14 ideas
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion. | |
| From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'. |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'. |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| Full Idea: A class of sentences can be called 'analytical' if every sequence of objects is a model of it. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.418) | |
| A reaction: See Idea 13344 and Idea 13343 for the context of this assertion. |
| 19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
| Full Idea: The aim of all political associations is the conservation of the natural and imprescriptible rights of man. These rights are liberty, property, security, and resistance to oppression. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 02) | |
| A reaction: Radical thinkers will obviously be doubtful about property being on the list, because that entrenches huge inequalities, between peasants and their landlords. Resistance to oppression will bother the likes of Edmund Burke. |
| 19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
| Full Idea: The law is the expression of the general will. All citizens have the right to take part in person or through their representatives in its formulation. It must be the same for all, whether it protects or whether it punishes. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: Now you are wondering who qualifies as a 'citizen'. Rousseau would have been excited until he found that the citizens could send 'representatives', instead of voting themselves. Rousseau aimed at foundational laws, not all of the laws. |
| 19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
| Full Idea: Any society in which the guarantee of Rights is not assured, nor the separation of Power determined, has no Constitution. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 16) | |
| A reaction: I wonder if they had Britain in mind with this one? The British latched onto Magna Carta in the early 19th century, because it offered some semblance of a constitution. |
| 19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
| Full Idea: No man is to be molested on account of his opinions, even his religious opinions, provided that their manifestation does not disturb the public order established by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 10) | |
| A reaction: Virtually any opinion will 'disturb' the established order a little bit, so this gives the option of suppressing quite mild beliefs, on the grounds of their small disturbance. It is still a wonderful proposal, though. |
| 19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
| Full Idea: The free communication of thoughts and opinions is one of man's most precious rights. Every citizen may therefore speak, write, and publish freely; except that he shall be responsible for the abuse of that freedom in cases determined by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 11) | |
| A reaction: Wonderful, and very nicely expressed. Tom Paine will have been a huge influence on this clause. |
| 19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
| Full Idea: All citizens being equal in the eyes of the law are equally eligible to all honours, offices, and public employments, according to their abilities and without other distinction than that of their virtues and talents. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: This proclamation of meritocracy must have rung bells around the cities of Europe, and was a reason why many people enjoyed being invaded by Napoleon. |
| 19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
| Full Idea: Since property is an inviolable and sacred right, no man may be deprived of it except when public necessity, lawfully constituted, evidently requires it; and on condition that a just indemnity be paid in advance. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 17) | |
| A reaction: This covers compulsory purchase orders. Is the ownership of slaves inviolable? Will aristocrats be compensated for the confiscation of their vast estates? |
| 19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |
| Full Idea: For the maintenance of public force and the expenses of administration, a common contribution is indispensable. It must be equally apportioned among all citizens according to their abilities. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 13) | |
| A reaction: Presumably this enshrines graduated income tax, an eighteenth century invention. Could you contribute just by your labour, or by fighting for the army? Those may be greater contributions than mere money. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |