43 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) |
| 18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
| Full Idea: For a language L there is a predicate 'true-in-L' which one can employ for all scientific purposes in place of intuitive truth, and this predicate admits of a precise definition using only the vocabulary of L itself plus set theory. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
| A reaction: He refers, of course, to Tarski's theory. I'm unclear of the division between 'scientific purposes' and the rest of life (which is why some people embrace 'minimal' theories of ordinary truth). I'm struck by set theory being a necessary feature. |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| Full Idea: In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory. |
| 18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
| Full Idea: On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.1) | |
| A reaction: A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'. |
| 18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
| Full Idea: The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities. |
| 18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
| Full Idea: In the theory of types, 'x ∈ y' is well defined only if x and y are of the appropriate type, where individuals count as the zero type, sets of individuals as type one, sets of sets of individuals as type two. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.6) |
| 18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
| Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right. |
| 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. |
| 18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
| Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers. |
| 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) |
| 18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
| Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) | |
| A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic. |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| Full Idea: Instead of identifying functions with certain sets, I might have identified sets with certain functions. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) |
| 18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
| Full Idea: I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'. |
| 18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example) should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.7) | |
| A reaction: This attitude goes back to Hilbert, but it fits with Quine's view of what is indispensable for science. It is hard to see a reason for the cut-off, just looking at the logic of expanding sets. |
| 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). |
| 18957 | Nominalism only makes sense if it is materialist [Putnam] |
| Full Idea: Nominalists must at heart be materialists, or so it seems to me: otherwise their scruples are unintelligible. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.5) | |
| A reaction: This is modern nominalism - the rejection of abstract objects. I largely plead guilty to both charges. |
| 18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
| Full Idea: Physics is full of references to such 'non-physical' entities as state-vectors, Hamiltonians, Hilbert space etc. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
| A reaction: I take these to be concepts which are 'abstracted' from the physical facts, and so they don't strike me as being much of an ontological problem, or an objection to nominalism (which Putnam takes them to be). |
| 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. |
| 18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
| Full Idea: Scientists want successful predictions in order to confirm their theories; they do not want theories in order to obtain the predictions, which are in some cases of not the slightest interest in themselves. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.8) | |
| A reaction: Equally, we might only care about the prediction, and have no interest at all in the theory. Farmers want weather predictions, not a PhD in meteorology. |
| 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) |
| 16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
| Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object. | |
| From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1 | |
| A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…). |