31 ideas
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 23154 | We divide mankind into friend and foe, and cooperate with one and compete with the other [Russell] |
| Full Idea: Instinctively we divide mankind into friends and foes - friends, towards whom we have a morality of co-operation; foes, towards whom we have that of competition. | |
| From: Bertrand Russell (Authority and the Individual [1949], 1) | |
| A reaction: Interesting, because I have though of cooperation and competition as intrinsic features of people, internal to their nature, but this idea observes that it is more external, as two responses to two sharply distinct aspects of experience. |
| 23152 | Increasingly war expands communities, and unifies them through fear [Russell] |
| Full Idea: From early days down to modern times war has been the chief engine in enlarging the size of communities, and fear has increasingly replaced tribal solidarity as a source of social cohesion. | |
| From: Bertrand Russell (Authority and the Individual [1949], 1) | |
| A reaction: It is a feature of modern nationalism to try to generate fear of various outsiders, even in times of peace. Most of us despise such things, but the underlying desire for greater national unity is not unworthy. What enemies would a world state have? |
| 23153 | Gradually loyalty to a creed increased, which could even outweigh nationality [Russell] |
| Full Idea: At a later stage in the development of civilization, a new kind of loyalty began to be developed, based on identity of creed. …Its military strength was displayed in Islam …and later loyalities of Catholics or Protestants could outweigh nationality. | |
| From: Bertrand Russell (Authority and the Individual [1949], 1) | |
| A reaction: [compressed] The only examples of creed loyalty that come to mind are religious. With increased migration in the modern world the phenomenon of divided loyalties has grown. Can a political theory cope with divided loyalties? |
| 23155 | In early societies the leaders needed cohesion, but the rest just had to obey [Russell] |
| Full Idea: In historical societies such as ancient Egypt only a minority at the top of the social scale - the king, the aristocracy and the priests - needed any psychological mechanism towards social cohesion; all the rest merely obeyed. | |
| From: Bertrand Russell (Authority and the Individual [1949], 2) | |
| A reaction: This is why even now I take obedience to be a key right-wing virtue, though it is usually reinforced through national myths and distorted proganda. Quasi-worship of the leader also seems to be a major ingredient. Obedience unifies armies. |
| 23156 | The economic and political advantages of great size seem to have no upper limit [Russell] |
| Full Idea: Short of the whole planet there is no visible limit to the advantages of size, both in economic and in political organisation. | |
| From: Bertrand Russell (Authority and the Individual [1949], 2) | |
| A reaction: Obviously there are also disadvantages, such as the vast distances, and the alienation of people far from the centre. I take economies of scale to be one of the advantages of socialist nationalisations. |
| 23157 | Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires [Russell] |
| Full Idea: Government has a negative function, to prevent private violence, to protect life and property, to enact criminal law and secure its enforcement. It also has a positive purpose, to facilitate the realisation of desires common to most of the citizens. | |
| From: Bertrand Russell (Authority and the Individual [1949], 2) | |
| A reaction: [compressed] Interesting because the second purpose is rarely cited. Governments improve communications, facilitate trade, and encourage health and education services, which we all want. |
| 23151 | A monarch is known to everyone in the group, and can thus unite large groups [Russell] |
| Full Idea: At a very early stage loyalty to a group must have been reinforced by loyalty to a leader. In a large tribe the king or chief may be known the everybody even when individuals are strangers. This makes possible increase in the size of the group. | |
| From: Bertrand Russell (Authority and the Individual [1949], 1) | |
| A reaction: In this way humanity could move from hunter-gatherer groups to tribes or clans. In the UK even people who couldn't name the current Prime Minister are all fully aware of the monarch. In this way a merely constitutional monarch makes sense, |
| 23167 | Power should be with smaller bodies, as long as it doesn't restrict central powers [Russell] |
| Full Idea: The general principle of delimiting powers should be to leave to smaller bodies all functions which do not prevent larger bodies from fulfilling their purpose. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: In recent years in the UK smaller local bodies have been severely reduced in power by central government. This is nominally in favour of individuals, but in practice seems to have strengthened the centre. Russell was keen on devolving powers. |
