34 ideas
| 17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
| Full Idea: My idea is that conceptual examination might be a way of recovering information previously obtained through the senses. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.8) | |
| A reaction: Now you're talking! This is really interesting conceptual analysis, rather than the sort of stamp-collecting approach to analsis practised by the duller sort of philosopher. But why bother with conceptual examination, when you have senses? |
| 17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
| Full Idea: Instead of considering only a proposition's 'correspondence to the facts', we should also consider the correspondence between parts of the proposition and parts of the world (a 'correspondence-as-congruence' view). | |
| From: Carrie Jenkins (Grounding Concepts [2008], Final - Branching) | |
| A reaction: This is something like Russell's Othello example (1912), except that the parts there, with relations seemed to add up to the whole proposition. For Jenkins, presumably parts might correspond, but the whole proposition fail to. |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| Full Idea: The Axiom of Choice is a pure existence statement, without defining conditions. It was necessary to provide a foundation for Cantor's theory of transfinite cardinals and ordinal numbers, but its nonconstructive character engendered heated controversy. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) |
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| Full Idea: In 1938 Gödel proved that the Axiom of Choice is consistent with the other axioms of set theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: Hence people now standardly accept ZFC, rather than just ZF. |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| Full Idea: The Trichotomy Principle (any number is less, equal to, or greater than, another number) turned out to be equivalent to the Axiom of Choice. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: [He credits Sierpinski (1918) with this discovery] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| Full Idea: Zermelo's Axiom of Choice asserts that for any set of non-empty sets that (pairwise) have no elements in common, then there is a set that 'simultaneously chooses' exactly one element from each set. Note that this is an existential claim. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The Axiom is now widely accepted, after much debate in the early years. Even critics of the Axiom turn out to be relying on it. |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| Full Idea: The Axiom of Choice seems clearly true from the Platonistic point of view, independently of how sets may be defined, but is rejected by those who think such existential claims must show how to pick out or define the object claimed to exist. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The typical critics are likely to be intuitionists or formalists, who seek for both rigour and a plausible epistemology in our theory. |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| Full Idea: A structure is said to be a 'model' of an axiom system if each of its axioms is true in the structure (e.g. Euclidean or non-Euclidean geometry). 'Model theory' concerns which structures are models of a given language and axiom system. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This strikes me as the most interesting aspect of mathematical logic, since it concerns the ways in which syntactic proof-systems actually connect with reality. Tarski is the central theoretician here, and his theory of truth is the key. |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| Full Idea: In the late 1950s Tarski and Vaught defined and established basic properties of the relation of elementary equivalence between two structures, which holds when they make true exactly the same first-order sentences. This is fundamental to model theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This is isomorphism, which clarifies what a model is by giving identity conditions between two models. Note that it is 'first-order', and presumably founded on classical logic. |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| Full Idea: The Löwenheim-Skolem Theorem, the earliest in model theory, states that if a countable set of sentences in a first-order language has a model, then it has a countable model. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: There are 'upward' (sentences-to-model) and 'downward' (model-to-sentences) versions of the theory. |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| Full Idea: Before Tarski's work in the 1930s, the main results in model theory were the Löwenheim-Skolem Theorem, and Gödel's establishment in 1929 of the completeness of the axioms and rules for the classical first-order predicate (or quantificational) calculus. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| Full Idea: Completeness is when, if a sentences holds in every model of a theory, then it is logically derivable from that theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| Full Idea: 'Recursion theory' is the subject of what can and cannot be solved by computing machines | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Ch.9) | |
| A reaction: This because 'recursion' will grind out a result step-by-step, as long as the steps will 'halt' eventually. |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| Full Idea: In 1936 Church showed that Principia Mathematica is undecidable if it is ω-consistent, and a year later Rosser showed that Peano Arithmetic is undecidable, and any consistent extension of it. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int IV) |
| 17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
| Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 5.3) | |
| A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it. |
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| Full Idea: The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
| A reaction: This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else. |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| Full Idea: I propose that arithmetical truths are known through an examination of our own arithmetical concepts; that basic arithmetical concepts map the arithmetical structure of the world; that the map obtains in virtue of our normal sensory apparatus. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Pref) | |
| A reaction: She defends the nice but unusual position that arithmetical knowledge is both a priori and empirical (so that those two notions are not, as usually thought, opposed). I am a big Carrie Jenkins fan. |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| Full Idea: A problem for the neo-Fregeans is that it has not proved easy to establish that Hume's Principle is analytic or definitive in the required sense. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
| A reaction: It is also asked how we would know the principle, if it is indeed analytic or definitional (Jenkins p.119). |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| Full Idea: What concept grounding does for us is ensure that our concepts, like the results of our empirical tests, can be treated as a source of information about the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
