17 ideas
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. |
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. |
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. |
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. |
23529 | Conduct is not isolated from its effect on the moral code [Hart,HLA] |
Full Idea: We must not view conduct in isolation from its effect on the moral code. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], II 'Moderate') | |
A reaction: The moral code may be excessively conservative, but there is no denying this point. Extreme individualistic libertarians must recognise that 'no man is an island'. |
23530 | The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA] |
Full Idea: For Mill and De Tocqueville the greatest of the dangers was not that in fact the majority might use their power to oppress a minority, but that, with the spread of democratic ideas, it might come to be thought unobjectionable that they should do so. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], III 'Populism') | |
A reaction: This was vivid in the 2016 Brexit referendum, which was 52-48 in favour of leaving. There were lots voices saying 'you lost, get over it'. It should be a basic (if neglected) principle that the winners of elections now represent the whole population. |
23522 | In an organised society all actions have some effect on other people [Hart,HLA] |
Full Idea: In an organised society it is impossible to identify classes of actions which harm no one, or no one but the individual who does them. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], I 'Enforcement') | |
A reaction: This is attributed to 'some critics' of Mill. I agree with this. The idea that actions performed behind close doors never come to influence social life is an illusion, held by people whose quest for freedom is selfish. |
23528 | The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA] |
Full Idea: Recognition of individual liberty as a value involves, as a minimum, acceptance of the principle that the individual may do what he wants, even if others are distressed when the learn what it is that he does. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], II 'Private') | |
A reaction: He notes that there could be other reasons to block the freedom, such as harm done. This idea seems to identify a key component of liberalism - that we must all tolerate actions which we dislike. |
23523 | The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA] |
Full Idea: The principle of legality requires criminal offences to be as precisely defined as possible, so that it can be known with reasonable certainty beforehand what acts are criminal and what are not. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], I 'Conspiracy') | |
A reaction: Hart is discussing a breach of this, where moral judgements are used to condemn something which was not obviously illegal. Families and schools don't have such precise rules, but it seems needed in a vast and pluralistic society. |
23524 | Some private moral issues are no concern of the law [Hart,HLA] |
Full Idea: An official report [of 1957] on homosexuality declared that 'there must remain a realm of private morality and immorality which is, in brief and crude terms, not the law's business'. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], I 'Conspiracy') | |
A reaction: We might wonder whether these issues are actually moral, if the law is not interested in them. Are they just a matter of taste? The law doesn't enforce a preference for Mozart over Salieri. |
23521 | Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA] |
Full Idea: Four questions: 1) Has the development of law been influenced by morals? 2) Must reference to morality enter into an adequate definition of law or legal system? 3) Is law open to moral criticism? 4) Does immorality justify legal punishment? | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], I 'Enforcement') | |
A reaction: [compressed] Three nice questions, which are his agenda for the book. It is obvious that immoral laws can be created, and that laws can be criticised for being too concerned with morality, so there is no clear general answer to these dilemmas. |
23525 | Is the enforcement of morality morally justifiable? [Hart,HLA] |
Full Idea: The question about morality and the law is also a question of morality - of whether the enforcement of morality is morally justified. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], I 'Positive') | |
A reaction: This is a very nice meta-moral question. What moral standards are used to justify the enforcement of moral standards? Presumably there should be no contradiction between the levels, to brutally enforce softness, or softly recommend brutality? |
23526 | Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA] |
Full Idea: English and American law still [in1963] contain rules which suppress practices condemned as immoral by positive morality though they involve nothing that would be ordinarily thought of as harm to other persons. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], II 'Use') | |
A reaction: He says most of the examples of this concern sexual practices. In the UK we have moved away from such laws, but many states of the USA still maintain them (or are reintroducing them, in 2023). |
23527 | Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA] |
Full Idea: Leslie Stephen argued that when the question is how severely an offender should be punished, an estimate of the degree of moral wickedness involved in the crime is always relevant. | |
From: H.L.A. Hart (Law,Liberty and Morality [1963], II 'Moral') | |
A reaction: [Stephen 'Liberty, Equality, Fraternity' 1873] The degree of responsibility (after excuses etc.) is obviously also highly relevant. If vicious murder is punished more harshly, that seems to be an assessment of the character of the murderer. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |