Quote: a definable collection does not necessarily form a totality

Quote: no complete set of effectively calculable invariants of conversion exist; for example, if Principia Mathematica is omega-consistent, its Enthscheidungsproblem is unsolvable [»churA_1936]

Quote: although Principia mathematica and Zermelo-Fraenkel set theory formalize all of mathematics, they contain simple, undecidable problems [»godeK_1931]

Quote: the consistency of a recursive consistent class of formulas is not provable in the system [»godeK_1931]

Quote: Russell's paradox shook the foundations of Frege's arithmetic; substitution of equality is not always valid [»russB6_1902]

Quote: can not prove the consistency of any consistent formal system that contains a certain amount of number theory

Quote: the sequence of computable numbers is not computable because of the halting problem; get an infinite loop when processing its own description number [»turiAM11_1936]

Quote: there is no general process to determine whether a given formula is provable; contrast with Godel's proof that there exist propositions U such that neither U nor -U is provable [»turiAM11_1936]

Quote: conjecture of inconsistency: any axiomatizations of human knowledge is uniformly inconsistent [»hewiC4_1985]

Quote: conjecture of perpetual inconsistency: any axiomatizations of human knowledge will always be inconsistent [»hewiC4_1985]

Quote: rational views of the universe are idealized models which approximate reality [»kentW_1978]

Quote: we observers invent the codes in order to codify what nature is about [»matuHR_1980]

Quote: there is no absolute definition of truth and beauty; but for purposes of daily living, we reconcile divergent views [»kentW_1978]

Quote: all structures and hierarchies are totally arbitrary [»nelsTH_1974]

Quote: need a theory of truth because truth can not be identified with mathematical provability; Godel [»tarsA_1944, OK]

Quote: we introduce Maturana's terminology without giving definitions; precise definitions are impossible anyway [»winoT_1986]

Quote: if we want to understand others, we must count them right in most matters [»daviD11_1974]

Quote: reality is not separate from our understanding of reality; reality makes our sentences true or false [»daviD11_1974]

Quote: Frege did not claim to prove the analytic character of number; there may be a gap in his proof or a missing premise [»fregG_1884]

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]

Quote: if complexes are knowable then one knows the syllable SO but not the letters S and O; this is absurd [»plat_368]

Quote: a demonstration in analytic logic leads to an immense tautology. Logic is sterile unless made fruitful by intuition [»poinH_1908, OK]

Quote: in a formalized theory, the tools are completely prescribed by its syntax; in proof-analysis, tools are unconstrained [»lakaI_1976]

Quote: a real proof is fruitful, its conclusion is in a sense more general than its premises

Quote: proof verification is analytical and leads to nothing but the premises translated into another language [»poinH_1902, OK]

Quote: nothing can be proved but the supposing something intuitively known, and evident, without proof

Quote: construction rules for mathematics leads to intense concern about syntax, the way in which things are written

Quote: cryptography can not protect us with mathematics; it can not keep our secrets safe, nor protect our electronic interactions [»schnB_2000]

Quote: in science, we cannot define anything precisely; we have to agree that we are talking about roughly the same thing; avoids paralysis of thought [»feynRP_1963]

Quote: many scientists believe the world is governed by simple mathematical laws; but in practice, all consequences can not be predicted [»hoarCA8_1986]

Quote: it is by definition that 'f=ma', that action and reaction are equal and opposite, that objects remain in uniform motion [»poinH_1902, OK]

Quote: most physics professors do not believe that the world is truly deterministic; but most theories are deterministic [»pylyZW_1986]

Quote: very few phenomena depend on simple, mathematical laws--gravitation, light, and electricity; tied to geometry of space and statistical effects [»thomR_1975]

Quote: Pappian heuristic--derive consequences of a conjecture; if true, rederive the original conjecture, thus yielding a final truth; failed for science [»lakaI_1976]

Quote: perhaps the phoneme is constructed, if at all, as a consequence of perception, not as a step of perception [»oettAG_1972]

Quote: life and reality are amorphous, inconsistent, non-rational [»kentW_1978]

Quote: rationality works much slower than most people tend to think, and, even then, fallibly

Quote: human practices are a hopeless tangle, yet it forms the background that determines our judgment and concepts; must accept as is [»dreyHL_1991]

Quote: though formal reasoning may obey mathematical laws, the mind is much more; e.g., sentiment, action, and the duties of life [»boolG_1854, OK]

Quote: cocktail parties are real but they do not undergo a smooth reduction to physics [»searJR_1992]

Quote: although syntax and semantic competence can be scientific, the understanding of language in specific situations runs into serious problems [»dreyHL_1979]

Quote: to tell if a speaker mis-spoke, need to infer some of the speaker's meaning prior to the utterance; implies, decoding theories are incomplete [»blaiDC6_1992]

Quote: compare "Bring me the broom" with "Bring me the broomstick and its brush"; the decomposition is nonsensical [»wittL_1958a]

Quote: program correctness is more than a calculable relation between its specification and its text [»tursWM10_2003]

