40 ideas
| 9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
| Full Idea: Modal logic by its very nature is not monolithic, but fragmented into multiple systems of modal qualifications, reflected in the plurality of accessibility relations on modal model structures or logically possible worlds. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §3) | |
| A reaction: He implies the multiplicity is basic, and is only 'reflected' in the relations, but maybe the multiplicity is caused by incompetent logicians who can't decide whether possible worlds really are reflexive or symmetrical or transitive in their relations. |
| 7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
| Full Idea: The modal syntax and axiom systems of C.I.Lewis (1918) were formally interpreted by Kripke and Hintikka (c.1965) who, using Z-F set theory, worked out model set-theoretical semantics for modal logics and quantified modal logics. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: A historical note. The big question is always 'who cares?' - to which the answer seems to be 'lots of people', if they are interested in precision in discourse, in artificial intelligence, and maybe even in metaphysics. Possible worlds started here. |
| 9457 | The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette] |
| Full Idea: Philosophy of logic has (roughly) two camps: extensionalists and intensionalists, with the former view dominant. ...There is a close connection between this and eliminativist or reductivist versus folk psychological and intentionalist philosophy of mind. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: Hm. I think I favour intensionalism in the logic, and reductivism about the mind, so I may have a bit of bother here. I'm convinced that this jigsaw can be completed, despite all appearances. |
| 7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
| Full Idea: It is fundamental that logic depends on logical possibilities, in which logically possible properties are predicated of logically possible objects. Logic describes inferential structures among sentences expressing the predication of properties to objects. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: If our imagination is the only tool we have for assessing possibilities, this leaves the domain of logic as being a bit subjective. There is an underlying Platonism to the idea, since inferences would exist even if nothing else did. |
| 9463 | Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette] |
| Full Idea: Classical logic (of Whitehead, Russell, Gödel, Church) is a two-valued system of propositional and predicate logic, in which all propositions are exclusively true or false, and quantification and predication are over existent objects only. | |
| From: Dale Jacquette (Intro to I: Classical Logic [2002], p.9) | |
| A reaction: All of these get challenged at some point, though the existence requirement is the one I find dubious. |
| 7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
| Full Idea: At one level logic can be regarded as a theory of signs and formal rules, but we cannot neglect the meaning of propositions as they relate to states of affairs, and hence to possible properties and objects... there must be the possibility of truth-values. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: Thus if you define logical connectives by truth tables, you need the concept of T and F. You could, though, regard those too as purely formal (like 1 and 0 in electronics). But how do you decide which propositions are 1, and which are 0? |
| 7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
| Full Idea: It is infamous that on Russell's analysis the sentences "The winged horse has wings" and "The winged horse is a horse" are false, because in the extant domain of actual existent entities there contingently exist no winged horses | |
| From: Dale Jacquette (Ontology [2002], Ch. 6) | |
| A reaction: This is the best objection I have heard to Russell's account of definite descriptions. The connected question is whether 'quantifies over' is really a commitment to existence. See Idea 6067. |
| 9466 | Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette] |
| Full Idea: Some substitutional quantificationists in logic hope to avoid philosophical entanglements about the metaphysics of objects, ..and nominalists can find aid and comfort there. | |
| From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143) | |
| A reaction: This has an appeal for me, particularly if it avoids abstract objects, but I don't see much problem with material objects, so we might as well have a view that admits those. |
| 9465 | Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette] |
| Full Idea: The substitutional interpretation says the universal quantifier is true just in case it remains true for all substitutions of terms of the same type as that of the universally bound variable. | |
| From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143) | |
| A reaction: This doesn't seem to tell us how it gets started with being true. |
| 9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
| Full Idea: Extensionalists hold that quantifiers in predicate logic presuppose the existence of whatever objects can be referred to by constants or bound variables, or enter into true predication of properties. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: I have strong sales resistance to this view. Why should a procedure for correctly reasoning from one proposition to another have anything whatever to do with ontology? A false world picture can be interconnected by perfect logic. |
