28 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. |
| 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. |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 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? |
| 19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
| Full Idea: The aim of all political associations is the conservation of the natural and imprescriptible rights of man. These rights are liberty, property, security, and resistance to oppression. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 02) | |
| A reaction: Radical thinkers will obviously be doubtful about property being on the list, because that entrenches huge inequalities, between peasants and their landlords. Resistance to oppression will bother the likes of Edmund Burke. |
| 19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
| Full Idea: The law is the expression of the general will. All citizens have the right to take part in person or through their representatives in its formulation. It must be the same for all, whether it protects or whether it punishes. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: Now you are wondering who qualifies as a 'citizen'. Rousseau would have been excited until he found that the citizens could send 'representatives', instead of voting themselves. Rousseau aimed at foundational laws, not all of the laws. |
| 19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
| Full Idea: Any society in which the guarantee of Rights is not assured, nor the separation of Power determined, has no Constitution. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 16) | |
| A reaction: I wonder if they had Britain in mind with this one? The British latched onto Magna Carta in the early 19th century, because it offered some semblance of a constitution. |
| 19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
| Full Idea: No man is to be molested on account of his opinions, even his religious opinions, provided that their manifestation does not disturb the public order established by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 10) | |
| A reaction: Virtually any opinion will 'disturb' the established order a little bit, so this gives the option of suppressing quite mild beliefs, on the grounds of their small disturbance. It is still a wonderful proposal, though. |
| 19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
| Full Idea: The free communication of thoughts and opinions is one of man's most precious rights. Every citizen may therefore speak, write, and publish freely; except that he shall be responsible for the abuse of that freedom in cases determined by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 11) | |
| A reaction: Wonderful, and very nicely expressed. Tom Paine will have been a huge influence on this clause. |
| 19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
| Full Idea: All citizens being equal in the eyes of the law are equally eligible to all honours, offices, and public employments, according to their abilities and without other distinction than that of their virtues and talents. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: This proclamation of meritocracy must have rung bells around the cities of Europe, and was a reason why many people enjoyed being invaded by Napoleon. |
| 19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
| Full Idea: Since property is an inviolable and sacred right, no man may be deprived of it except when public necessity, lawfully constituted, evidently requires it; and on condition that a just indemnity be paid in advance. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 17) | |
| A reaction: This covers compulsory purchase orders. Is the ownership of slaves inviolable? Will aristocrats be compensated for the confiscation of their vast estates? |
| 19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |
| Full Idea: For the maintenance of public force and the expenses of administration, a common contribution is indispensable. It must be equally apportioned among all citizens according to their abilities. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 13) | |
| A reaction: Presumably this enshrines graduated income tax, an eighteenth century invention. Could you contribute just by your labour, or by fighting for the army? Those may be greater contributions than mere money. |