Quote: program correctness includes the reality in which the need for a program emerged in the first place

Quote: a theory of names is inherently wrong [»kripSA_1980]

Quote: very important, unscientific knowledge of particular circumstances of time and place [»hayeFA9_1945]

Quote: every individual has unique information about particular jobs, people, local conditions, and special circumstances

Quote: how can subjective mental phenomena accord with an objective, scientific reality? [»searJR_1984]

Quote: Berkely refused to accept the redefinition of subjective concepts to objective ones

Quote: when you philosophize, don't leave your commonsense outside like an umbrella, bring it in with you [»wittL_1939]

Quote: common sense can be lost when an individual or organization tries to follow proper procedures [»stroB_1991]

Quote: if require a Euclidean programme with perfectly known concepts, must translate vague concepts and perhaps lose part of their meaning [»lakaI_1976]

Quote: every idea can be wrong

Quote: blind necessity could produce no variety of things; diversity is due to the ideas and will of a Being necessarily existing [»newtI_1685, OK]

Quote: there is no science but the science of the general

Quote: include freedom from bias among the criteria used to judge a system; helps avoid injustices [»frieB7_1996]

Quote: if objectivity is the foundation of knowledge than ethics is not part of knowledge [»monoJ_1971]

Quote: automata theory and classical physics use a global, system state determined by the global, real time [»petrCA1_1966]

Quote: Carnap was not able to connect 'quality at location x;y;z;t' with his language of sense data and logic

Quote: there is no absolute space, no absolute time, no simultaneity across distance, not even geometry; these concepts are no more than a language [»poinH_1902, OK]

Quote: a mechanical computer does not literally follow rules; it only behaves as if it does [»searJR_1992]

Quote: services are expected to fail; the computer disappears; mass appeal from new, updated, improved, etc. [»tursWM10_2003]

Quote: when imprecision of dramatic representation works, it is more rewarding with less effort than the precision of programming

Quote: imprecision of dramatic representation is the price people pay to gain a kind of lifelikeness, surprise and delight [»laurB_1991]

Quote: the program itself is the only complete description of what the program will do [»daviPJ3_1972]

Quote: even if a complete description of a machine is unavailable, run a program and you will see what it does

Quote: formal methods are less understandable than actual program text

Quote: computer programs are mathematical expressions of behavior, but they are not treated as such in practice [»hoarCA8_1986]

Quote: constraint solvers can be unpredictable, difficult to debug, and difficult to master [»myerB3_2000]

Note: formalism tries to make programs tightly structured, but it just isn't so; programs are loosely structured because applications are loosely structured [»cbb_1990, OK]

Quote: use formal methods to verify a design instead of proving correctness; forces engineers to be precise about details; resolves differences of interpretation between implementers and testers [»tretJ9_2001]

Quote: formal methods do not help with conceptual models and high-level structuring; both require experience; formal specification gives a false feeling of confidence [»tretJ9_2001]

Quote: used TRIO formalisms for industrial projects; required formalism experts that often include the formalism developers [»ciapE1_1999]

Quote: need a formal methods guru when using formal methods in a project [»boweJP4_1995]

Quote: type systems do more than any other formal method to ensure correctness; constrains interface; ensures compatibility [»leeEA9_2000]

Quote: it is easy to express sequencing in formal UI systems; does not work for direct-manipulation user interfaces [»myerB3_2000]

Quote: formal systems have a high threshold for using them; e.g., define a grammar to express sequencing in dialogs [»myerB3_2000]

Quote: ten commandments for successful projects using formal methods [»boweJP4_1995]

Quote: do not use formalized methods everywhere; formal methods used for only 10% of CICS [»boweJP4_1995]

Quote: formal methods are inappropriate for user interface design

Quote: produce an informal specification in parallel with a formal project description; helps clarify the formal text [»boweJP4_1995]

Quote: formal methods do not guarantee correctness; they achieve higher system integrity when applied appropriately [»boweJP4_1995]

Quote: avoid dogmatism when using formal methods; modify specifications as needed; be skeptical about proofs [»boweJP4_1995]

Quote: testing remains important with formal methods; bugs will be found in the requirements and their refinement [»boweJP4_1995]

Quote: formal requirements are often meaningless to end users; everything is based on the designer's explanations, just as before; specialized, isolated participants [»huntA_2000]

Quote: formal methods use static data models and event/activity-charting; poorly suited for dynamic systems

Quote: full formal development with machine-checked proofs is too expensive except for failure-critical applications

Quote: estimate costs when using formal methods; high-integrity systems are intrinsically expensive [»boweJP4_1995]

Quote: SPIN found five errors in part of the LISP code for NASA's Remote Agent; took 12 man weeks to model and one week to verify [»haveK8_2001]

Quote: programmers do not agree about the value of a formal descriptive technique [»naurP4_1993]

Quote: Smalltalk has fallen into the formalist trap of too few primitives; requires subtle distinctions to differentiate parts of the system

Quote: Smalltalk has only a few, very general rules for constructing objects; can not infer sufficient information to help the user [»nielJ5_1989]