43 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. |
| 18767 | Free logics has terms that do not designate real things, and even empty domains [Anderson,CA] |
| Full Idea: Free logics say 1) singular terms are allowed that do not designate anything that exists; sometimes 2) is added: the domain of discourse is allowed to be empty. Logics with both conditions are called 'universally free logics'. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.3) | |
| A reaction: I really like the sound of this, and aim to investigate it. Karel Lambert's writings are the starting point. Maybe the domain of logic is our concepts, rather than things in the world, in which case free logic sounds fine. |
| 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. |
| 18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |
| Full Idea: Under its now standard principal interpretation, the monadic predicate variables in second-order logic range over subsets of the domain on individuals. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5) | |
| A reaction: This is an interpretation in which properties are just sets of things, which is fine if you are a logician, but not if you want to talk about anything important. Still, we must play the game. Boolos introduced plural quantification at this point. |
| 18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |
| Full Idea: Ontological quantifiers might just as well range over all the entities needed for the semantics. ...The minimal way would be to just stop calling '∃' an 'existential quantifier', and always read it as 'there is...' rather than 'there exists...'. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6) | |
| A reaction: There is no right answer here, but it seems to be the strategy adopted by most logicians, and the majority of modern metaphysicians. They just allow abstracta, and even fictions, to 'exist', while not being fussy what it means. Big mistake! |
| 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. |
| 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. |
| 18769 | Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA] |
| Full Idea: A cursory examination shows that mathematicians have no aversion to saying that this-or-that mathematical entity exists. But is this a different sense of 'existence'? | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6) | |
| A reaction: For those of us like me and my pal Quine who say that 'exist' is univocal (i.e. only one meaning), this is a nice challenge. Quine solves it by saying maths concerns sets of objects. I, who don't like sets, am puzzled (so I turn to fictionalism...). |
| 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. |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| Full Idea: I. Nothing exists. a) Not-Being does not exist. b) Being does not exist as everlasting, as created, as both, as One, or as Many. II. If anything does exist, it is incomprehensible. III. If existence is comprehensible, it is incommunicable. | |
| From: report of Gorgias (fragments/reports [c.443 BCE], B03) by Diogenes Laertius - Lives of Eminent Philosophers 09 | |
| A reaction: [Also Sextus Empiricus, Against Logicians I.65-] For Part I he works through all the possible modes of being he can think of, and explains why none of them are possible. It is worth remembering that Gorgias loved rhetoric, not philosophy! |
| 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. |
| 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. |
| 18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA] |
| Full Idea: There are sensible ways to maike a distinction between different kinds of being. ..One need not fear that this leads to a 'bloated ontology'. ...We need only distinguish 'ontological commitment' from 'existential commitment' | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6) | |
| A reaction: He speaks of giving fictional and abstract entities a 'lower score' in existence. I think he means the 'ontological' commitment to be the stronger of the two. |
| 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. |
| 18766 | 's is non-existent' cannot be said if 's' does not designate [Anderson,CA] |
| Full Idea: The paradox of negative existentials says that if 's' does not designate something, then the sentence 's is non-existent' is untrue. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.1) | |
| A reaction: This only seems be a problem for logicians. Everyone else can happily say 'my coffee is non-existent'. |
| 18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA] |
| Full Idea: Parmenides was correct - one cannot speak of that which is not, even to say that it is not. But one can speak of concepts and say of them that they do not correspond to anything real. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.5) | |
| A reaction: [This summarises Alonso Church, who was developing Frege] This sounds like the right thing to say about non-existence, but then the same principle must apply to assertions of existence, which will also be about concepts and not things. |
| 18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA] |
| Full Idea: The medieval philosophers and then Leibniz were keen on finding 'principles of individuation', and the idea appears again in Frege, to be taken up in some respects by Wittgenstein. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.6) | |
| A reaction: I take a rather empirical approach to this supposed problem, and suggest we break 'individuation' down into its component parts, and then just drop the word. Discussions of principles of individuations strike me as muddled. Wiggins and Lowe today. |
| 18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
| Full Idea: In the Identity of Indiscernibles, one speaks about properties, and the notion of a property is by no means clearly fixed and formalized in modern symbolic logic. | |
| From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5) | |
| A reaction: The unclarity of 'property' is a bee in my philosophical bonnet, in speech, and in metaphysics, as well as in logic. It may well be the central problem in our attempts to understand the world in general terms. He cites intensional logic as promising. |
| 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. |
| 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. |
| 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. |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| Full Idea: Gorgias insists that the art of persuasion is superior to all others because it enslaves all the rest, with their own consent, not by force, and is therefore by far the best of all the arts. | |
| From: report of Gorgias (fragments/reports [c.443 BCE]) by Plato - Philebus 58a | |
| A reaction: A nice point, and it is not unreasonable to rank the arts in order of their power. To enchant, without achieving agreement, and to speak truth without persuading, are both very fine, but there is something about success that cannot be gainsaid. |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| Full Idea: Destroy the seriousness of others with laughter, and their laughter with seriousness. | |
| From: Gorgias (fragments/reports [c.443 BCE]), quoted by Aristotle - The Art of Rhetoric 1419b | |
| A reaction: This sounds like brilliant tactical advice, which should be on the wall of every barrister's chambers. This is a case of rhetoric having something to teach us which is nothing at all to do with truth. It is more like learning karate. |