102 ideas
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| Full Idea: In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth. |
| 13643 | Aristotelian logic is complete [Shapiro] |
| Full Idea: Aristotelian logic is complete. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5) | |
| A reaction: [He cites Corcoran 1972] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| Full Idea: If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.2) | |
| A reaction: The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set. |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| Full Idea: The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| Full Idea: Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper? | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference. |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| Full Idea: In set theory it is central to the iterative conception that the membership relation is well-founded, ...which means there are no infinite descending chains from any relation. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.4) |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| Full Idea: The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20. |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| Full Idea: Iterative sets do not exhibit a Boolean structure, because the complement of an iterative set is not itself an iterative set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| Full Idea: A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3) | |
| A reaction: So there is a beginning, an ongoing sequence, and no retracing of steps. |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| Full Idea: There is no question of finding the 'correct' or 'true' logic underlying a part of natural language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: One needs the context of Shapiro's defence of second-order logic to see his reasons for this. Call me romantic, but I retain faith that there is one true logic. The Kennedy Assassination problem - can't see the truth because drowning in evidence. |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| Full Idea: A logic can be seen as the ideal of what may be called 'relative justification', the process of coming to know some propositions on the basis of others. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.3.1) | |
| A reaction: This seems to be the modern idea of logic, as opposed to identification of a set of 'logical truths' from which eternal necessities (such as mathematics) can be derived. 'Know' implies that they are true - which conclusions may not be. |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| Full Idea: Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1) |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| Full Idea: In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2) |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| Full Idea: Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2) |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| Full Idea: Almost all the systems developed in the first part of the twentieth century are higher-order; first-order logic was an afterthought. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| Full Idea: The 'triumph' of first-order logic may be related to the remnants of failed foundationalist programmes early this century - logicism and the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: Being complete must also be one of its attractions, and Quine seems to like it because of its minimal ontological commitment. |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| Full Idea: Tharp (1975) suggested that compactness, semantic effectiveness, and the Löwenheim-Skolem properties are consequences of features one would want a logic to have. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: I like this proposal, though Shapiro is strongly against. We keep extending our logic so that we can prove new things, but why should we assume that we can prove everything? That's just what Gödel suggests that we should give up on. |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| Full Idea: The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1) | |
| A reaction: Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic. |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| Full Idea: Shapiro preferred second-order logic to set theory because second-order logic refers only to the relations and operations in a domain, and not to the other things that set-theory brings with it - other domains, higher-order relations, and so forth. | |
| From: report of Stewart Shapiro (Foundations without Foundationalism [1991]) by Shaughan Lavine - Understanding the Infinite VII.4 |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| Full Idea: Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: [my summary] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
|
Full Idea:
In 'Henkin' semantics, in a given model |
|
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| Full Idea: In the standard semantics of second-order logic, by fixing a domain one thereby fixes the range of both the first-order variables and the second-order variables. There is no further 'interpreting' to be done. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) | |
