46 ideas
| 7454 | Gassendi is the first great empiricist philosopher [Hacking] |
| Full Idea: Gassendi is the first in the great line of empiricist philosophers that gradually came to dominate European thought. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.5) | |
| A reaction: Epicurus, of course, was clearly an empiricist. British readers should note that Gassendi was not British. |
| 8658 | For there was never yet philosopher/ That could endure the toothache patiently [Shakespeare] |
| Full Idea: For there was never yet philosopher/ That could endure the toothache patiently. | |
| From: William Shakespeare (Much Ado About Nothing [1600], V.i) | |
| A reaction: You can't argue with that. I do think that people who have studied philosophy at length are more likely to be 'philosophical' when faced with human misery, but only up to a point. |
| 22708 | Good reasons must give way to better [Shakespeare] |
| Full Idea: Good reasons must of force give way to better. | |
| From: William Shakespeare (Julius Caesar [1599], 4.3.205) | |
| A reaction: [Brutus to Cassius] This remark is an axiom of rationality. But, of course, reasons can come in groups, and three modest reasons may compete with one very good reason. |
| 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. |
| 12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
| Full Idea: The fallacy of 'ad obscurum per obscurius' is to explain the obscure by appeal to what is more obscure. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §3) | |
| A reaction: Not strictly a fallacy, so much as an example of inadequate explanation, along with circularity and infinite regresses. |
| 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... |
| 12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
| Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd. |
| 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. |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5) | |
| A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism. |
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical. |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?) | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 3) | |
| A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right. |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute. |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
| A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure. |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 8) | |
| A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading. |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1) |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2) | |
| A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting. |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| Full Idea: A third way has been offered to 'make sense' of neo-Fregeanism: we should reject Quine's well-known criterion of ontological commitment in favour of one based on 'truth-maker theory'. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4 n19) | |
| A reaction: [The cite Ross Cameron for this] They reject this proposal, on the grounds that truth-maker theory is not sufficient to fix the grounding truth-conditions of statements. |
| 12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
| Full Idea: It is claimed that neo-Fregeans are committed to 'maximalism' - that whatever can exist does. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4) | |
| A reaction: [The cite Eklund] They observe that maximalism denies contingent non-existence (of the £20 note I haven't got). There seems to be the related problem of 'hyperinflation', that if abstract objects are generated logically, the process is unstoppable. |
| 12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
| Full Idea: Identity is sometimes read so that 'Pegasus is Pegasus' expresses a truth, the non-existence of any winged horse notwithstanding. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: This would give you ontological commitment to truth, without commitment to existence. It undercuts the use of identity statements as the basis of existence claims, which was Frege's strategy. |
| 12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
| Full Idea: There is a compatibilist view which says that it is for the abundant properties to play the role of 'bedeutungen' in semantic theory, and the sparse ones to address certain metaphysical concerns. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Only a philosopher could live with the word 'property' having utterly different extensions in different areas of discourse. They similarly bifurcate words like 'object' and 'exist'. Call properties 'quasi-properties' and I might join in. |
| 18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
| Full Idea: The good standing of a predicate is already trivially sufficient to ensure the existence of an associated property, a (perhaps complex) way of being which the predicate serves to express. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: 'Way of being' is interesting. Is 'being near Trafalgar Sq' a way of being? I take properties to be 'features', which seems to give a clearer way of demarcating them. They say they are talking about 'abundant' (rather than 'sparse') properties. |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1) | |
| A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning. |
| 7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
| Full Idea: There is hardly any history of probability to record before Pascal (1654), and the whole subject is very well understood after Laplace (1812). | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.1) | |
| A reaction: An interesting little pointer on the question of whether the human race is close to exhausting all the available intellectual problems. What then? |
| 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
