29 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
| Full Idea: An 'obscurum per obscurius' explanation is explaining something mysterious by something even more mysterious, | |
| From: Peter Schulte (Mental Content [2023], 6) | |
| A reaction: Schulte's example is trying to explain mental content in terms of phenomenal experience. That is, roughly, explaining content by qualia, when the latter is the 'hard problem'. |
| 23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
| Full Idea: Some theorists maintain that all states with representational content or intentionality must have phenomenal character …and we can also ask whether all states with phenomenal character also have representional content. | |
| From: Peter Schulte (Mental Content [2023], 2.4) | |
| A reaction: He mentions that beliefs could involve inner speech. And pains and moods may be phenomenal but lack content. He also asks which determines which. |
| 23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
| Full Idea: A 'naturalistic' explanation of content excludes primitive mental or normative notions, but allows causation, counterfactual dependence, probabilistic dependence or structural similarity. | |
| From: Peter Schulte (Mental Content [2023], 4) | |
| A reaction: Apart from causation, what is permissible to naturalists (like me) all sounds rather superficial (and thus not very explanatory). I'm sure we can do better than this. How about using non-primitive mental notions? |
| 23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
| Full Idea: The phenomenal intentionality approach says that the content properties of mental states can be explained in terms of the phenomenal properties of mental states. | |
| From: Peter Schulte (Mental Content [2023], 6) | |
| A reaction: [Searle and Loar are cited] Tends to be 'non-naturalistic'. We might decide that content derives from the phenomenal, but still without saying anything interesting about content. Mathematical content? Universally generalised content? |
| 23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
| Full Idea: Recent naturalisation of content now also has to offer a matching account of representational explanations in cognitive science. | |
| From: Peter Schulte (Mental Content [2023], 08.1) | |
| A reaction: [He cites Cummins, Neander and Shea] This is in addition to the 'status' and 'content' questions of Idea 23796. This seems to be an interesting shift to philosophers working backwards from the theories of empirical science. Few are qualified for this job! |
| 23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
| Full Idea: We can say that non-Fregean content [reference] is (virtually) always contrued as broad, while Fregean content [sense] is usually contrued as narrow. | |
| From: Peter Schulte (Mental Content [2023], 3.2) | |
| A reaction: I can't make sense of mental content actually being outside the mind, so I see all content as narrow - but that doesn't mean that externals are irrelevant to it. If I think that is an oak, and it's an elm, the content is oak. |
| 23796 | Naturalists must explain both representation, and what is represented [Schulte] |
| Full Idea: Naturalistic accounts of content ask 1) what makes a state qualify as a representational state?, and 2) what makes a representational state have one specific content rather than another? | |
| From: Peter Schulte (Mental Content [2023], 4) | |
| A reaction: [As often in this collection, the author uses algebraic letters, but I prefer plain English] I would say that the first question looks more amenable to an answer than the second. Do we know the neuronal difference between seeing red and blue? |
| 23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
| Full Idea: Conceptual role semantics says the content of a representation is determined by the cognitive role it plays with a system. | |
| From: Peter Schulte (Mental Content [2023], 4.5) | |
| A reaction: Obvious problem: if 'swordfish' is the password, its role is quite different from its content. I've never thought that the role of something tells you anything about what it is. Hearts pump blood, but how do they fulfil that role? |
| 23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
| Full Idea: A simple causal theory of content has the 'content indeterminacy' problem - that the presence of a cow causes 'a cow is present', but also 'an animal is present' and 'a biological organism is present'. | |
| From: Peter Schulte (Mental Content [2023], 4.1) | |
| A reaction: That only rules out the 'simple' version. We just need to add that the cause (cow experience) is shaped by current knowledge and interests. Someone buying cows and someone terrified of them thereby produce different concepts. |
| 23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
| Full Idea: The core idea of teleosemantics is that we need to explain how content can be accurate or inaccurate, true or false, realised or unrealised …which must appeal to the distinction between proper functioning and malfunctioning. | |
| From: Peter Schulte (Mental Content [2023], 4.4) | |
| A reaction: My immediate reaction to this is that you don't learn about content by assessing its success. Surely (as with eyesight) you first need to understand what it does, and only then judge its success. …Though success and failure are implicit in function. |
| 23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
| Full Idea: Teleosemantic theories usually give a causal account of mental functions …where some trait has a particular function if it was selected for that function by a process of natural selection. | |
| From: Peter Schulte (Mental Content [2023], 4.4) | |
| A reaction: This is an idea I like - that something has a specific function if without that function it wouldn't have come into existence (eyes, for example). But presumably the function of a mind is to collect content - which does nothing to explain content! |
| 23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |
| Full Idea: Information theories of content [usually assume that] a column of smoke over there carries the information that fire is over there because it raises the probability of fire being over there. | |
| From: Peter Schulte (Mental Content [2023], 4.2) | |
| A reaction: Theorists usually add further conditions to this basic one. Fred Dretske is the source of this approach. Not promising, in my opinion. Surely the content is just smoke, and fire is one of dozens of possible inferences from it? |