| A reaction: This contrasts with 'Henkin' semantics (Idea 13650), or first-order semantics, which involve more than one domain of quantification. |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| Full Idea: The counterparts of Completeness, Compactness and the Löwenheim-Skolem theorems all fail for second-order languages with standard semantics, but hold for Henkin or first-order semantics. Hence such logics are much like first-order logic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: Shapiro votes for the standard semantics, because he wants the greater expressive power, especially for the characterization of infinite structures. |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| Full Idea: It follows from Gödel's incompleteness theorem that the semantic consequence relation of second-order logic is not effective. For example, the set of logical truths of any second-order logic is not recursively enumerable. It is not even arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I don't fully understand this, but it sounds rather major, and a good reason to avoid second-order logic (despite Shapiro's proselytising). See Peter Smith on 'effectively enumerable'. |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| Full Idea: Second-order logic is inherently incomplete, so its semantic consequence relation is not effective. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| Full Idea: It is sometimes difficult to find a formula that is a suitable counterpart of a particular sentence of natural language, and there is no acclaimed criterion for what counts as a good, or even acceptable, 'translation'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) |
| 4098 | The theory of descriptions supports internalism, since they are thinkable when the object is non-existent [Crane] |
| Full Idea: The theory of descriptions gives a model of internalist intentionality, in that it describes cases where the thinkability of a belief does not depend on the existence of a specific object. | |
| From: Tim Crane (Elements of Mind [2001], 4.36) | |
| A reaction: So what do externalists say about the theory? Surely a reference to 'water' can't entail the existence of water? |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise. |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| Full Idea: The 'satisfaction' relation may be thought of as a function from models, assignments, and formulas to the truth values {true,false}. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: This at least makes clear that satisfaction is not the same as truth. Now you have to understand how Tarski can define truth in terms of satisfaction. |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| Full Idea: Typically, model-theoretic semantics is formulated in set theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5.1) |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| Full Idea: An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904]. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| Full Idea: Categoricity cannot be attained in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.3) |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| Full Idea: A language has the Downward Löwenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't employ an infinite model to represent a fact about a countable set. |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| Full Idea: A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't have a countable model to represent a fact about infinite sets. |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorems mean that no first-order theory with an infinite model is categorical. If Γ has an infinite model, then it has a model of every infinite cardinality. So first-order languages cannot characterize infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: So much of the debate about different logics hinges on characterizing 'infinite structures' - whatever they are! Shapiro is a leading structuralist in mathematics, so he wants second-order logic to help with his project. |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| Full Idea: The Upward Löwenheim-Skolem theorem fails (trivially) with substitutional semantics. If there are only countably many terms of the language, then there are no uncountable substitution models. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: Better and better. See Idea 13674. Why postulate more objects than you can possibly name? I'm even suspicious of all real numbers, because you can't properly define them in finite terms. Shapiro objects that the uncountable can't be characterized. |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| Full Idea: A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: Similarly, 'weakly complete' is when every logical truth is a theorem. |
| 13628 | We can live well without completeness in logic [Shapiro] |
