28 ideas
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| Full Idea: Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic | |
| A reaction: An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797. |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| Full Idea: Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic). | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3 | |
| A reaction: Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical. |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| Full Idea: Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6 | |
| A reaction: Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough. |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| Full Idea: Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3 | |
| A reaction: I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss. |
| 15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
| Full Idea: I shall beg off talking of a) whether genera and species are real or situated in bare thoughts alone, b) whether as real they are bodies or incorporeals, and c) whether they are separated or in sensibles and have their reality in connection with them. | |
| From: Porphyry (Isagoge ('Introduction') [c.295], (2)) | |
| A reaction: This passage, picking up on Aristotle, seems to be the original source that grew into the medievel debate about universals. It seems to rather neatly lay out the agenda for the universals debate which is still with us. |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| Full Idea: Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3 | |
| A reaction: This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times. |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| Full Idea: Bolzano took the entities of which truth is predicated to be not propositions in the subjective sense but 'propositions-in-themselves' - objective entities existing independent of our apprehension. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Emp' | |
| A reaction: A serious mistake. Presumably the objective propositions are all true (or there would be endless infinities of them). So what is assessed in the case of error? Something other than the objective propositions! We assess these other things! |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| Full Idea: Bolzano conceived of propositions as abstract objects which are structured compounds of concepts and potential contents of judgements and assertions. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3 | |
| A reaction: Personally I think of propositions as brain events, the constituents of thought about the world, but that needn't contradict the view of them as 'abstract'. |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
| Full Idea: What I mean by 'propositions' is not what the grammarians call a proposition, namely the linguistic expression, but the mere sense of this expression, is what is meant by proposition in itself or object proposition. This sense can be true or false. | |
| From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref?) | |
| A reaction: This seems to be the origin of what we understand by 'proposition'. The disputes are over whether such things exists, and whether they are features of minds or features of the world (resembling facts). |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| Full Idea: We can find the ground of a pure conceptual truth only in other conceptual truths. | |
| From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref) | |
| A reaction: Elsewhere he insists that these grounds must be in 'truths', and not just in the attributes of the concepts of involved. This conflicts with Kit Fine's view, that the concepts themselves are the source of conceptual truth and necessity. |
| 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. |
| 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? |
| 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? |
| 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. |
| 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. |
| 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. |
| 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. |