| Full Idea: Probability has two aspects: the degree of belief warranted by evidence, and the tendency displayed by some chance device to produce stable relative frequencies. These are the epistemological and statistical aspects of the subject. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.1) | |
| A reaction: The most basic distinction in the subject. Later (p.124) he suggests that the statistical form (known as 'aleatory' probability) is de re, and the other is de dicto. |
| 7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
| Full Idea: Epistemological probability is torn between Keynes etc saying it depends on the strength of logical implication, and Ramsey etc saying it is personal judgement which is subject to strong rules of internal coherence. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.2) | |
| A reaction: See Idea 7449 for epistemological probability. My immediate intuition is that the Ramsey approach sounds much more plausible. In real life there are too many fine-grained particulars involved for straight implication to settle a probability. |
| 7450 | In the medieval view, only deduction counted as true evidence [Hacking] |
| Full Idea: In the medieval view, evidence short of deduction was not really evidence at all. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.3) | |
| A reaction: Hacking says the modern concept of evidence comes with probability in the 17th century. That might make it one of the most important ideas ever thought of, allowing us to abandon certainties and live our lives in a more questioning way. |
| 7451 | Formerly evidence came from people; the new idea was that things provided evidence [Hacking] |
| Full Idea: In the medieval view, people provided the evidence of testimony and of authority. What was lacking was the seventeenth century idea of the evidence provided by things. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.4) | |
| A reaction: A most intriguing distinction, which seems to imply a huge shift in world-view. The culmination of this is Peirce's pragmatism, in Idea 6948, of which I strongly approve. |
| 7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG] |
| Full Idea: An experiment is a test (if T, then E implies R, so try E, and if R follows, T seems right), an adventure (no theory, but try things), a diagnosis (reading the signs), or a dissection (taking apart). | |
| From: report of Ian Hacking (The Emergence of Probability [1975], Ch.4) by PG - Db (ideas) | |
| A reaction: A nice analysis. The Greeks did diagnosis, then the alchemists tried adventures, then Vesalius began dissections, then the followers of Bacon concentrated on the test, setting up controlled conditions. 'If you don't believe it, try it yourself'. |
| 7459 | Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking] |
| Full Idea: Mathematics is the model for reasoning about necessary truths, but jurisprudence must be our model when we deliberate about contingencies. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.10) | |
| A reaction: Interesting. Certainly huge thinking, especially since the Romans, has gone into the law, and creating rules of evidence. Maybe all philosophers should study law and mathematics? |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind. | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept? |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle). | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them. |
| 12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
| Full Idea: Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
| A reaction: They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent. |
| 12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
| Full Idea: Abstraction principles purport to introduce fundamental means of reference to a range of objects, to which there is accordingly no presumption that we have any prior or independent means of reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §8) | |
| A reaction: There's the rub! They make it sound like a virtue, that we open up yet another heaven of abstract toys to play with. As fictions, they are indeed exciting new fun. As platonic discoveries they strike me as Cloud-Cuckoo Land. |
| 12231 | Reference needs truth as well as sense [Hale/Wright] |
| Full Idea: It takes, over and above the possession of sense, the truth of relevant contexts to ensure reference. | |
| From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
| A reaction: Reference purely through sense was discredited by Kripke. The present idea challenges Kripke's baptismal realist approach. How do you 'baptise' an abstract object? But isn't reference needed prior to the establishment of truth? |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions). | |
| From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
| A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings. |
| 20304 | The cause of my action is in my will [Shakespeare] |
| Full Idea: The cause is in my will. I will not come./That is enough to satisfy the senate./But for your private satisfaction,/Because I love you, I will let you know. | |
| From: William Shakespeare (Julius Caesar [1599], II.ii) | |
| A reaction: This asserts the purest form of volitionism, but then qualifies it, because Caesar's will has been influenced by his wife's dreams. |
| 23565 | Our obedience to the king erases any crimes we commit for him [Shakespeare] |
| Full Idea: We know enough if we know we are the king's men. Our obedience to the king wipes the crime of it out of us. | |
| From: William Shakespeare (Henry V [1599]), quoted by Michael Walzer - Just and Unjust Wars 03 | |
| A reaction: He is referring to the slaughter of the French servants behind the lines at Agincourt. A classic expression of 'I was just obeying orders', which was rejected at Nurnberg in 1946. Depends on the seriousness of the crime. |