| A reaction: Presumably we learn our concepts hand-in-hand with experience, so learning our concepts is itself learning about the world. Later checking of concepts and their relations largely confirms what we already knew? |
| 17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
| Full Idea: Dependence comes in essential, modal, explanatory, conceptual, metaphysical and constitutive forms. | |
| From: report of Carrie Jenkins (Grounding Concepts [2008], 1.2) by PG - Db (ideas) | |
| A reaction: You'll have to look up Jenkins for the details. |
| 17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
| Full Idea: Concepts which are indispensably useful for categorising, understanding, explaining, and predicting our sensory input are likely to be ones which map the structure of that input well. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.6) | |
| A reaction: Anti-realists about classification seem to think that we just invent an array of concepts, and then start classifying with them. The truth seems to be that the actual classes of worldly thing have generated our concepts. |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
| Full Idea: Examining accurate concepts can help us acquire true beliefs about the world, examining justified concepts can help us acquire justified beliefs about the world, and examining grounded concepts can help us acquire knowledge of it. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
| A reaction: This summarises Jenkins's empirical account of concepts, and I love it all to bits. I feel that contemporary philosophy is beginning to produce a coherent naturalistic worldview which can replace religion. Bar the rituals. We can have priests... |
| 17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
| Full Idea: The mere reliability of intuition is not a satisfactory ground for saying it is a source of knowledge - we need to know why it is reliable to understand whether it can be a source of knowledge. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 6.5) | |
| A reaction: My theory is that intuition is simply believing things for reasons which we have either forgotten, or (more likely) reasons which are too complex or subtle to be articulated. Intuition feels rational, because it is rational. Updated view of mind needed. |
| 17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
| Full Idea: I propose that knowledge is true belief which can be well explained .....just by citing the proposition believed. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 3.1) | |
| A reaction: I don't find this appealing, and my reservation about Jenkins's book is her reliabilist, externalist epistemology. I would add an internalist coherentist epistemology to her very nice theory. 'I believe there are fairies at the bottom of my garden'? |
| 17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
| Full Idea: Grounded concepts are like trustworthy on-board maps of the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
| A reaction: You'll probably need more than one concept for it to qualify as a 'map', but I like this idea a lot. The world, rather than we ourselves, creates our concepts. The opposite of the view of Geach in 'Mental Acts'. |
| 17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
| Full Idea: I think the physical effects of the world on the brain explain our possessing the concepts we do. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 8.2) | |
| A reaction: A nice slogan for a thought which strikes me as exactly right. |
| 17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
| Full Idea: I find an updated verificationism plausible, in which we say something meaningful just in case we employ only concepts whose possession could be justified or disjustified by sensory input. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 5.6) | |
| A reaction: Wow! This is the first time I have ever had the slightest sympathy for verificationism. It saves my favourite problem case - of wild but meaningful speculation, for example about the contents of another universe. A very nice idea. |
| 17732 | Success semantics explains representation in terms of success in action [Jenkins] |
| Full Idea: Success semantics is the attempt to understand mental representation by thinking about the ways in which representing the world can lead to success in action. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 6.3) | |
| A reaction: I take this to be what is also known as 'teleological semantics'. It sounds to me as if this might help to explain success in action, but isn't going to explain the representations that result in the success. |
| 17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |
| Full Idea: 'Analytic' might mean conceptually true, or true in virtue of meaning, or where the predicate is contained in the subject, or for sentences which define something, or where meaning is sufficient for the truth. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
| A reaction: The second one says meaning grounds the truth, where the last one says meaning entails the truth. |
| 8430 | Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim] |
| Full Idea: The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.207) | |
| A reaction: He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little. |
| 8396 | Many counterfactuals have nothing to do with causation [Kim, by Tooley] |
| Full Idea: Kim has pointed out that there are a number of counterfactuals that have nothing to do with causation. If John marries Mary, then if John had not existed he would not have married Mary, but that is not the cause of their union. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973], 5.2) by Michael Tooley - Causation and Supervenience | |
| A reaction: One might not think that this mattered, but it leaves the problem of distinguishing between the causal counterfactuals and the rest (and you mustn't mention causation when you are doing it!). |
| 8429 | Counterfactuals can express four other relations between events, apart from causation [Kim] |
| Full Idea: Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: [Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'. |
| 8428 | Causation is not the only dependency relation expressed by counterfactuals [Kim] |
| Full Idea: The sort of dependency expressed by counterfactual relations is considerably broader than strictly causal dependency, and causal dependency is only one among the heterogeneous group of dependency relationships counterfactuals can express. | |
| From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205) | |
| A reaction: In 'If pigs could fly, one and one still wouldn't make three' there isn't even a dependency. Kim has opened up lines of criticism which make the counterfactual analysis of causation look very implausible to me. |
| 4781 | Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos] |
| Full Idea: Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'. | |
| From: report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3 | |
| A reaction: This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is. |