Topic: limitations of formalism

topics > philosophy > Group: formalism


chaotic behavior
formal methods and languages
frame problem
Godel's incompleteness theorem
language and life as a game
Liar's paradox and Russell's paradox
limitations of artificial intelligence and cognitive science
limitations of hierarchical structures
limitations of system security
mathematical proof as a social process
mathematics as a formal system
mathematics by proofs and refutations
meaning by social context
open systems
people vs. computers
private language argument for skepticism about meaning
problems with analytic truth
problems with logic programming
program proving is infeasible
program source as truth
scientific paradigms and research programs
self reference
semantic truth; s iff p
skepticism about knowledge
specification is infeasible
vitalism, the soul


Formalism has its limits. Well known limits include Godel's theorems and Turing and Church's undecidable problems.

Formalism concerns the world of numbers. The study of numbers is through computation, but computation is a number. The vast majority of numbers are not computable by programs shorter than themselves. Furthermore, computation is a state machine that may cycle forever, never producing a number.

These are limits intrinsic to formalism itself. The world provides further limits. There are questions of doubt, the rich diversity of the world, the world's irrationality, ethical questions, subjective experiences, inconsistencies, the need to get things done, and so forth. In brief, formalism is only one part of the world. It is a mistake to force the world into formalism. (cbb 4/94)

Subtopic: formalism and undecidability -- cannot prove consistency up

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]

Subtopic: rationality as approximation up

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]

Subtopic: truth is not formal up

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]

Subtopic: knowledge is not formal up

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

Subtopic: logic is not formal up

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

Subtopic: mathematics is not formal up

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

Subtopic: security is not formal up

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

Subtopic: science is not formal up

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]

Subtopic: perception is not formal up

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

Subtopic: people are not theoritical up

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]

Subtopic: language is not theoritical up

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]

Subtopic: specification is not formal up

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

Subtopic: naming is not theoritical up

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

Subtopic: particular vs. universal up

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

Subtopic: subjective vs. objective up

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]

Subtopic: commonsense up

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

Subtopic: lost in translation up

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

Subtopic: error up

Quote: every idea can be wrong

Subtopic: diversity up

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

Subtopic: ethics up

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]

Subtopic: time-space up

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]

Subtopic: computers are not formal up

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]

Subtopic: systems shouldn't be formal up

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]

Subtopic: programs are not formal up

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]

Subtopic: limits of formal methods up

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

Subtopic: cost of formal methods up

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]

Subtopic: programming is not formal up

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]

Related Topics up

Group: philosophy   (60 topics, 2323 quotes)

Topic: change (28 items)
Topic: chaotic behavior (27 items)
Topic: formal methods and languages (53 items)
Topic: frame problem (13 items)
Topic: Godel's incompleteness theorem (19 items)
Topic: language and life as a game (30 items)
Topic: Liar's paradox and Russell's paradox (25 items)
Topic: limitations of artificial intelligence and cognitive science (64 items)
Topic: limitations of hierarchical structures (10 items)
Topic: limitations of system security (39 items)
Topic: mathematical proof as a social process (14 items)
Topic: mathematics as a formal system (30 items)
Topic: mathematics by proofs and refutations (31 items)
Topic: meaning by social context (33 items)
Topic: open systems (33 items)
Topic: people vs. computers (55 items)
Topic: private language argument for skepticism about meaning (34 items)
Topic: problems with analytic truth (20 items)
Topic: problems with logic programming (10 items)
Topic: program proving is infeasible (47 items)
Topic: program source as truth (17 items)
Topic: randomness (20 items)
Topic: reductionism (51 items)
Topic: scientific paradigms and research programs (30 items)
Topic: self reference (27 items)
Topic: semantic truth; s iff p (34 items)
Topic: skepticism about knowledge (34 items)
Topic: specification is infeasible (46 items)
Topic: vitalism, the soul
(73 items)

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