63 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) |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VII.4) |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: [if you don't follow that, you'll have to keep rereading it till you do] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.4) |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.1) |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) | |
| A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far). |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) |
| 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. |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
| A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
| 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) |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.2) | |
| A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians. |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.3) | |
| A reaction: That is, with rations every division operation has an answer. |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], 2.5) |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], II.6) | |
| A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many. |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Cantor didn't mean that you could literally count the set, only in principle. |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) | |
| A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.3) |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'! |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people. |
| 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. |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33) |
| 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). |
| 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) |