24 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 16456 | For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker] |
| Full Idea: Lewis was suspicious of boxes and diamonds as regimenting ordinary modal thought, …preferring a first-order extensional theory including possible worlds in its domain and an indexical singular term for the actual world. | |
| From: report of David Lewis (Anselm and Actuality [1970]) by Robert C. Stalnaker - Mere Possibilities 3.8 |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 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'. |
| 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? |
| 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. |
| 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? |
| 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. |
| 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! |
| 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? |