39 ideas
| 8820 | Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock] |
| Full Idea: Rather than truth being fundamental and rules for reasoning being derived from it, the rules for reasoning come first and truth is characterized by the rules for reasoning about truth. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Cog.Mach') | |
| A reaction: This nicely disturbs our complacency about such things. There is plenty of reasoning in Homer, but I bet there is no talk of 'truth'. Pontius Pilate seems to have been a pioneer (Idea 8821). Do the truth tables define or describe logical terms? |
| 8819 | We need the concept of truth for defeasible reasoning [Pollock] |
| Full Idea: It might be wondered why we even have a concept of truth. The answer is that this concept is required for defeasible reasoning. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Cog.Mach') | |
| A reaction: His point is that we must be able to think critically about our beliefs ('is p true?') if we are to have any knowledge at all. An excellent point. Give that man a teddy bear. |
| 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) |
| 14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
| Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures. |
| 14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
| Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary. |
| 14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
| Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue). | |
| From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
| A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue. |
| 14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
| Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §5) | |
| A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness. |
| 14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
| Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial. |
| 14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
| Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers. |
| 14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
| Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with. |
| 14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
| Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia. | |
| From: L.A. Paul (In Defense of Essentialism [2006], §3) | |
| A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world. |
| 8822 | Statements about necessities need not be necessarily true [Pollock] |
| Full Idea: True statements about the necessary properties of things need not be necessarily true. The well-known example is that the number of planets (9) is necessarily an odd number. The necessity is de re, but not de dicto. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Nat.Internal') | |
| A reaction: This would be a matter of the scope (the placing of the brackets) of the 'necessarily' operator in a formula. The quick course in modal logic should eradicate errors of this kind in your budding philosopher. |
| 14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
| Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta. | |
| From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
| A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world. |
| 8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
| Full Idea: Defeasible reasoning requires us to be able to think about our thoughts. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Cog.Mach') | |
| A reaction: This is why I do not think animals 'know' anything, though they seem to have lots of true beliefs about their immediate situation. |
| 8811 | What we want to know is - when is it all right to believe something? [Pollock] |
| Full Idea: When we ask whether a belief is justified, we want to know whether it is all right to believe it. The question we must ask is 'when is it permissible (epistemically) to believe P?'. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Ep.Norms') | |
| A reaction: Nice to see someone trying to get the question clear. The question clearly points to the fact that there must at least be some sort of social aspect to criteria of justification. I can't cheerfully follow my intuitions if everyone else laughs at them. |
| 8817 | Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock] |
| Full Idea: Epistemologists have noted that logical entailments do not always constitute reasons. P may entail Q without the connection between P and Q being at all obvious. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Ref.of Extern') | |
| A reaction: Graham Priest and others try to develop 'relevance logic' to deal with this. This would deny the peculiar classical claim that everything is entailed by a falsehood. A belief looks promising if it entails lots of truths about the world. |
| 8814 | Epistemic norms are internalised procedural rules for reasoning [Pollock] |
| Full Idea: Epistemic norms are to be understood in terms of procedural knowledge involving internalized rules for reasoning. | |
| From: John L. Pollock (Epistemic Norms [1986], 'How regulate?') | |
| A reaction: He offers analogies with bicycly riding, but the simple fact that something is internalized doesn't make it a norm. Some mention of truth is needed, equivalent to 'don't crash the bike'. |
| 8823 | Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock] |
| Full Idea: When one makes a perceptual judgement on the basis of a perceptual state, I want to say that the perceptual state itself is one's reason. ..Reason are always reasons for beliefs, but the reasons themselves need not be beliefs. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Dir.Realism') | |
| A reaction: A crucial issue. I think I prefer the view of Davidson, in Ideas 8801 and 8804. Three options: a pure perception counts as a reason, or perceptions involve some conceptual content, or you only acquire a reason when a proposition is formulated. |
| 8813 | If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock] |
| Full Idea: If we had to make explicit appeal to epistemic norms for justification (the 'intellectualist model') we would find ourselves in an infinite regress. The norms, their existence and their application would themselves have to be justified. | |
| From: John L. Pollock (Epistemic Norms [1986], 'How regulate?') | |
| A reaction: This is counter to the 'space of reasons' picture, where everything is rationally assessed. There are regresses for both reasons and for experiences, when they are offered as justifications. |
| 8812 | Norm Externalism says norms must be internal, but their selection is partly external [Pollock] |
| Full Idea: Norm Externalism acknowledges that the content of our epistemic norms must be internalist, but employs external considerations in the selection of the norms themselves. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Ep.Norms') | |
| A reaction: It can't be right that you just set your own norms, so this must contain some truth. Equally, even the most hardened externalist can't deny that what goes on in the head of the person concerned must have some relevance. |
| 8816 | Externalists tend to take a third-person point of view of epistemology [Pollock] |
| Full Idea: Externalists tend to take a third-person point of view in discussing epistemology. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Ref.of Extern') | |
| A reaction: Pollock's point, quite reasonably, is that the first-person aspect must precede any objective assessment of whether someone knows. External facts, such as unpublicised information, can undermine high quality internal justification. |
| 8815 | Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock] |
| Full Idea: External considerations of reliability could not be internalized. Consequently, it is in principle impossible for us to actually employ externalist norms. I take this to be a conclusive refutation of belief externalism. | |
| From: John L. Pollock (Epistemic Norms [1986], 'Ref.of Extern') | |
| A reaction: Not so fast. He earlier rejected the 'intellectualist model' (Idea 8813), so he doesn't think norms have to be fully conscious and open to criticism. So they could be innate, or the result of indoctrination (sorry, teaching), or just forgotten. |