23 ideas
| 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. |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 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! |
| 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...). |
| 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. |
| 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. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 6968 | Some people think there are ethical facts, but of a 'queer' sort [Ayer] |
| Full Idea: If someone wishes to say that ethical statements are statements of fact, only it is a queer sort of fact, he is welcome to do so. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.233) | |
| A reaction: The word 'queer' was picked up by Mackie and developed into his error theory, that moral facts are a misunderstanding. Personally I think that moral facts might be teleological facts, but that is rather hard to demonstrate. |
| 6972 | A right attitude is just an attitude one is prepared to stand by [Ayer] |
| Full Idea: Asking whether the attitude that one has adopted is the right attitude comes down to asking whether one is prepared to stand by it. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.244) | |
| A reaction: I would have thought that someone who persisted in being ruthlessly selfish might nevertheless distinguish their behaviour from the grudging concession that the 'right' thing to do might be quite different. |
| 6973 | Moral theories are all meta-ethical, and are neutral as regards actual conduct [Ayer] |
| Full Idea: All moral theories, intuitionist, naturalistic, objectivist, emotive, and the rest, in so far as they are philosophical theories, are neutral as regards actual conduct; they belong to the field of meta-ethics, not ethics proper. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949]) | |
| A reaction: Interestingly, Ayer doesn't seem willing to accept 'ethics proper' as being 'philosophical'. Given the modern rise of applied ethics, it seems suprising to say that even normative ethics is not philosophical. Utilitarianism seems not to be philosophical. |
| 6974 | Moral judgements cannot be the logical consequence of a moral philosophy [Ayer] |
| Full Idea: A moral philosopher will have his moral standards and will sometimes make moral judgements, but these moral judgements cannot be a logical consequence of his philosophy. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.247) | |
| A reaction: I take this to be an assertion of the is-ought distinction. Personally this strikes me as totally false. Ayer needs to think more deeply about moral philosophy! |
| 6971 | I would describe intuitions of good as feelings of approval [Ayer] |
| Full Idea: I suspect that the experiences which some philosophers want to describe as intuitions, or a quasi-sensory apprehensions, of good are not significantly different from those that I want to describe as feelings of approval. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.239) | |
| A reaction: This is the standard ground for rejecting intuitionism, along with the point that even if intuitions are not just feelings of approval, it seems impossible to tell the difference. |
| 6969 | Approval of historical or fictional murders gives us leave to imitate them [Ayer] |
| Full Idea: In saying that Brutus or Raskolnikov acted rightly, I am giving myself and others leave to imitate them should similar circumstances arise. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.237) | |
| A reaction: This seems to be a reply to the Frege-Geach Problem, of why we have emotional attitudes to crimes that mean nothing to us. Such crimes, however, involve our virtues, and don't depend on awaiting 'similar circumstances'. |
| 6970 | Moral judgements are not expressions, but are elements in a behaviour pattern [Ayer] |
| Full Idea: To say, as I once did, that moral judgements are merely expressive of certain feelings is an oversimplification; ..moral attitudes consist in certain patterns of behaviour, and the expression of a judgement is an element in the pattern. | |
| From: A.J. Ayer (On the analysis of moral judgements [1949], p.238) | |
| A reaction: This seems to switch from emotivism to what Frank Jackson calls 'moral functionalism', where morality is what gets us from certain emotional responses to willed actions. This strikes me, like most functional explanations, as wrong. |