Topic: classification
Topic: formal methods and languages
Topic: hierarchical structures
Topic: limitations of formalism
Topic: limitations of hierarchical structures
Topic: logic
Topic: reductionism
Topic: state
Topic: taxonomy
Group: computer science
Group: data type
Group: function
Group: grammar
Group: hypertext
Group: mathematics
Group: meaning and truth
Group: philosophy
Group: philosophy of mathematics
Group: program proving
Group: relationship between brain and behavior
Group: requirement specification
Group: science
Group: systems
Topic: abstraction
Topic: abstraction by name
Topic: analytic truth
Topic: logic programming
Topic: mathematical proof
Topic: mathematics as a formal system
Topic: model checker
Topic: natural language as a system
Topic: people vs. computers
Topic: programming as mathematics
Topic: rules
Topic: temporal relationships
Topic: what is a computer
 
Summary
Formalism is the use of symbols for logical arguments. It is an important part of the foundation for mathematics. It insures that arguments are rigorous, without gaps in the chain of inferences. For many, formalism appears to solve the problem of knowledge. From a small number of laws and rules, one can develop a boundless number of laws and relationships.
Yet a formal system is just another version of a Turing machine, and a Turing machine is just a number. (cbb 4/94)
Subtopic: formalism as knowledge
Quote: elements are unknowable; while complexes are knowable and explicable via written letters
 Quote: Leibniz developed the idea of a formal system as a means to knowledge, and the possibility of transforming a formal system into a real machine [»kramS2_1996]
 Quote: for Leibniz, formal systems and mechanized symbolic operations establish a norm for how we should think. They do not describe how we think [»kramS2_1996]
 Subtopic: logic as symbolic system
Quote: logic is a system of processes that follow laws concerning symbols with a fixed interpretation [»boolG_1854, OK]
 Quote: Frege developed concept writing to prevent gaps in a chain of inferences; found that language and intuition were inadequate
 Quote: a proof must be a stepbystep procedure; devised a concept writing to reduce their length; conforms with rules [»fregG_1884]
 Quote: Frege's ideography will unify the formula languages and extend them to new fields [»fregG_1879]
 Quote: replace the concepts of subject and predicate with argument and function respectively [»fregG_1879]
 Quote: concept writing provides symbols for implication and negation [»fregG_1879]
 Quote: in ontological symbolism, a symbol refers to an independent object or thing; with operative symbolism (Leibniz), the meaning of symbols is irrelevant to their manipulation [»kramS2_1996]
 Subtopic: formalism as rules, syntactic
Quote: if complexes are knowable then one knows the syllable SO but not the letters S and O; this is absurd [»plat_368]
 Quote: computer programs are formal (syntactic); they manipulate symbols through precisely stated rules; abstract, manipulated without meaning [»searJR1_1990]
 Quote: a nonlinguistic writing system allows a formal language in which signs are independent of the signified objects; e.g., decimal numbers and Leibniz's characteres [»kramS2_1996]
 Quote: Leibniz's infinitesimal calculus was independent of what differentials actually are; avoids metaphysical disputes [»kramS2_1996]
 Quote: elements have only a name; combine names into descriptions of complex things [»plat_368]
 Quote: use a small vocabulary for formal methods; easier to understand though longer, more abstract, little implementation bias; e.g., Hoare's CSP [»boweJP4_1995]
 Quote: how to construct a relay switching circuit from equations of the independent and dependent variables [»shanCE6_1938]
 Quote: to produce an utterance one has to refer back to general rules and forward to specific rules while reconstructing the rules from continuity, context, and exceptions [»misrVN_1966]
 Subtopic: concise
Quote: in India, conciseness of composition, especially in scientific matters, was highly prized; more pronounced in earlier works [»dattB_1935]
 Quote: Panini's mathematical grammar described the language as spoken, concisely defined by enumerations and rules; transmitted orally; transform from syntactic relationship to phonemic realization [»misrVN_1966]
 Subtopic: universal system
Quote: a small number of laws and rules can include the content of all the laws, albeit in an undeveloped state [»fregG_1879]
 Quote: since the number of laws is boundless, need to find a basic set of laws that generates the rest; not unique [»fregG_1879]
 Subtopic: formalization of evaluation
Quote: algorithm for evaluating an applicative expression relative to an environment; first formalization of expression evaluation
 Subtopic: Turing machine
Quote: formal systems or formalisms are the same as Turing machines [»godeK_1931]
 Subtopic: formalism without boundaries
Quote: there is no boundary between 'clearly' and 'not clearly' yet 'clearly' has formal properties [»holtAW11_1980]

Group: formalism
Topic: classification (65 items)
Topic: formal methods and languages (53 items)
Topic: hierarchical structures (46 items)
Topic: limitations of formalism (93 items)
Topic: limitations of hierarchical structures (10 items)
Topic: logic (84 items)
Topic: reductionism (51 items)
Topic: state (35 items)
Topic: taxonomy (16 items)
Related Topics
Group: computer science (871 topics, 23489 quotes)
Group: data type (34 topics, 730 quotes)
Group: function (12 topics, 232 quotes)
Group: grammar (8 topics, 181 quotes)
Group: hypertext (44 topics, 786 quotes)
Group: mathematics (23 topics, 560 quotes)
Group: meaning and truth (18 topics, 634 quotes)
Group: philosophy (60 topics, 2323 quotes)
Group: philosophy of mathematics (11 topics, 330 quotes)
Group: program proving (10 topics, 311 quotes)
Group: relationship between brain and behavior (9 topics, 332 quotes)
Group: requirement specification (11 topics, 307 quotes)
Group: science (45 topics, 1960 quotes)
Group: systems (17 topics, 530 quotes)
Topic: abstraction (62 items)
Topic: abstraction by name (29 items)
Topic: analytic truth (51 items)
Topic: logic programming (34 items)
Topic: mathematical proof (23 items)
Topic: mathematics as a formal system (30 items)
Topic: model checker (49 items)
Topic: natural language as a system (43 items)
Topic: people vs. computers (55 items)
Topic: programming as mathematics (27 items)
Topic: rules (43 items)
Topic: temporal relationships (40 items)
Topic: what is a computer (62 items)
