18 ideas
| 9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
| Full Idea: An argument is 'premise-circular' if it aims to establish a conclusion that is assumed as a premise of that very argument. An argument is 'rule-circular' if it aims to establish a conclusion that asserts the goodness of the rule used in that argument. | |
| From: report of R.B. Braithwaite (Scientific Explanation [1953], p.274-8) by Michael Devitt - There is no a Priori §2 | |
| A reaction: Rule circularity is the sort of thing Quine is always objecting to, but such circularities may be unavoidable, and even totally benign. All the good things in life form a mutually supporting team. |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 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. |