| Full Idea: We can live without completeness in logic, and live well. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: This is the kind of heady suggestion that American philosophers love to make. Sounds OK to me, though. Our ability to draw good inferences should be expected to outrun our ability to actually prove them. Completeness is for wimps. |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| Full Idea: It is sometimes said that non-compactness is a defect of second-order logic, but it is a consequence of a crucial strength - its ability to give categorical characterisations of infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: The dispute between fans of first- and second-order may hinge on their attitude to the infinite. I note that Skolem, who was not keen on the infinite, stuck to first-order. Should we launch a new Skolemite Crusade? |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| Full Idea: Compactness is a corollary of soundness and completeness. If Γ is not satisfiable, then, by completeness, Γ is not consistent. But the deductions contain only finite premises. So a finite subset shows the inconsistency. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: [this is abbreviated, but a proof of compactness] Since all worthwhile logics are sound, this effectively means that completeness entails compactness. |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| Full Idea: 'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.1) | |
| A reaction: On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before. |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| Full Idea: The main problem of characterizing the natural numbers is to state, somehow, that 0,1,2,.... are all the numbers that there are. We have seen that this can be accomplished with a higher-order language, but not in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| Full Idea: By convention, the natural numbers are the finite ordinals, the integers are certain equivalence classes of pairs of finite ordinals, etc. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.3) |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| Full Idea: The 'continuum' is the cardinality of the powerset of a denumerably infinite set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.2) |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| Full Idea: Few theorists consider first-order arithmetic to be an adequate representation of even basic number theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5 n28) | |
| A reaction: This will be because of Idea 13656. Even 'basic' number theory will include all sorts of vast infinities, and that seems to be where the trouble is. |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| Full Idea: There are sets of natural numbers definable in set-theory but not in arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3) |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| Full Idea: It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic. |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| Full Idea: I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics. |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| Full Idea: Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics. |
| 4077 | Aesthetic properties of thing supervene on their physical properties [Crane] |
| Full Idea: It is sometimes said that the aesthetic properties of a thing supervene on its physical properties. | |
| From: Tim Crane (Elements of Mind [2001], 2.16) | |
| A reaction: A confusing example, as aesthetic properties only exist if there is an observer. Is 'supervenience' just an empty locution which tries to avoid reduction? |
| 4078 | Constitution (as in a statue constituted by its marble) is supervenience without identity [Crane] |
| Full Idea: A statue is constituted by the marble that makes it up. It is plausible to say that constitution is not the same as identity - since identity is symmetrical and identity is not - but nonetheless constitution is a supervenience relation. | |
| From: Tim Crane (Elements of Mind [2001], 2.16) | |
| A reaction: So what makes it a statue, as opposed to a piece of marble? It may well be an abstraction which only exists relative to observers. |
| 4082 | The distinction between 'resultant' properties (weight) and 'emergent' properties is a bit vague [Crane] |
| Full Idea: The distinction between 'resultant' properties like weight, and 'emergent' properties like colour, seems intuitive enough, but on examination it is very hard to make precise. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: It is no coincidence that the examples are of primary and secondary qualities. If 'the physical entails the mental' then all mental properties are resultant. |
| 4083 | If mental properties are emergent they add a new type of causation, and physics is not complete [Crane] |
| Full Idea: Whatever the causal process is, it remains true that if emergentism is true, the completeness of physics is false; there are some effects which would not have come about if mental things were absent from the world. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: Emergentism looks to me like an incoherent concept, unless it is another word for dualism. |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| Full Idea: Properties are often taken to be intensional; equiangular and equilateral are thought to be different properties of triangles, even though any triangle is equilateral if and only if it is equiangular. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: Many logicians seem to want to treat properties as sets of objects (red being just the set of red things), but this looks like a desperate desire to say everything in first-order logic, where only objects are available to quantify over. |
| 4079 | Properties are causes [Crane] |
| Full Idea: Properties are causes. | |
| From: Tim Crane (Elements of Mind [2001], 2.17) | |
| A reaction: We can't detect properties if they lack causal powers. This may be a deep confusion. Properties are what make causal powers possible, but that isn't what properties are? |