| 23168 | A state is essential, to control greedy or predatory impulses [Russell] |
| Full Idea: The control of greedy or predatory impulses is imperatively necessary, and therefore States …are needed for survival. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: The anarchist replies that the corruption of this benevolent state is precisely the problem they are trying to avoid. Perhaps the emphasis should be on the rule of law, rather than on people holding centralised power. |
| 23163 | In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell] |
| Full Idea: It is obvious that in a state of anarchy there could not be universities or scientific research or publication of books, or even such simple things as seaside holidays. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: A seaside holiday seems possible, though it obviously needs means of publicity, and of transport. Why is a private university impossible? The general thought seems to be that anything very complex would be impossible. Maybe. |
| 23166 | In democracy we are more aware of being governed than of our tiny share in government [Russell] |
| Full Idea: In a democracy you have a 20 millionth share in the government of others, but only a 20 millionth share in the government of yourself. You are therefore much more conscious of being governed than of governing. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: Nice. Add to that the fact that your share in governing others only occurs at election time. In between we are powerless spectators, but we are still governed. |
| 23162 | Managers are just as remote from workers under nationalisation as under capitalism [Russell] |
| Full Idea: Nationalisation leaves managers and officials almost as remote from the workers as they are under a capitalist regime. | |
| From: Bertrand Russell (Authority and the Individual [1949], 4) | |
| A reaction: Russell's solution is workplace democracy. Presumably that could be imposed on a nationalised industry much more easily than on a profit-driven private capitalist industry. |
| 23165 | Socialists say economic justice needs some state control of industries, and of foreign trade [Russell] |
| Full Idea: Economic justice is held by Socialists (rightly, in my opinion) to involve state ownership of key industries and considerable regulation of foreign trade. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: This must be to obtain greater control over the profits of industry, and also to prevent trade become too exploitative of weaker foreign nations. Britain had a socialist government when this book was written. |
| 23160 | Being a slave of society is hardly better than being a slave of a despot [Russell] |
| Full Idea: A society in which each is the slave of all is only a little better than one in which each is the slave of a despot. | |
| From: Bertrand Russell (Authority and the Individual [1949], 4) | |
| A reaction: This seems to apply quite accurately to the position of those state employees who have the lowest status and wages. Society as a whole exploits them, so it is hard to point the finger at their oppressors. |
| 23158 | Slavery began the divorce between the work and the purposes of the worker [Russell] |
| Full Idea: The introduction of slavery began the divorce between the purpose of the work and the purposes of the worker. | |
| From: Bertrand Russell (Authority and the Individual [1949], 4) | |
| A reaction: Worth saying, because marxists tend to blame more recent capitalism for creating this problem (of 'alienation'). There are many degrees of slavery. |
| 23161 | Slaves can be just as equal as free people [Russell] |
| Full Idea: There is equality where all are slaves, as well as where all are free. | |
| From: Bertrand Russell (Authority and the Individual [1949], 4) | |
| A reaction: A nice observation, though a person is only a slave if someone controls them, so it is not strictly true. |
| 23159 | Scarce goods may be denied entirely, to avoid their unequal distribution [Russell] |
| Full Idea: There is a risk that, in the pursuit of equality, good things which there is difficulty in distributing evenly may not be admitted to be good. | |
| From: Bertrand Russell (Authority and the Individual [1949], 4) | |
| A reaction: Lovely sentence. The clarity and economy with which he expresses an intricate idea. Why can't you philosophers all write like that? This is not just the unequal distribution of scarce goods, but a subtler problem. The finest wines, for example. |
| 23164 | Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [Russell] |
| Full Idea: Justice has come to be interpreted as equality, except where exceptional merit is thought to deserve an exceptional but still moderate reward. | |
| From: Bertrand Russell (Authority and the Individual [1949], 5) | |
| A reaction: Kekes rebels against this modern distortion of justice, which traditionally means everyone getting what they deserve - good or bad. The modern egalitarian view seems to be a rebellion against the harsh interpretation of the older view. |