18 ideas
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| Full Idea: The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems). |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| Full Idea: If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly. |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| Full Idea: Containing only logical notions is not a necessary condition for being a logical truth, since a logical truth such as 'all men are men' may contain non-logical notions such as 'men'. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) | |
| A reaction: [He attributes this point to Russell] Maybe it is only a logical truth in its general form, as ∀x(x=x). Of course not all 'banks' are banks. |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| Full Idea: The standard modern view of logical truth is that a statement is logically true if it comes out true in all interpretations in all (non-empty) domains. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
| A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| Full Idea: Formalism seems to exclude from consideration all creative, growing mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: [He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative. |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| Full Idea: Formalism is a bulwark of logical positivist philosophy. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get. |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| Full Idea: Logical positivists did not adopt old-style logicism, but rather logicism spiced with varying doses of If-thenism. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4) | |
| A reaction: This refers to their account of mathematics as a set of purely logical truths, rather than being either empirical, or a priori synthetic. |
| 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. |