| 4068 | Traditional substance is separate from properties and capable of independent existence [Crane] |
| Full Idea: The traditional concept of substance says substances bear properties which are distinct from them, and substances are capable of independent existence. | |
| From: Tim Crane (Elements of Mind [2001], 2.9) | |
| A reaction: Put like that, it sounds ridiculous as a physical theory. It is hard to dislodge substance, though, from a priori human metaphysics. |
| 3756 | Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske] |
| Full Idea: The basic sources of knowledge and justification are perception, introspection, testimony, memory, reason, and inference. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 4096 | Maybe beliefs don't need to be conscious, if you are not conscious of the beliefs guiding your actions [Crane] |
| Full Idea: The beliefs that are currently guiding your actions do not need to be in your stream of consciousness, which suggests that beliefs do not need to be conscious at all. | |
| From: Tim Crane (Elements of Mind [2001], 4.31) | |
| A reaction: Too bold, I think. Presumably this would eliminate all the other propositional attitudes from consciousness. There would only be qualia left! |
| 4097 | Maybe there are two kinds of belief - 'de re' beliefs and 'de dicto' beliefs [Crane] |
| Full Idea: Some philosophers have claimed that there are two kinds of belief, 'de re' belief and 'de dicto' belief. | |
| From: Tim Crane (Elements of Mind [2001], 4.35) | |
| A reaction: Interesting, though it may only distinguish two objects of belief, not two types. Internalist and externalist views are implied. |
| 4093 | Many cases of knowing how can be expressed in propositional terms (like how to get somewhere) [Crane] |
| Full Idea: There are plenty of cases of knowing how to do something, where that knowledge can also be expressed - without remainder, as it were - in propositional terms (such as knowing how to get to the Albert Hall). | |
| From: Tim Crane (Elements of Mind [2001], 3.28) | |
| A reaction: Presumably all knowing how could be expressed propositionally by God. |
| 4108 | Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless, so which is it? [Crane] |
| Full Idea: Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless. Is it really bitter, or really tasteless? | |
| From: Tim Crane (Elements of Mind [2001], 5.44) | |
| A reaction: A nice reinforcement of a classic Greek question. Good support for the primary/secondary distinction. Common sense, really. |
| 4105 | The traditional supports for the sense datum theory were seeing double and specks before one's eyes [Crane] |
| Full Idea: The traditional examples used to support the sense datum theory were seeing double and specks before one's eyes. | |
| From: Tim Crane (Elements of Mind [2001], 5.43) | |
| A reaction: Presumably, though, direct realists can move one eye, or having something wrong with a retina. |
| 4104 | One can taste that the wine is sour, and one can also taste the sourness of the wine [Crane] |
| Full Idea: One can taste that the wine is sour, and one can also taste the sourness of the wine. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: …so sense data are optional? We create sense data by objectifying them, but animals just taste the wine, and are direct realists. Tasting the sourness seems to be a case of abstraction. |
| 4101 | If we smell something we are aware of the smell separately, but we don't perceive a 'look' when we see [Crane] |
| Full Idea: Visual perception seems to differ from some of the other senses; when we become aware of burning toast, we become aware of the smell, ...but we don't see a garden by seeing a 'look' of the garden. | |
| From: Tim Crane (Elements of Mind [2001], 5.40) | |
| A reaction: Interesting. Do blind people transfer this more direct perception to a different sense (e.g. the one they rely on most)? |
| 4102 | The problems of perception disappear if it is a relation to an intentional state, not to an object or sense datum [Crane] |
| Full Idea: The solution to the problem of perception is to deny that it is related to real objects (things or sense-data); rather, perception is an intentional state (with a subject, mode and content), a relation to the intentional content. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: Not clear. This definition makes it sound like a propositional attitude. |
| 4109 | If perception is much richer than our powers of description, this suggests that it is non-conceptual [Crane] |
| Full Idea: The richness in information of perceptual experience outruns our modes of description of it, which has led some philosophers to claim that the content of perceptual experience is non-conceptual. | |
| From: Tim Crane (Elements of Mind [2001], 5.45) | |
| A reaction: It certainly implies that it can't be entirely conceptual, but it still may be that in humans concepts are always involved. Not when I'm waking up in the morning, though. |
| 3757 | Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske] |
| Full Idea: The causal theory of perceptions says that to perceive an object is to have a sense-datum caused by that object; it is not enough for the world to be the way we perceive it; the world must cause the perception. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) | |
