26 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. |
| 18996 | A statement S is 'partly true' if it has some wholly true parts [Yablo] |
| Full Idea: A statement S is 'partly true' insofar as it has wholly true parts: wholly true implications whose subject matter is included in that of S. | |
| From: Stephen Yablo (Aboutness [2014], 01.6) | |
| A reaction: He suggests that if we have rival theories, we agree that it is one or the other. And 'we may have pork for dinner, or human flesh' is partly true. |
| 19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
| Full Idea: An 'enthymeme' is a deductive argument with an unstated assumption that must be true for the premises to lead to the conclusion. | |
| From: Stephen Yablo (Aboutness [2014], 11.1) |
| 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) |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| Full Idea: The principle of Supplementation says that y is properly part of x, only if a z exists that 'makes up the difference' between them. [note: that is, z is disjoint from y and sums with y to form x] | |
| From: Stephen Yablo (Aboutness [2014], 03.2) |
| 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... |
| 19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
| Full Idea: 'Pegasus does not exist' has a paradoxical, self-undermining flavour. On the one hand, the empty name makes it untrue. But now, why is the name empty? Because Pegasus does not exist. 'Pegasus does not exist' is untrue because Pegasus does not exist. | |
| From: Stephen Yablo (Aboutness [2014], 05.7 n20) | |
| A reaction: Beautiful! This is Yablo's reward for continuing to ask 'why?' after everyone else has stopped in bewilderment at the tricky phenomenon. |
| 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. |
| 18091 | Infinitesimals are ghosts of departed quantities [Berkeley] |
| Full Idea: The infinitesimals are the ghosts of departed quantities. | |
| From: George Berkeley (The Analyst [1734]), quoted by David Bostock - Philosophy of Mathematics 4.3 | |
| A reaction: [A famous phrase, but as yet no context for it] |
| 19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
| Full Idea: If I am a nominalist non-Platonist, I think it is false that 'there are primes over 10', but I want to be able to say it like everyone else. I argue that this because the statement has a part that I do believe, a part that remains interestingly true. | |
| From: Stephen Yablo (Aboutness [2014], 05.8) | |
| A reaction: This is obviously a key motivation for Yablo's book, as it reinforces his fictional view of abstract objects, but aims to capture the phenomena, by investigating what such sentences are 'about'. Admirable. |
| 18998 | Parthood lacks the restriction of kind which most relations have [Yablo] |
| Full Idea: Most relations obtain only between certain kinds of thing. To learn that x is a part of y, however, tells you nothing about x and y taken individually. | |
| From: Stephen Yablo (Aboutness [2014], 03.2) | |
| A reaction: Too sweeping. To be a part of crowd you have to be a person. To be part of the sea you have to be wet. It might depend on whether composition is unrestricted. |
| 19004 | Gettier says you don't know if you are confused about how it is true [Yablo] |
| Full Idea: We know from Gettier that if you are right to regard Q as true, but you are sufficiently confused about HOW it is true - about how things stand with respect to its subject matter - then you don't know that Q. | |
| From: Stephen Yablo (Aboutness [2014], 07.4) | |
| A reaction: I'm inclined to approach Gettier by focusing on the propositions being expressed, where his cases tend to focus on the literal wording of the sentences. What did the utterer mean by the sentences - not what did they appear to say. |
| 19007 | A theory need not be true to be good; it should just be true about its physical aspects [Yablo] |
| Full Idea: A physical theory need not be true to be good, Field has argued, and I agree. All we ask of it truth-wise is that its physical implications should be true, or, in my version, that it should be true about the physical. | |
| From: Stephen Yablo (Aboutness [2014], 12.5) | |
| A reaction: Yablo is, of course, writing a book here about the concept of 'about'. This seems persuasive. The internal terminology of the theory isn't committed to anything - it is only at its physical periphery (Quine) that the ontology matters. |
| 18993 | If sentences point to different evidence, they must have different subject-matter [Yablo] |
| Full Idea: 'All crows are black' cannot say quite the same as 'All non-black things are non-crows', for the two are confirmed by different evidence. Subject matter looks to be the distinguishing feature. One is about crows, the other not. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: You might reply that they are confirmed by the same evidence (but only in its unobtainable totality). The point, I think, is that the sentences invite you to start your search in different places. |
| 19003 | Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo] |
| Full Idea: The standard response to the raven paradox is to say that a nonblack nonraven does confirm that all ravens are black. But it confirms it just the teeniest little bit - not as much as a black raven does. | |
| From: Stephen Yablo (Aboutness [2014], 06.5) | |
| A reaction: It depends on the proportion between the relevant items. How do you confirm 'all the large animals in this zoo are mammals'? Check for size every animal which is obviously not a mammal? |
| 18992 | Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo] |
| Full Idea: A sentence's meaning is to do with its truth-value in various possible scenarios, AND the factors responsible for that truth-value. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: The thesis of his book, which I welcome. I'm increasingly struck by the way in which much modern philosophy settles for a theory being complete, when actually further explanation is possible. Exhibit A is functional explanations. Why that function? |
| 18994 | The content of an assertion can be quite different from compositional content [Yablo] |
| Full Idea: Assertive content - what a sentence is heard as saying - can be at quite a distance from compositional content. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: This is the obvious reason why semantics cannot be entirely compositional, since there is nearly always a contextual component which then has to be added. In the case of irony, the compositional content is entirely reversed. |
| 18997 | Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo] |
| Full Idea: If the subject-matter of S is how it is true, we get three unfortunate results: S has truth-value in worlds where its subject-matter draws a blank; learning what S is about tells you its truth-value; negating S changes what it's about. | |
| From: Stephen Yablo (Aboutness [2014], 02.8) | |
| A reaction: Together these make fairly devastating objections to the truth-conditions (in possible worlds) theory of meaning. The first-objection concerns when S is false |
| 19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |
| Full Idea: The idea that negation is, or can be, a cancellation device raises an interesting question. What does one do to wipe the slate clean after an improper assertion? Not-A is too strong; it reverses our stand on A rather than nullifying it. | |
| From: Stephen Yablo (Aboutness [2014], 09.8) | |
| A reaction: [He is discussing a remark of Strawson 1952] It seems that 'not' has two meanings or uses: a weak use of 'nullifying' an assertion, and a strong use of 'reversing' an assertion. One could do both: 'that's not right; in fact, it's just the opposite'. |