Goodbye, Descartes: The End of Logic and the Search for a New Cosmology of Mind
Keith Devlin
(New York: John Wiley & Sons, Inc., 1997)
page 29 – Stoic school found by Zeno of Citium, not Zeno of Elea (ca. 450 BC)
34 – p ––> q, p arrows q, antecedent arrows consequent
35 – modus ponens
36 – the –| is called turnstile
37 – 1159, John of Salisbury wrote Metalogicon, first Organon–based logic manual
41 – MaP, SaM | SaP [major, minor, conclusion]
42 – "A syllogistic inference amounts to elimination of the middle term…."
"" – four figures x 64 syllogisms each
48 – …the conditional, as defined by the Stoics and by present-day logicians, is not the same as implication."
52 – Cicero wrote of the propositio and the assumptio producing the complexio
55 – Peter of Spain (later, Pope John XXI) wrote Summulae Logicales, became standard medieval logic textbook
56 – proprietates terminorum: study of different roles played by different words in propositions
57 – Stoic antecedent and consequent came to characterize the entire study of logic in the Middle Ages, named consequentiae
59 – English logician, Augustus De Morgan, and his laws ¬(p /\ q) = (¬p) V (¬q) and ¬(p V q) = (¬p) /\ (¬q)
61 – 1620, Francis Bacon aimed to usurp Aristotle's Organon with his Novum Organon
63 – De Arte Combinatoria, Leibniz "envisioned a kind of mental alphabet in which all thought could be represented as suitable combinations of symbols…."
66 – Italian Gerolmo Saccheri, Logica Demonstratia, applied Aristotelian syllogisms to Euclidean geometry; 1761, Leonhard Euler pictorialized syllogisms [Euler circles]; 1881, Symbolic Logic, John Venn improved Euler circles into Venn diagrams
69 – discovery of other geometries betrayed limitations of analytical school as promoted by Newton, Leibniz, and Descartes
73 – 1847, George Boole (b. 1815) published The Mathematical Analysis of Logic; then, in 1854, an expanded version, An Investigation of the Laws of Thought…
77 – "The separation of symbols from their meaning is at the very heart of modern logic."
78 – W. S. Jevons built a mechanical logic machine which demonstrated to the Royal Society in 1870
80 – "…deductions in propositional logic are carried out using just one rule of inference: modus ponens."
86 – Chomskyan lexical items and well-formed formulas replaced words and sentences
88 – 'X |= Y' means 'Y is taken to refer to X, when Y is true'
91 – ˜760AD al-Khowarizmi wrote a book explaining Hindu arithmetic ––> algorithm
"" – "the very first electronic digital computer ran its first program on June 21, 1948, in a laboratory at the University of Manchester…"
94 – ¬(p /\ q) and ¬(p V q) are called nand gates and nor gates
97 – Chomsky is one of the ten most-quoted people of all time, and the only one to make the list while still alive
"" – BC and AD, before Chomsky and After Dissertation; Chomsky's PhD dissertation was submitted to the U. of Penn in 1955
101 – 1863, Darwin's Theory and Linguistic, August Schleicher explicated link between Darwinism and historical linguistics
102 – Mongin-Ferdinand de Saussure (b. 1857 in Geneva), developed new 'synchronic linguistics' based on l'état de langue; parole as discrete language acts, langue as the entire language state
103 – de Saussure's students collected his posthumous writings into the Course in General Linguistics, 1916, the first linguistics textbook
106 – 1911, Franz Boas (b. 1858) published Handbook of American Indian Languages, the first account of descriptive linguistics
107 – linguistic positivist, Leonard Bloomfield: "Accept everything a native speaker says in his language and nothing he says about it."
108 – Edward Sapir (1884–1939) and Benjamin Lee Whorf (1897–1941) as basis for Hopi timeless and Eskimo snows myths
115 – Chomsky's linguistic approach depends on 1) adapting a rule-based view of languages, i.e., sentences produced by rules (i.e., novelty within certain rule-parameters don't faze us), 2) seeing syntactic structure is not inherent in words but is a matter of the relationships between them, and 3) grammaticality does not seem essentially to involve meaning (e.g., Colorless green ideas sleep furiously)
119 – S, DNP, VP are syntactic structures
120 – DET ––> a, the is a lexical rule
121 – a Chomsky-style generative grammar aka phrase structure grammar
123 – "The kernel sequence from which a grammatical sentence is produced by means of a series of transformations is sometimes called the deep structure of the sentence; the syntactic structure of the final, natural form that our ears recognize as grammatical is called the surface structure."
130 – Steven Pinker refers to our language instinct as 'a biological adaptation to communicate information.' This puts language in the same camp as rationality, which can be described as 'a biological adaptation to survive and further one's goals.'"
