave behind Ryle's dichotomy between knowing how and knowing that as being too simplistic. | |
| From: Barry Maund (Perception [2003], Ch. 2) | |
| A reaction: [John Campbell is mentioned as source of this idea] I find this proposal immediately appealing. I was taught that riding a bicycle shows the division, as hardly anyone knows the theory, but I am sure children need some propositional information. |
| 22012 | Kant says things-in-themselves cause sensations, but then makes causation transcendental! [Henry of Ghent, by Pinkard] |
| Full Idea: Kant claimed that things-in-themselves caused our sensations; but causality was a transcendental condition of experience, not a property of things-in-themselves, so the great Kant had contradicted himself. | |
| From: report of Henry of Ghent (Quodlibeta [1284], Supplement) by Terry Pinkard - German Philosophy 1760-1860 04 | |
| A reaction: This early objection by the conservative Jacobi (who disliked Enlightenment rational religion) is the key to the dispute over whether Kant is an idealist. Kant denied being an idealist, but how can he be, if this idea is correct? |
| 7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
| Full Idea: Three forms of (cognitive) direct realism are: two stages - non-conceptual sensory experience, then a non-sensory conceptual state; directly acquiring non-sensuous conceptual states; and sensuous states saturated with concepts. | |
| From: Barry Maund (Perception [2003], Ch. 3) | |
| A reaction: [First: Reid, Dretske, Evans, Sellars. Second: Armstrong, Heil, Pitcher, Clark. Third: Kant, McDowell, Strawson, McGinn, Searle]. I find the first one plausible, because of the ambiguity in language, and because unusual experiences separate them. |
| 7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
| Full Idea: Sense-data have an epistemological purpose (to serve as foundations on which the edifice of knowledge is to be constructed), and a metaphysical purpose (to provide an accurate account of the phenomenology of perceptual experience). | |
| From: Barry Maund (Perception [2003], Ch. 6) | |
| A reaction: This is very important, because there is a real danger (e.g. in Russell) that the epistemological convenience of sense-data for giving reliability in knowledge means that we are too quick in making the assumption that they actually exist. |
| 7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
| Full Idea: The representationalist/intentionalist thesis about perception is that we are not aware of the intrinsic qualities of experience in normal perception; we are instead aware of those objects and their qualities that are specified in the content. | |
| From: Barry Maund (Perception [2003], Ch. 9) | |
| A reaction: If secondary qualities are in the mind, not in objects, how come people always thought they were in objects? Answer: because this thesis is right? The primary mode of the mind is projected outwards, though we can introspect about colours. [Dretske] |
| 7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
| Full Idea: The so-called 'myth of the given' is the view that conceptual content can be rationally supported by experiences construed as states with non-conceptual content. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The myth is attacked by Sellars and McDowell, the latter claiming that concepts must be embedded in the experiences. Maybe only realism is required to make the Given work. The experiences are definitely of something, and off we go... |
| 7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
| Full Idea: Metaphysically, mountains are only adverbial modifications of the Earth's belt. They have no existence independent of being part of the earth. Yet for all that, they have some rather strong 'object'-characteristics. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The point being that you don't give up all the advantages of a sense-data view if you switch to adverbialism. I'm not convinced by the analogy, but we can only be aware of adverbial qualities if they have causal powers. |
| 7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
| Full Idea: The two primary motivations of the adverbialist analysis are thought to be to avoid commitment to sensory particulars such as sense-data, and to allow us to hold on to a version of direct realism. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: Maund says that the adverbialist's fears about indirect/representative theories are unfounded. My feeling is that neither account will do the job properly once we get a better account of consciousness. Maybe adverbialism is only for secondary qualities. |
| 7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |
| Full Idea: The content of thought can either be expressed as satisfaction conditions (e.g. truth-conditions for beliefs), or as the exercise of at least two concepts. | |
| From: report of Barry Maund (Perception [2003], Ch. 8) by PG - Db (ideas) | |
| A reaction: I think I favour the first view, because not all conjunctions of concepts would count as thoughts (e.g. rhubarb-plus-contradiction). A bunch of concepts becomes a thought when it connects in some way to reality? |