25 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| Full Idea: We are able to reason about inconsistent beliefs, stories, and theories in useful and important ways | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| Full Idea: Intuitionist logic appears most attractive in the form of a natural deduction system. | |
| From: Edwin D. Mares (Negation [2014], 5.5) |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| Full Idea: In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation. | |
| From: Edwin D. Mares (Negation [2014], 5.5) | |
| A reaction: How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome. |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| Full Idea: One reason for wanting a three-valued logic is to act as a basis of a theory of presupposition. | |
| From: Edwin D. Mares (Negation [2014], 3.1) | |
| A reaction: [He cites Strawson 1950] The point is that you can get a result when the presupposition does not apply, as in talk of the 'present King of France'. |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| Full Idea: The problem with material implication, and classical logic more generally, is that it considers only the truth value of formulas in deciding whether to make an implication stand between them. It ignores everything else. | |
| From: Edwin D. Mares (Negation [2014], 7.1) | |
| A reaction: The obvious problem case is conditionals, and relevance is an obvious extra principle that comes to mind. |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| Full Idea: Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction. | |
| From: Edwin D. Mares (Negation [2014], 2.2) | |
| A reaction: Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool. |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| Full Idea: On its standard reading, excluded middle tells us that bivalence holds. To reject excluded middle, we must reject either non-contradiction, or ¬(A∧B) ↔ (¬A∨¬B) [De Morgan 3], or the principle of double negation. All have been tried. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| Full Idea: If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false. | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: Mates's point is to show that passively taking the normal account of negation for granted has important implications. |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| Full Idea: In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning). | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: [compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating. |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| Full Idea: Many-valued logics do not have reasonable natural deduction systems. | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| Full Idea: Situation semantics for logics consider not what is true in worlds, but what information is contained in situations. | |
| From: Edwin D. Mares (Negation [2014], 6.2) | |
| A reaction: Since many theoretical physicists seem to think that 'information' might be the most basic concept of a natural ontology, this proposal is obviously rather appealing. Barwise and Perry are the authors of the theory. |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| Full Idea: The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| Full Idea: For the intuitionist, talk of mathematical objects is rather misleading. For them, there really isn't anything that we should call the natural numbers, but instead there is counting. What intuitionists study are processes, such as counting and collecting. | |
| From: Edwin D. Mares (Negation [2014], 5.1) | |
| A reaction: That is the first time I have seen mathematical intuitionism described in a way that made it seem attractive. One might compare it to a metaphysics based on processes. Apparently intuitionists struggle with infinite sets and real numbers. |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| Full Idea: In 'situation semantics' individuals, properties, facts, and events are treated as abstractions from situations. | |
| From: Edwin D. Mares (Negation [2014], 6.1) | |
| A reaction: [Barwise and Perry 1983 are cited] Since I take the process of abstraction to be basic to thought, I am delighted to learn that someone has developed a formal theory based on it. I am immediately sympathetic to situation semantics. |
| 23865 | Morality would improve if people could pursue private interests [Weil] |
| Full Idea: The common run of moralists complain that man is moved by his private interest: would to heaven it were so! | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.65) | |
| A reaction: Her point is that currently people have to sacrifice their own interests to communal activities which offer dubious benefits. |
| 23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
| Full Idea: Every oppressive society is cemented by a religion of power, which falsifies all social relations by enabling the powerful to command over and above what they are able to impose. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.69) | |
| A reaction: A rather acute and accurate observation, I think. Flashy cars, grand uniforms, lots of medals, rituals of deference….. Sometimes I like the order and security this brings, but Simone Weil could quickly change my view. |
| 23871 | No central authority can initiate decentralisation [Weil] |
| Full Idea: It is quite patently impossible for decentralisation to be initiated by the central authority. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.113) | |
| A reaction: This is contradicted by the creation of regional parliaments and mayors, but we see nothing beyond that. A state could crumble into small parts if there were'lots of autonomous regional groups. Easier for weird minorities to take control. |
| 23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
| Full Idea: There is no real break in continuity after a bloody struggle for regime change; for the victory just sanctions forces that before the struggle were the decisive factor in community life, patterns which were replacing those of the declining regime. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.73) | |
| A reaction: [from Marx] I assume she has in mind the French Revolution, and perhaps the Russian Revolution, though in the latter the new bourgeois leaders also got swept away. So revolutions are not nearly as dramatic as they appear to be. |
| 23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
| Full Idea: The only possibility of salvation would lie in a co-operation between weak and strong, with a view to accomplishing a progressive decentralisation of social life; but the absurdity of such an idea strikes one immediately. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.113) | |
| A reaction: I take this to be a judgement on the anarchist ideal, rather than a bit of modest devolution. The UK government set up regional parliaments. She says centralisation is remorseless. |
| 23863 | Only individual people of good will can achieve social progress [Weil] |
| Full Idea: The enlightened goodwill of men acting in an individual capacity is the only possible principle of social progress. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.57) | |
| A reaction: I identify with this. Virtually every admirable institution in a society can be traced back to the initiative of a few individuals. Every helpful technology was someone's brainwave. |
| 23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
| Full Idea: The least evil society is that in which the general run of men are most often obliged to think while acting, have the most opportunities for exercising control over collective life as a whole, and enjoy the greatest amount of independence. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.97) | |
| A reaction: So Simone Weil was a liberal. How do you stop the most dynamic thinkers, social controllers, and exercisers of their own independence from coming to dominate the others? Only liberal institutions, such as the law and education, can do this. |
| 23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
| Full Idea: Marx gives a first-rate account of the mechanism of capitalist oppression; but so good is it that one finds it hard to visualise how this mechanism could cease to function. …The exploitation is the competitive need to expand as rapidly as possible. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.39) | |
| A reaction: [Last bit compressed] This pinpoints the main motivation for desiring to overthrow capitalism. Resistance to that view is presumably the fear that an even worse oppression might replace it. |
| 23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
| Full Idea: The sight of the unfinished task attracts the free man as powerfully as the over-seer's whip stimulates the slave. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.94) | |
| A reaction: This is Weil's key social idea - that freely performed productive work can be, and should be, a joy, as long as it is accompanied by respect and friendship, rather than oppression. Did this idea ever occur to a slave owner? |
| 23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |
| Full Idea: Inequality could easily be mitigated by the resistance of the weak and the feeling for justice of the strong, …were it not for the intervention of a further factor, namely, the struggle for power. | |
| From: Simone Weil (Reflections on Liberty and Social Oppression [1934], p.62) | |
| A reaction: The implication is that many of 'the strong' are inclined to diminish inequality, but find themselves trapped and unable to do so, because of irresistable capitalist forces. Sounds plausible. |