33 ideas
13252 | Some truths have true negations [Beall/Restall] |
Full Idea: Dialetheism is the view that some truths have true negations. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
13255 | Relevant logic may reject transitivity [Beall/Restall] |
Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
13253 | There are several different consequence relations [Beall/Restall] |
Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
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: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
A reaction: This why the symbol |= is often referred to as 'models'. |
13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
5500 | Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan] |
Full Idea: Biologists don't split living things into a 'structural' level and an 'abstract' level; ..rather, they are organised at many levels, each level 'abstract' with respect to those beneath it, but 'structural' as it realises those levels above it. | |
From: William Lycan (Introduction - Ontology [1999], p.9) | |
A reaction: This is a very helpful distinction. Compare Idea 4601. It seems to fit well with the 'homuncular' picture of a hierarchical mind, and explains why there are so many levels of description available for mental life. |
5494 | 'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan] |
Full Idea: There is such a thing as synthetic and a posteriori identity that is nonetheless genuine identity, as in lightning being electrical discharge, and the Morning Star being Venus. | |
From: William Lycan (Introduction - Ontology [1999], p.5) | |
A reaction: It is important to note that although these identities are synthetic a posteriori, that doesn't make them contingent. The early identity theorists like Smart seemed to think that it did. Kripke must be right that they are necessary identities. |
13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
6871 | We can't only believe things if we are currently conscious of their justification - there are too many [Goldman] |
Full Idea: Strong internalism says only current conscious states can justify beliefs, but this has the problem of Stored Beliefs, that most of our beliefs are stored in memory, and one's conscious state includes nothing that justifies them. | |
From: Alvin I. Goldman (Internalism Exposed [1999], §2) | |
A reaction: This point seems obviously correct, but one could still have a 'fairly strong' version, which required that you could always call into consciousness the justificiation for any belief that you happened to remember. |
6872 | Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman] |
Full Idea: Even weak internalism has the problem of Forgotten Evidence; the agent once had adequate evidence that she subsequently forgot; at the time of epistemic appraisal, she no longer has adequate evidence that is retrievable from memory. | |
From: Alvin I. Goldman (Internalism Exposed [1999], §3) | |
A reaction: This is certainly a basic problem for any account of justification. It will rule out any strict requirement that there be actual mental states available to support a belief. Internalism may be pushed to include non-conscious parts of the mind. |
6874 | Internal justification needs both mental stability and time to compute coherence [Goldman] |
Full Idea: The problem for internalists of Doxastic Decision Interval says internal justification must avoid mental change to preserve the justification status, but must also allow enough time to compute the formal relations between beliefs. | |
From: Alvin I. Goldman (Internalism Exposed [1999], §4) | |
A reaction: The word 'compute' implies a rather odd model of assessing coherence, which seems instantaneous for most of us where everyday beliefs are concerned. In real mental life this does not strike me as a problem. |
6873 | Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman] |
Full Idea: The problem of Concurrent Retrieval is a problem for internalism, notably coherentism, because an agent could ascertain coherence of her entire corpus only by concurrently retrieving all of her stored beliefs. | |
From: Alvin I. Goldman (Internalism Exposed [1999], §3) | |
A reaction: Sounds neat, but not very convincing. Goldman is relying on scepticism about short-term memory, but all belief and knowledge will collapse if we go down that road. We couldn't do simple arithmetic if Goldman's point were right. |
6875 | Reliability involves truth, and truth is external [Goldman] |
Full Idea: Reliability involves truth, and truth (on the usual assumption) is external. | |
From: Alvin I. Goldman (Internalism Exposed [1999], §6) | |
A reaction: As an argument for externalism this seems bogus. I am not sure that truth is either 'internal' or 'external'. How could the truth of 3+2=5 be external? Facts are mostly external, but I take truth to be a relation between internal and external. |
5496 | Functionalism has three linked levels: physical, functional, and mental [Lycan] |
Full Idea: Functionalism has three distinct levels of description: a neurophysiological description, a functional description (relative to a program which the brain is realising), and it may have a further mental description. | |
From: William Lycan (Introduction - Ontology [1999], p.6) | |
A reaction: I have always thought that the 'levels of description' idea was very helpful in describing the mind/brain. I feel certain that we are dealing with a single thing, so this is the only way we can account for the diverse ways in which we discuss it. |
5499 | A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan] |
Full Idea: Some theorists have said that the one-to-one correspondence between the organism and parts of its 'program' is too liberal, and suggest that the state and its functional role are seen teleologically, as functioning 'for' the organism. | |
From: William Lycan (Introduction - Ontology [1999], p.9) | |
A reaction: This seems an inevitable development, once the notion of a 'function' is considered. It has to be fitted into some sort of Aristotelian teleological picture, even if the functions are seen subjectively (by what?). Purpose is usually seen as evolutionary. |
13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
5501 | People are trying to explain biological teleology in naturalistic causal terms [Lycan] |
Full Idea: There is now a small but vigorous industry whose purpose is to explicate biological teleology in naturalistic terms, typically in terms of causes. | |
From: William Lycan (Introduction - Ontology [1999], p.10) | |
A reaction: This looks like a good strategy. In some sense, it seems clear that the moon has no purpose, but an eyeball has one. Via evolution, one would expect to reduce this to causation. Purposes are real (not subjective), but they are reducible. |