12 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. |
| 7301 | The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones] |
| Full Idea: Where the idealist says that to be (i.e. to exist) is to be perceived, the phenomenalist says that to be is to be perceivable. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: This is a nice phenomenalist slogan to add to Mill's well known one (Idea 3583). Expressed in this form, it looks false to me. What about neutrinoes? They weren't at all perceivable until recently. Maybe some physical stuff can never be perceived. |
| 7302 | Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones] |
| Full Idea: Linguistic phenomenalism argues that it is possible to remove all talk of physical objects from our speech with no loss of meaning. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: I find this proposal unappealing. My basic objection is that I cannot understand why anyone would refuse to even contemplate the question of WHY I am having a given group of consistent experiences, of (say) a table kind. |
| 7303 | If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones] |
| Full Idea: The problem with taking sense-data as basic is that some data can appear indeterminate. If we can't discern the colour of someone's eyes, or the number of sides of a complex figure, are we to say that there is no fact about those things? | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: I like that. How many electrons are there in the sun? Such things cannot just be reduced to talk of sense-data, as there is obviously a vast gap between the data and the facts. As usual, ontology and epistemology must be kept separate. |
| 7299 | Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones] |
| Full Idea: All the primary qualities lend themselves readily to mathematical or geometric description. ...but it seems that secondary qualities are less amenable to being represented mathematically. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: As a believer in the primary/secondary distinction, I welcome this point. This is either evidence for the external reality of primary qualities, or an interesting observation about maths. Do we make the primary/secondary distinction because we do maths? |
| 7300 | An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones] |
| Full Idea: An object cannot lack shape, size, position or motion and remain an object. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.4) | |
| A reaction: This points towards the essentialist view (see Idea 5453). This does raise the question of whether an object could lose its colour with impugnity, or the quality of sound that it makes when struck. |
| 7297 | My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones] |
| Full Idea: My beliefs could be well justified in coherentist terms, while not accurately representing the world, and my system of beliefs could be completely free-floating. | |
| From: Cardinal/Hayward/Jones (Epistemology [2004], Ch.3) | |
| A reaction: This nicely encapsulates to correspondence objection to coherence theory. One thing missing from the coherence account is that beliefs aren't chosen for their coherence, but are mostly unthinkingly triggered by experiences. |
| 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. |
| 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. |