| 9461 | Intensionalists say meaning is determined by the possession of properties [Jacquette] |
| Full Idea: According to intensionalist semantics the meaning of a proposition is determined by the properties an object possesses. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: This sounds good to me. Extensionalist don't seem to care what sets they put things in, but if property possession comes first, then things will fall into their own sets without any help for us. We can add silly sets afterwards, if we fancy. |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
| Full Idea: The Barber Paradox refers to the non-existent property of being a barber who shaves all and only those persons who do not shave themselves. | |
| From: Dale Jacquette (Ontology [2002], Ch. 9) | |
| A reaction: [Russell spotted this paradox, and it led to his Theory of Types]. This paradox may throw light on the logic of indexicals. What does "you" mean when I say to myself "you idiot!"? If I can behave as two persons, so can the barber. |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
| Full Idea: We grasp the concept of being only when we have satisfactorily answered the question why there is something rather than nothing and why there is only one logically contingent actual world. | |
| From: Dale Jacquette (Ontology [2002], Conclusion) | |
| A reaction: See Ideas 7688 and 7692 for a glimpse of Jacquette's answer. Personally I don't yet have a full grasp of the concept of being, but I'm sure I'll get there if I only work a bit harder. |
| 7692 | Being is maximal consistency [Jacquette] |
| Full Idea: Being is maximal consistency. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: You'll have to read Ch.2 of Jacquette to see what this is all about, but as it stands it is a lovely slogan, and a wonderful googly/curve ball to propel at Parmenides or Heidegger. |
| 7687 | Existence is completeness and consistency [Jacquette] |
| Full Idea: A combinatorial ontology holds that existence is nothing more or less than completeness and consistency, or what is also called 'maximal consistency'. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: You'll have to read Jacquette to understand this one! The claim is that existence is to be defined in terms of logic (and whatever is required for logic). I take this to be a bit Platonist (rather than conventionalist) about logic. |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
| Full Idea: The principles of pure philosophical ontology are indistinguishable ... from the conceptual foundations of logic. | |
| From: Dale Jacquette (Ontology [2002], Pref) | |
| A reaction: I would take Russell to be an originator of this view. If the young Wittgenstein showed that the foundations of logic are simply conventional (truth tables), this seems to make ontology conventional too, which sounds very odd indeed (to me). |
| 7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
| Full Idea: The entities included in a theoretical ontology are those minimally required for an adequate philosophical semantics. ...These are the objects that we say exist, to which we are ontologically committed. | |
| From: Dale Jacquette (Ontology [2002], Pref) | |
| A reaction: Worded with exquisite care! He does not say that ontology is reducible to semantics (which is a silly idea). We could still be committed, as in a ghost story, to existence of some 'nameless thing'. Things utterly beyond our ken might exist. |
| 7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
| Full Idea: Logic involves the possibilities of predicating properties of objects in a conceptual scheme wherein either objects and properties are included in altogether separate categories, or objects are reducible to combinations of properties. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: In the first view, he says that objects are just 'logical pegs' for properties. Objects can't be individuated without properties. But combinations of properties would seem to need essences, or else they are too unstable to count as objects. |
| 7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
| Full Idea: We can reduce references to states-of-affairs to object-property combinations, and we can reduce logically possible worlds to logically possible states-of-affairs combinations. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: If we further reduce object-property combinations to mere combinations of properties (Idea 7683), then we have reduced our ontology to nothing but properties. Wow. We had better be very clear, then, about what a property is. I'm not. |
| 7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
| Full Idea: If classes alone cannot be eliminated from ontology on Quine's terms, and if classes are defined as property combinations, then neither are all properties, universals in the tradition sense, entirely eliminable. | |
| From: Dale Jacquette (Ontology [2002], Ch. 9) | |
| A reaction: If classes were totally conventional (and there was no such things as a 'natural' class) then you might admit something to a class without knowing its properties (as 'the thing in the box'). |
| 7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
| Full Idea: To be an object is to be a predication subject, and to be this as opposed to that particular object, whether existent or not, is to have a distinctive combination of properties. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: The last part depends on Leibniz's Law. The difficulty is that two objects may only be distinguishable by being in different places, and location doesn't look like a property. Cf. Idea 5055. |
| 7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
| Full Idea: Roughly, numbers, sets and propositions are assumed to be abstract particulars, while properties, including qualities and relations, are usually thought to be universals. | |
| From: Dale Jacquette (Ontology [2002], Ch. 9) | |
| A reaction: There is an interesting nominalist project of reducing all of these to particulars. Numbers to patterns, sets to their members, propositions to sentences, properties to causal powers, relations to, er, something else. |
| 7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
| Full Idea: The actual world is a maximally consistent state-of-affairs combination involving all and only the existent objects, which in turn exist because they are maximally consistent property combinations. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: [This extends Idea 7688]. This seems to invite the standard objections to the coherence theory of truth, such as Ideas 5422 and 4745. Is 'maximal consistency' merely a test for actuality, rather than an account of what actuality is? |
| 7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
| Full Idea: The actual world can be defined as a maximally consistent combination of actual states of affairs, or maximally consistent states-of-affairs combination. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: A key part of Jacquette's program of deriving ontological results from the foundations of logic. Is the counterfactual situation of my pen being three centimetres to the left of its current position a "less consistent" situation than the actual one? |
| 7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
| Full Idea: Many modal logicians in their philosophical moments have raised doubts about whether structures of propositions not associated with the actual world deserved to be called worlds at all. | |
| From: Dale Jacquette (Ontology [2002], Ch. 2) | |
| A reaction: A good question. Consistency is obviously required, but we also need a lot of propositions before we would consider it a 'world'. Very remote but consistent worlds quickly become unimaginable. Does that matter? |
| 7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
| Full Idea: Conventional modal semantics, in which all logically possible worlds are defined in terms of maximally consistent proposition sets, has no choice except to allow that the actual world is the world we experience in sensation, or that we inhabit. | |
| From: Dale Jacquette (Ontology [2002], Ch. 9) | |
| A reaction: Jacquette dislikes this because he is seeking an account of ontology that doesn't, as so often, merely reduce to epistemology (e.g. Berkeley). See Idea 7691 for his preferred account. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
| Full Idea: If qualia supervene on intentional states, then intentionality is also more explanatorily fundamental than qualia. | |
| From: Dale Jacquette (Ontology [2002], Ch.10) | |
| A reaction: See Idea 7272 for opposite view. Maybe intentional states are large mental objects of which we are introspectively aware, but which are actually composed of innumerable fine-grained qualia. Intentional states would only explain qualia if they caused them. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |
| 7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
| Full Idea: If intentionality sometimes involves a relation to nonexistent objects, like my dreamed-of visit to a Greek island, then such thoughts cannot be explained physically or causally, because only actual physical entities and events can be mentioned. | |
| From: Dale Jacquette (Ontology [2002], Ch.10) | |
| A reaction: Unimpressive. Thoughts of a Greek island will obviously reduce to memories of islands and Greece and travel brochures. Memory clearly retains past events in the present, and hence past events can be part of the material used in reductive accounts. |
| 9460 | Extensionalist semantics forbids reference to nonexistent objects [Jacquette] |
| Full Idea: In extensionalist semantics only existent objects can be referred to, ...but in everyday thought and discourse we regularly and apparently without undue confusion speak about nonexistent objects. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: This is the reason why Meinong, whose views are presented by Russell as absurd, are undergoing a revival. The full-blown view will even treat 'round squares' as objects about which we can reason - and why not? Don't open a shop which sells them. |
| 9459 | Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette] |
| Full Idea: Extensional semantics is blatantly circular. For 'Fa' to be interpreted as true, we must know that object a belongs to the extension of the predicate F, so we must already know which objects belong to the extension. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: I'm delighted to read this, because it was the first thought that occurred to me when I encountered the theory. Presumably this leads Quine to take predication as basic, because you can't break into the circle. Or, vote for intensionalism? |
| 7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |
| Full Idea: The extreme ontological alternatives with respect to the metaphysics of propositions are a Fregean Platonism (his "gedanken", 'thoughts'), and a radical nominalism or inscriptionalism, as in Quine, where they are just marks related to stimuli. | |
| From: Dale Jacquette (Ontology [2002], Ch. 9) | |
| A reaction: Personally I would want something between the two - that propositions are brain events of a highly abstract kind. I say that introspection reveals pre-linguistic thoughts, which are propositions. A proposition is an intentional state. |