| A reaction: All causal theories seem dubious to me; what causes something is not the same was what it means, or refers to, or what justifies it. The hallmark of successful perception is truth. I would perceive a tree if God planted the perception in me. |
| 4103 | The adverbial theory of perceptions says it is the experiences which have properties, not the objects [Crane] |
| Full Idea: The Adverbial Theory of perception holds that the predicates which other theories take as picking out the properties of objects are really adverbs of the perceptual verb; ..instead of strange objects, we just have properties of experiences. | |
| From: Tim Crane (Elements of Mind [2001], 5.42) | |
| A reaction: Promising. It fits secondary qualities all right, but what about primary? I 'see bluely', but can I 'see squarely'? |
| 3759 | You can acquire new knowledge by exploring memories [Bernecker/Dretske] |
| Full Idea: You can first come to know by remembering, as in learning how many windows there were in your childhood home by imagining a tour. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 3752 | Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske] |
| Full Idea: There is a distinction between a person being justified in holding a belief, and the belief itself being justified. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.II Int) | |
| A reaction: This is the crucial and elementary distinction which even the most sophisticated of epistemologists keep losing sight of. Epistemology is about persons. All true beliefs are justified - by the facts! |
| 3753 | Foundationalism aims to avoid an infinite regress [Bernecker/Dretske] |
| Full Idea: The driving force behind foundationalism has always been the threat of an infinite regress. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: You could just live with the regress (Peter Klein), or say that the regress fades away, or that it is cut off by social epistemological convention, or the regress circles round and rejoins. |
| 3754 | Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske] |
| Full Idea: If sense experiences are non-epistemic they may be infallible, but they are unsuitable for providing the foundations for other beliefs. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: If we experience flashing lights in the retina, or an afterimage, we don't think we are seeing objects, so why is normal perception different? Ans: because it is supported by judgement. |
| 4065 | Is knowledge just a state of mind, or does it also involve the existence of external things? [Crane] |
| Full Idea: It is controversial whether knowledge is a state of mind, or a composite state involving a thought about something, plus its existence. | |
| From: Tim Crane (Elements of Mind [2001], 1.5) | |
| A reaction: Pinpoints the internalism/externalism problem. Knowledge is a special type of belief (but maybe belief with external links!). Tricky. I vote for internalism. |
| 3755 | Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske] |
| Full Idea: The concept of justification is absolutely central to epistemology; but this concept is normative (i.e. it lays down norms), so epistemology can't be reduced to factual cognitive psychology. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: A simple rejection of the 'epistemology naturalised' idea. Best to start with slugs rather than people. You can confuse a slug, so it has truth or falsehood, but what is slug normativity? This is an interesting discussion point, not an argument. |
| 3761 | Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske] |
| Full Idea: In modern epistemology the three strategies to rebut the sceptic are 1) epistemological externalism, 2) the 'relevant alternative account of knowledge' (that scepticism is too extreme to be relevant), and 3) semantic externalism. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.IV Int) |
| 3760 | Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske] |
| Full Idea: The new riddle of induction ('grue') seems to demonstrate that sound inductive inferences are arbitrary because they depend on the actual language people use to formulate predictions. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 4092 | The core of the consciousness problem is the case of Mary, zombies, and the Hard Question [Crane] |
| Full Idea: The three arguments that have been used to articulate the problem of consciousness are the knowledge argument ('Mary'), the possibility of 'zombies' (creatures like us but lacking phenomenal consciousness), and the explanatory gap (the Hard Question). | |
| From: Tim Crane (Elements of Mind [2001], 3.26) | |
| A reaction: All of these push towards the implausible claim that there could never be a physical explanation of why we experience things. Zombies are impossible, in my opinion. |
| 4087 | Intentionalism does not require that all mental states be propositional attitudes [Crane] |
| Full Idea: Intentionalism (the doctrine that all mental states are intentional) need not be the thesis that all mental states are propositional attitudes. | |
| From: Tim Crane (Elements of Mind [2001], 3.22) | |
| A reaction: This points to the requirement for an intentionalist to prove that so-called 'qualia' states are essentially intentional, which is not implausible. |
| 4095 | Object-directed attitudes like love are just as significant as propositional attitudes [Crane] |
