46 ideas
| 11051 | Frege's logical approach dominates the analytical tradition [Hanna] |
| Full Idea: Pure logic constantly controls Frege's philosophy, and in turn Frege's logically oriented philosophy constantly controls the analytic tradition. | |
| From: Robert Hanna (Rationality and Logic [2006], 1.1) | |
| A reaction: Hanna seeks to reintroduce the dreaded psychological aspect of logic, and I say 'good for him'. |
| 11054 | Scientism says most knowledge comes from the exact sciences [Hanna] |
| Full Idea: Scientism says that the exact sciences are the leading sources of knowledge about the world. | |
| From: Robert Hanna (Rationality and Logic [2006], 1.2) | |
| A reaction: I almost agree, but I would describe the exact sciences as the chief 'evidence' for our knowledge, with the chief 'source' being our own ability to make coherent sense of the evidence. Exact sciences rest on mathematics. |
| 11070 | 'Denying the antecedent' fallacy: φ→ψ, ¬φ, so ¬ψ [Hanna] |
| Full Idea: The fallacy of 'denying the antecedent' is of the form φ→ψ, ¬φ, so ¬ψ. | |
| From: Robert Hanna (Rationality and Logic [2006], 5.4) |
| 11071 | 'Affirming the consequent' fallacy: φ→ψ, ψ, so φ [Hanna] |
| Full Idea: The fallacy of 'affirming the consequent' is of the form φ→ψ, ψ, so φ. | |
| From: Robert Hanna (Rationality and Logic [2006], 5.4) |
| 11088 | We can list at least fourteen informal fallacies [Hanna] |
| Full Idea: Informal fallacies: appeals to force, circumstantial factors, ignorance, pity, popular consensus, authority, generalisation, confused causes, begging the question, complex questions, irrelevance, equivocation, black-and-white, slippery slope etc. | |
| From: Robert Hanna (Rationality and Logic [2006], 7.3) |
| 11059 | Circular arguments are formally valid, though informally inadmissible [Hanna] |
| Full Idea: A circular argument - one whose conclusion is to be found among its premises - is inadmissible in most informal contexts, even though it is formally valid. | |
| From: Robert Hanna (Rationality and Logic [2006], 2.1) | |
| A reaction: Presumably this is a matter of conversational implicature - that you are under a conventional obligation to say things which go somewhere, rather than circling around their starting place. |
| 11089 | Formally, composition and division fallacies occur in mereology [Hanna] |
| Full Idea: Informal fallacies of composition and division go over into formal fallacies of mereological logic. | |
| From: Robert Hanna (Rationality and Logic [2006], 7.3) |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 11058 | Logic is explanatorily and ontologically dependent on rational animals [Hanna] |
| Full Idea: Logic is explanatorily and ontologically dependent on rational animals. | |
| From: Robert Hanna (Rationality and Logic [2006], 1.6) | |
| A reaction: This is a splendid defiance of the standard Fregean view of logic as having an inner validity of its own, having nothing to do with the psychology of thinkers. But if Hanna is right, why does logical consequence seem to be necessary? |
| 11072 | Logic is personal and variable, but it has a universal core [Hanna] |
| Full Idea: Beyond an innate and thus universally share protologic, each reasoner's mental logic is only more or less similar to the mental logic of any other reasoner. | |
| From: Robert Hanna (Rationality and Logic [2006], 5.7) | |
| A reaction: This is the main thesis of Hanna's book. I like the combination of this idea with Stephen Read's remark that each student should work out a personal logic which has their own private endorsement. |
| 11061 | Intensional consequence is based on the content of the concepts [Hanna] |
| Full Idea: In intensional logic the consequence relation is based on the form or content of the concepts or properties expressed by the predicates. | |
| From: Robert Hanna (Rationality and Logic [2006], 2.2) |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 11063 | Logicism struggles because there is no decent theory of analyticity [Hanna] |
| Full Idea: All versions of the thesis that arithmetic is reducible to logic remain questionable as long as no good theory of analyticity is available. | |
| From: Robert Hanna (Rationality and Logic [2006], 2.4) | |
| A reaction: He rejects the attempts by Frege, Wittgenstein and Carnap to provide a theory of analyticity. |
| 11055 | Supervenience can add covariation, upward dependence, and nomological connection [Hanna] |
| Full Idea: 'Strong supervenience' involves necessary covariation of the properties, and upward dependence of higher level on lower level. ...If we add a nomological connection between the two, then we have 'superdupervenience'. | |
| From: Robert Hanna (Rationality and Logic [2006], 1.2) | |
| A reaction: [compressed] Very helpful. A superdupervenient relationship between mind and brain would be rather baffling if they were not essentially the same thing. (which is what I take them to be). |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 11083 | A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna] |
| Full Idea: On my view, necessity is the truth of a sentence in every member of a set of possible worlds, together with its nonfalsity in every other possible worlds. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) |
| 11086 | Metaphysical necessity can be 'weak' (same as logical) and 'strong' (based on essences) [Hanna] |
| Full Idea: Weak metaphysical necessity is either over the set of all logically possible worlds (in which case it is the same as logical necessity), or it is of a smaller set of worlds, and is determined by the underlying essence or nature of the actual world. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: I take the first to be of no interest, as I have no interest in a world which is somehow rated as logically possible, but is not naturally possible. The second type should the principle aim of all human cognitive enquiry. The strong version is synthetic. |
| 11084 | Logical necessity is truth in all logically possible worlds, because of laws and concepts [Hanna] |
| Full Idea: Logical necessity is the truth of a sentence by virtue of logical laws or intrinsic conceptual connections alone, and thus true in all logically possible worlds. Put in traditional terms, logical necessity is analyticity. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) |
| 11085 | Nomological necessity is truth in all logically possible worlds with our laws [Hanna] |
