9 ideas
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 9138 | An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen] |
| Full Idea: Banning self-reference is too narrow to avoid the liar paradox. With 1) all the subsequent sentences are false, 2) all the subsequent sentences are false, 3) all the subsequent... the paradox still arises. Self-reference is a special case of this. | |
| From: report of Stephen Yablo (Paradox without Self-Reference [1993]) by Roy Sorensen - Vagueness and Contradiction 11.1 | |
| A reaction: [Idea 9137 pointed out that the ban was too narrow. Sorensen p.168 explains why this one is paradoxical] This is a nice example of progress in philosophy, since the Greeks would have been thrilled with this idea (unless they knew it, but it was lost). |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 3785 | You can't separate acts from the people performing them [Glover] |
| Full Idea: A mistake of consequentialists is to treat actions as though they can somehow be isolated from the people performing them. | |
| From: Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Five) | |
| A reaction: I agree. The weather produces consequences. Morality is about people. Crocodiles, for example, are exempt. |
| 3786 | Aggression in defence may be beneficial but morally corrupting [Glover] |
| Full Idea: Forming the intention to use nuclear retaliation if attacked may both be the best way to avoid the catastrophe of nuclear war and at the same time be morally corrupting. | |
| From: Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Five) | |
| A reaction: A famous moment in 2017 when Jeremy Corbyn refused to say he would be willing to use the weapons, if elected. It would be hard to sustain a determination to do it, and then reject it at the crucial moment. |
| 3784 | Duty prohibits some acts, whatever their consequences [Glover] |
| Full Idea: The deontological view is that some acts are absolutely prohibited, regardless of consequences. | |
| From: Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Five) |
| 3782 | Satisfaction of desires is not at all the same as achieving happiness [Glover, by PG] |
| Full Idea: Objections to utilitarianism as maximisation of preferences: faded past desires or the desires of the dead; obtaining desires and happiness are different; fewer desires are easier to satisfy; pain is good if it can be removed. | |
| From: report of Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Two) by PG - Db (ideas) |
| 3787 | Rule-utilitarianism is either act-utilitarianism, or not really utilitarian [Glover] |
| Full Idea: Rule-utilitarianism seems either to collapse into act-utilitarianism, or else it is only partly utilitarian. | |
| From: Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Six) |
| 3783 | How can utilitarianism decide the ideal population size? [Glover] |
| Full Idea: There are deep problems for utilitarianism in trying to work out what the ideal population size would be. | |
| From: Jonathan Glover (Introductions to Utilitarianism and its Critics [1990], Pt Four) |