| Full Idea: Love, hate, and the other object-directed attitudes have as much of a role in explaining behaviour as the propositional attitudes. | |
| From: Tim Crane (Elements of Mind [2001], 4.34) | |
| A reaction: A good clarification of the range of intentional states. Objects seem to be external, where propositions are clearly internal. |
| 4106 | If someone removes their glasses the content of experience remains, but the quality changes [Crane] |
| Full Idea: There is a phenomenal difference between a short-sighted person wearing glasses and not; they do not judge that the world is different, but the properties of the experience (the qualia) have changed. | |
| From: Tim Crane (Elements of Mind [2001], 5.43) | |
| A reaction: Could be challenged. If a notice becomes unreadable, that is more than the qualia changing. |
| 4089 | Pains have a region of the body as their intentional content, not some pain object [Crane] |
| Full Idea: The intentional object of a pain-state is a part or region of the body, not a pain-object. | |
| From: Tim Crane (Elements of Mind [2001], 3.24) | |
| A reaction: Plausible. Has anyone ever suffered from pain without some sense of what part of the body is actually in pain? |
| 4090 | Weak intentionalism says qualia are extra properties; strong intentionalism says they are intentional [Crane] |
| Full Idea: Weak intentionalism says all mental states are intentional, but qualia are higher-order properties of these states. ..Strong intentionalists say the phenomenal character of a sensation consists purely in that state's intentionality. | |
| From: Tim Crane (Elements of Mind [2001], 3.25) | |
| A reaction: The weak version sounds better. Asking 'how could a thought have a quality of experience just by being about something?' is a restatement of the traditional problem, which won't go away. The Hard Question. |
| 4107 | With inverted qualia a person's experiences would change, but their beliefs remain the same [Crane] |
| Full Idea: The right thing to say about inverted qualia is that the person's experiences are different from other people's, but their beliefs are the same. | |
| From: Tim Crane (Elements of Mind [2001], 5.44) | |
| A reaction: Right - which reinforces the idea that all beliefs are the result of judgement, and none come directly from perception. |
| 4069 | Descartes did not think of minds as made of a substance, because they are not divisible [Crane] |
| Full Idea: It would be wrong to represent Descartes' view as the idea that bodies are made of one kind of stuff and minds of another; he did not think minds are made of stuff at all, because then they would be divisible. | |
| From: Tim Crane (Elements of Mind [2001], 2.10) | |
| A reaction: I'm not convinced. It could be an indivisible substance. Without a mental substance, Descartes may have to say the mind is an abstraction, perhaps a pattern of Platonic forms. |
| 4074 | Functionalism defines mental states by their causal properties, which rules out epiphenomenalism [Crane] |
| Full Idea: Functionalism holds that it is in the nature of certain mental states to have certain effects; therefore there can be no mental epiphenomena. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: I strongly resist the idea that a thing's identity is its function. Functionalism may not say that. Mind is an abstraction referring to a causal nexus of unknowable components. |
| 4091 | The problems of misrepresentation and error have dogged physicalist reductions of intentionality [Crane] |
| Full Idea: The fundamental problems of misrepresentation and error have dogged physicalist reductions of intentionality. | |
| From: Tim Crane (Elements of Mind [2001], 3.26) | |
| A reaction: If footprints or tree-rings are the model for reductions of intentionality, there doesn't seem much scope in them for giving false information, except by some freak event. |
| 4070 | Properties dualism says mental properties are distinct from physical, despite a single underlying substance [Crane] |
| Full Idea: According to property dualism, mental properties are distinct from physical properties, even though they are properties of one substance. | |
| From: Tim Crane (Elements of Mind [2001], 2.10) | |
| A reaction: Two properties may be phenomenologically different (transparent and magnetic), but that doesn't put them in different ontological categories. |
| 4084 | Non-reductive physicalism seeks an explanation of supervenience, but emergentists accept it as basic [Crane] |
| Full Idea: While the non-reductive physicalist believes that mental/physical supervenience must be explained, the emergentist is willing to accept it as a fact of nature. | |
| From: Tim Crane (Elements of Mind [2001], 2.18) | |
| A reaction: A good reason not to be an emergentist. No philosopher should abandon the principle of sufficient reason. |
| 4080 | If mental supervenes on the physical, then every physical cause will be accompanied by a mental one [Crane] |
| Full Idea: If the mental supervenes on the physical, then whenever a physical cause brings about some effect, a mental cause comes along for the ride. | |
| From: Tim Crane (Elements of Mind [2001], 2.17) | |
| A reaction: This is why supervenience seems to imply epiphenomenalism. The very concept of supervenience is dubious. |
| 4075 | Identity theory is either of particular events, or of properties, depending on your theory of causation [Crane] |