| Full Idea: Physical or nomological necessity is the truth of a sentence in all logically possible worlds governed by our actual laws of nature. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: Personally I think 'natural necessity' is the best label for this, as it avoids firm commitment to reductive physicalism, and it also avoids commitment to actual necessitating laws. |
| 11077 | Intuition includes apriority, clarity, modality, authority, fallibility and no inferences [Hanna] |
| Full Idea: The nine features of intuition are: a mental act, apriority, content-comprehensiveness, clarity and distinctness, strict-modality-attributivity, authoritativeness,noninferentiality, cognitive indispensability, and fallibility. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.4) | |
| A reaction: [See Hanna for a full explanation of this lot] Seems like a good stab at it. Note the trade-off between authority and fallibility. |
| 11080 | Intuition is more like memory, imagination or understanding, than like perception [Hanna] |
| Full Idea: There is no reason why intuition should be cognitively analogous not to sense perception but instead to either memory, imagination, or conceptual understanding. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.5) | |
| A reaction: It is Russell's spotting the analogy with memory that made me come to believe that a priori knowledge is possible, as long as we accept it as being fallible. [Hanna has a good discussion of intuition; he votes for the imagination analogy] |
| 11078 | Intuition is only outside the 'space of reasons' if all reasons are inferential [Hanna] |
| Full Idea: Intuition is outside the 'space of reasons' if we assume that all reasons are inferential, but inside if we assume that reasons need not always be inferential. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.4) | |
| A reaction: I take it that intuition can be firmly inside the space of reasons, and that not all reasons are inferential. |
| 11053 | Explanatory reduction is stronger than ontological reduction [Hanna] |
| Full Idea: As standardly construed, reduction can be either explanatory or ontological. Explanatory reduction is the strongest sort of reduction. ...Ontological reduction can still have an 'explanatory gap'. | |
| From: Robert Hanna (Rationality and Logic [2006], 1.1) |
| 11081 | Imagination grasps abstracta, generates images, and has its own correctness conditions [Hanna] |
| Full Idea: Three features of imagination are that its objects can be abstract, that it generates spatial images directly available to introspection, and its correctness conditions are not based on either efficacious causation or effective tracking. | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: Hanna makes the imagination faculty central to our grasp of his proto-logic. |
| 11082 | Should we take the 'depictivist' or the 'descriptivist/propositionalist' view of mental imagery? [Hanna] |
| Full Idea: In the debate in cognitive science on the nature of mental imagery, there is a 'depictivist' side (Johnson-Laird, Kosslyn, Shepard - good images are isomorphic), and a 'descriptivist' or 'propositionalist' side (Pylyshyn and others). | |
| From: Robert Hanna (Rationality and Logic [2006], 6.6) | |
| A reaction: Hanna votes firmly in favour of the first view, and implies that they have more or less won the debate. |
| 11067 | Rational animals have a normative concept of necessity [Hanna] |
| Full Idea: A rational animal is one that is a normative-reflective possessor of the concepts of necessity, certainty and unconditional obligation. | |
| From: Robert Hanna (Rationality and Logic [2006], 4.0) | |
| A reaction: The addition of obligation shows the Kantian roots of this. It isn't enough just to possess a few concepts. You wouldn't count as rational if you didn't desire truth, as well as understanding it. Robots be warned. |
| 11068 | One tradition says talking is the essence of rationality; the other says the essence is logic [Hanna] |
| Full Idea: In the tradition of Descartes, Chomsky and Davidson, rational animals are essentially talking animals. But in the view of Kant, and perhaps Fodor, it is the cognitive capacity for logic that is the essence of human rationality. | |
| From: Robert Hanna (Rationality and Logic [2006], 4.9) |
| 11047 | Hegelian holistic rationality is the capacity to seek coherence [Hanna] |
| Full Idea: The 'holistic' (Hegelian) sense of rationality means the capacity for systematically seeking coherence (or 'reflective equilibrium') across a network or web of beliefs, desires, emotions, intentions and volitions. Traditionally 'the truth is the whole'. | |
| From: Robert Hanna (Rationality and Logic [2006], Intro) | |
| A reaction: On the whole this is my preferred view (which sounds Quinean as well as Hegelian), though I reject the notion that truth is a whole. I take coherence to be the hallmark of justification, though not of truth, and reason aims to justify. |
| 11048 | Humean Instrumental rationality is the capacity to seek contingent truths [Hanna] |
| Full Idea: The 'instrumental' (Humean) sense of rationality means a capacity for generating or recognizing contingent truths, contextually normative rules, consequentialist obligations, and hypothetical 'ought' claims. Reason is 'the slave of the passions'. | |
| From: Robert Hanna (Rationality and Logic [2006], Intro) |
| 11046 | Kantian principled rationality is recognition of a priori universal truths [Hanna] |
| Full Idea: The 'principled' (Kantian) sense of rationality means the possession of a capacity for generating or recognizing necessary truths, a priori beliefs, strictly universal normative rules, nonconsequentialist moral obligations, and categorical 'ought' claims. | |
| From: Robert Hanna (Rationality and Logic [2006], Intro) |
| 11045 | Most psychologists are now cognitivists [Hanna] |
| Full Idea: Most psychologists have now dropped behaviourism and adopted cognitivism: the thesis that the rational human mind is essentially an active innately specified information-processor. | |
| From: Robert Hanna (Rationality and Logic [2006], Intro) |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red. | |
| From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5 | |
| A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts. |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |