20 ideas
| 20728 | Metaphysics is hopeless with its present epistemology; common-sense realism is needed [Colvin] |
| Full Idea: Despair over metaphysics will not change until it has shaken off the incubus of a perverted epistemology, which has left thought in a hopeless tangle - until common-sense critical realism is made the starting point for investigating reality. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.144) | |
| A reaction: It seems to me that this is what has happened to analytic metaphysics since Kripke. Careful discussions about the nature of an object, or a category, or a property, are relying on unquestioned robust realism. Quite right too. |
| 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) |
| 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. |
| 20726 | We can only distinguish self from non-self if there is an inflexible external reality [Colvin] |
| Full Idea: Were there no inflexible reality outside of the individual, opposing and limiting it, knowledge of the self and the non-self would never develop. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.140) | |
| A reaction: Presumably opponents would have to say that such 'knowledge' is an illusion. This is in no way a conclusive argument, but I approach the problem of realism in quest of the best explanation, and this idea is important evidence. |
| 20727 | Common-sense realism rests on our interests and practical life [Colvin] |
| Full Idea: It is the determination of the external world from the practical standpoint, from the standpoint of interest, that may be defined as the common-sense view of reality. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.141) | |
| A reaction: Probably more appropriately named the 'pragmatic' view of reality. Relying on what is 'practical' seems to offer some objectivity, but relying on 'interest' rather less so. Can I be an anti-realist when life goes badly, and a realist when it goes well? |
| 20729 | Arguments that objects are unknowable or non-existent assume the knower's existence [Colvin] |
| Full Idea: Arguments for the absolute unknowability or non-existence of an external object only works by assuming that another external object, an individual, is known completely in so far as that individual expresses a judgement about an external object. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.145) | |
| A reaction: Anti-realism is a decay that eats into everything. You can't doubt all the externals without doubting all the internals as well. |
| 20730 | If objects are doubted because their appearances change, that presupposes one object [Colvin] |
| Full Idea: If objects are doubted because the same object appears differently at different times and circumstances, in order that this judgement shall have weight it must be assumed that the object under question is the same in its different presentations. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.145) | |
| A reaction: [compressed] Scepticism could eat into the underlying object as well. Is the underlying object a 'substrate'? If so, what's that? Is the object just a bundle of a properties? If so, there is no underlying object. |
| 20731 | The idea that everything is relations is contradictory; relations are part of the concept of things [Colvin] |
| Full Idea: The doctrine [that all we can know is the relations between subject and object] is in its essence self-contradictory, since our very idea of thing implies that it is something in relation either actually or potentially. | |
| From: Stephen S. Colvin (The Common-Sense View of Reality [1902], p.150) | |
| A reaction: Ladyman and Ross try to defend an account of reality based entirely on relations. I'm with Colvin on this one. All accounts of reality based either on pure relations or pure functions have a huge hole in their theory. |
| 18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
| Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect. | |
| From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7 | |
| A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right. |
| 16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
| Full Idea: Prime matter has no essence, nor a nature that is determinate, distinct, and actual. Instead, it is pure potential, and determinable, so that it is indeterminately and indistinctly a material thing. | |
| From: Peter Auriol (Sentences [1316], II.12.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
| A reaction: Pasnau thinks Auriol has the best shot at explaining the vague idea of 'prime matter', with the thought that it exists, but indeterminateness is what gives it a lesser mode of existence. It strikes me as best to treat 'exist' as univocal. |
| 16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |
| Full Idea: If someone says 'God could make straightness without a line, and roughness and lightness in weight without parts', …then show me the reason why God can do whatever does not imply a contradiction, yet cannot do these things. | |
| From: Peter Auriol (Sentences [1316], IV.12.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 11.4 | |
| A reaction: How engagingly bonkers. The key idea preceding this is that God can do all sorts of things that are beyond our understanding. He is then obliged to offer some examples. |