132 – in support of Chomsky's Universal Grammar, there is 'the argument from the poverty of input', the rapid transition from pidgin to creole among pidgin-raised children, deaf children also learn to communicate grammatically
134 – "Words are nouns because they fit into grammatical sentences in certain places––they play a 'nouny' role in the sentence––and likewise for the other categories of words. [as opposed to inherently semantic lexica]"
138 – N, V, PP, AP read as N-bar, etc. for phrases
146 – "The initial choice of moves to be considered in detail is one of the things that marks the good human chess player."
150 – Aristotle's definition of the human as zoon logon echon
171 – computer hardware: 1940s vacuum tubes, mid-1950s transistors, early 1960s and 1970s integrated circuits, late 1970s and 1980s very large-scale integrated circuits (VLSI)
172 – "The assumption that it is, in principle, possible to achieve intelligence by symbol manipulation was put forward by Newell and Simon in 1976 as the 'Physical Symbol System Hypothesis.'"
178 – "To these elementary laws there leads no logical path, but only intuition, supported by being sympathetically in touch with experience." A. Einstein, in G. Holton, Thematic Origins of Scientific Thought: Kepler to Einstein, HUP, 1973, p357.)
181 – Devlin's last effort with his students in debates: "The person walking certainly acts in a manner that is consistent with all of the rules of physics, as does the bicycle rider. They are not breaking the rules. What's more, those rules can be reliably used by scientists who wish to study the physics of walking and bicycle riding. But the person walking or cycling neither needs to know nor uses those rules."
182 – to anyone steeped in the rationalist tradition, "there is always a desire to explain knowing how in terms of knowing that, to reduce skills to facts and rules, to explain the composite in terms of its constituents."
183 – "The original goal of machine intelligence is not possible, at least in terms of a program running on a digital computer, because human intelligent behavior involves knowing how, and knowing how cannot be reduced to knowing that."
192 – intensional logic, a framework to study meaning developed by the logician Richard Montague in the early 1970s.
196 – "Complexity is not the only problem with logical form [in the language-of-thought paradigm of programming intelligence]. A far more serious difficulty is that the use of logical form assumes that words have fixed, definite, and unique meanings."
199 – We went to the bank to get the money. Bob gad buried it by the river some months earlier. OR After we had cashed the check at the bank down by the bay, we sat by the bank and watched the boats go by.
200 – nonce sense as linguistic term for one-time usages in "everyday speech"; 'one water', 'do the lawn', 'very San Francisco', 'fax' [v.]
204 – Jon Barwise, in the late 1970s and early 1980s, employed Tarski's algebraic notation of truth-statements to denote a statement about a part of the world that makes a claim about that part of the world that is true or false. S |= SIGMA; SIGMA makes a claim about the situation s which is true about s. s supports the fact that SIGMA.
205 – « statement » denotes the fact expressed by that statement (rather than just the statement-token itself); s |= «John starts to speak at 4PM», coined by Devlin as infon: a single item of information; s is the soft entity, |= 'supports' s, and SIGMA is the hard entity on the right
216 – speech as a linguistic handshake
218 – "…the rules [of intelligent speech] are not sufficiently comprehensive so that we can program a computer to reproduce those human activities."
220 – "Join acts are intriguing. They are examples of phenomena where the whole is greater than the sum of its parts. Though shaking hands and playing a duet are obvious examples, perhaps a better example to compare to conversation is two people dancing a tango."
231 – Mutual knowledge of F is an item of information K such that K = F /\ [I know K] /\ [You know K].
233 – utterance as lone speech act, contribution as joint speech act
241 – "To say that the brain is a device that can acquire, store, and process information is not to say anything about the way the brain performs these feats."
244 – information gets in by being encoded or represented by markings on a page. "Being encoded or represented is not the same as being contained in."
245 – Societies do not process and store information; "rather, we store and process representations of information, … such as words on paper, bits on magnetic disks, and so forth."
246 – "Thus, one way information can arise is by virtue of systematic regularities in the world."
247–248 – Knowledge of appropriate constraint in a situation enables someone to gain information from that situation, for example, that smoke accompanies fire.
257 – Jon Barwise and John Echtemendy applied the formal techniques of situation theory to Epimenides's Liar Paradox to solve it in 1986.
259 – "But the context for making the observation that the claim is false cannot be c [in which the claim was uttered], since it it were, then that too leads to a contradiction."
271 – "Neither situation theory nor any other theory of contexts is a theory of human cognition. Such theories provide frameworks for the study of information flow.
273 – the quadrivium, AGMA, the trivium, GRD (arithmetic, geometry, music, astronomy; grammar, rhetoric, dialectic)
281 – "Surely there is no one way to view and to understand a flower, nor even a unique "best" way. There may be ways that are more suited to particular purpose, but that is another issue."
RECOMMENDED:
Bickerton, D. Language and Human Behavior.
Dreyfus, H.…, Mind Over Machine
No comments:
Post a Comment