| Full Idea: If causation concerns events, then we have an identity theory of mental and physical events (particulars) [Davidson]. If causation is by properties, then it is mental and physical properties which are identical [Lewis and Armstrong]. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: Events are tokens, and properties are types. Tricky. Events are dynamic, but properties can be static. |
| 4085 | Physicalism may be the source of the mind-body problem, rather than its solution [Crane] |
| Full Idea: Physicalism may be the source of the mind-body problem, rather than its solution. | |
| From: Tim Crane (Elements of Mind [2001], 2.19) | |
| A reaction: Certainly if the physical is seen as just a pile of atoms, it is hard to see how they could ever think (see idea 1909). |
| 4073 | Overdetermination occurs if two events cause an effect, when each would have caused it alone [Crane] |
| Full Idea: Causal overdetermination is when an effect has more than one cause, and each event would have caused the effect if the other one had not done so. | |
| From: Tim Crane (Elements of Mind [2001], 2.13) | |
| A reaction: Overdetermination is a symptom that an explanation is questionable, but it can occur. Two strong people can join to push over a light hatstand. |
| 4072 | The completeness of physics must be an essential component of any physicalist view of mind [Crane] |
| Full Idea: I claim that the completeness of physics must be an essential component of any physicalist view of mind. | |
| From: Tim Crane (Elements of Mind [2001], 2.12) | |
| A reaction: He does not convince me of this. The mind may be within physics, but why should we say a priori that no exceptions to physical law will ever be discovered. Crane is setting up straw men. |
| 4094 | Experience teaches us propositions, because we can reason about our phenomenal experience [Crane] |
| Full Idea: In experience we learn propositions, since someone can reason using the sentence 'Red looks like this' (e.g. 'If red looks like this, then either it looks like this to dogs or it doesn't'). | |
| From: Tim Crane (Elements of Mind [2001], 3.28) | |
| A reaction: The fact that we can create propositions about experiences doesn't prove that experience is inherently propositional. |
| 4100 | The Twin Earth argument depends on reference being determined by content, which may be false. [Crane] |
| Full Idea: The Twin Earth argument does not refute internalism, since it depends on the 'Content-Determines-Reference' principle, which internalists can reject. | |
| From: Tim Crane (Elements of Mind [2001], 4.37) | |
| A reaction: The idea is that content should be understood in a context (e.g. on a particular planet). Indexicals count against a totally narrow view of content (Twins thinking 'I am here'). |
| 3758 | Semantic externalism ties content to the world, reducing error [Bernecker/Dretske] |
| Full Idea: Semantic externalism ties our mental content down to our actual environment so there is no possibility of massive error. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) | |
| A reaction: This sounds more prescriptive than descriptive. People do make massive errors in their concepts. Maybe educated people are more externalist (respectful of experts) than uneducated people? |
| 4067 | Broad content entails the existence of the object of the thought [Crane] |
| Full Idea: If a mental state is broad, then the existence of the mental state entails the existence of its object. | |
| From: Tim Crane (Elements of Mind [2001], 1.7) | |
| A reaction: Hence thinking of non-existent things like unicorns is problematic for externalists. However, externalists can think about numbers or Platonic ideals. |
| 4063 | In intensional contexts, truth depends on how extensions are conceived. [Crane] |
| Full Idea: Intensional contexts are those where truth or falsehood depends on the way the extensions are conceived. | |
| From: Tim Crane (Elements of Mind [2001], 1.4) | |
| A reaction: An important distinction for anyone defending an internalist view of concepts or of knowledge |
| 4071 | Causation can be seen in counterfactual terms, or as increased probability, or as energy flow [Crane] |
| Full Idea: A theory of causation might say 'If A had not existed, B would not have existed' (counterfactual theory), or 'B is more likely if A occurs' (probabilistic), or 'energy flows from A to B'. | |
| From: Tim Crane (Elements of Mind [2001], 2.11) | |
| A reaction: As always, it is vital to separate epistemology from ontology. Energy won't cover agents. Whisper "Fire!" in a theatre. |
| 4076 | Causes are properties, not events, because properties are what make a difference in a situation [Crane] |
| Full Idea: My view is that causes are properties (not events); when we look for causes, we look for the aspect of a situation which made a difference, and aspects are properties or qualities. | |
| From: Tim Crane (Elements of Mind [2001], 2.14) | |
| A reaction: He is talking about explanations, which may not be causes, or at least they have a different emphasis. Don't events 'make a difference'? Events are ontologically weird |
| 4066 | It seems that 'exists' could sometimes be a predicate [Crane] |
| Full Idea: The view that 'exists' is never a predicate is not plausible. | |
| From: Tim Crane (Elements of Mind [2001], 1.7) | |
| A reaction: He doesn't enlarge. Russell says 'exists' is a quantifier. 'Your very existence offends me - I hope it is confiscated'. |