From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=0.1 required=5.0 tests=BAYES_00,LONGWORDS autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 10ad36,d2ff45cabdc6647c,start X-Google-Attributes: gid10ad36,public X-Google-Thread: f8c65,d2ff45cabdc6647c,start X-Google-Attributes: gidf8c65,public X-Google-Thread: 103376,d2ff45cabdc6647c,start X-Google-Attributes: gid103376,public From: z007400b@bc.seflin.org (Ralph Silverman) Subject: On Abstraction Date: 1998/07/10 Message-ID: <6o5cuc$1vr@nntp.seflin.org> X-Deja-AN: 370228617 Organization: SEFLIN Free-Net Newsgroups: comp.unix.bsd,comp.lang.ada,comp.lang.modula2 Date: 1998-07-10T00:00:00+00:00 List-Id: >From nntp.seflin.org!z007400b Wed May 6 15:10:13 1998 Path: nntp.seflin.org!z007400b From: z007400b@bc.seflin.org. (Ralph Silverman) Newsgroups: comp.ai.philosophy Subject: On Abstraction Date: 4 May 1998 19:54:26 GMT Organization: SEFLIN Free-Net Lines: 1354 Message-ID: <6il6di$4o6@nntp.seflin.org> NNTP-Posting-Host: bc.seflin.org X-Newsreader: TIN [version 1.2 PL2] --subtlety and artificial intelligence ( ai ) a) early ideas ... long before ai was realized in practice ... and before modern electronic binary digital computer ( @ 1945 ) ... idea of thinking automaton was based on model of precision calculator and subtlety of ideation and speech was ( largely ) ruled out ... especially in 'science fiction'. such speculation and supposition was reasonably based on fundamentals of operation of automated cybernetic systems then known ... to be rigid and formalistic ... b) general intelligence and general purpose computer ... advent of general purpose computer ( electronic binary digital programmable computer ) was, largely, intended simply to implement foundations of many 'special purpose' systems, substitutable on the same hardware by programming ... and the type of intelligence manifested by such may be termed specialized intelligence ... however, emergently, such capabilities have given rise to feasible capabilities of adaptive intelligence more closely reflecting general human intelligence ... ( as specialized systems become more adaptive ... feasibility emerges ... ) c) abstraction levels of abstraction relating similar ideas are very familiar as e.g. , all imaginable men all men all men known joe ( a named man ) joe now ( i.e. at this time ) ... much of the 'great tradition' of western philosophy ( especially 'metaphysics' ... ) has been devoted to untangling issues related to such abstraction ... ( at least since the time of plato and aristotle ) now, in software engineering, idea of 'abstraction' increasingly enters discussion ( e.g. on internet, as, e.g. comp.lang.c ) ... at least in regard to relation of higher level languages ( hll s ) to lower level languages ( lll s ) ; where an eerie echo of the issues of ancient philosophy may be noted ... d) emergence operations and data types ... in arithmetic, supposing just non-negative integer numbers, addition is relatively non-emergent, since addition of any two such will outcome same type ... however ... subtraction, ( viewable as 'undo' operation, related to addition ) , allows 'emergence' of negative outcome ( even when operands are limited to originating type ! ) ... and a similar relation between multiplication and division , whereby non-integer numbers emerge ... e) abstraction, generalization and vagueness abstraction is the fundamental feature of scientific and technical thought ... as developed by us ... through generalization ... specific systems may be understood in terms ultimately reduced to powerful, simple rules ... e.g. when ohm's law is found; dc circuit characteristics may be measured; ( e.g. voltage, resistance ), with devices commonly available ... however, frequently, abstraction and generalization lead to puzzling problems related to vagueness . e.g. newtonian generalized abstract idea of velocity has proven simplistic in application to physical systems, due to ( inter alia ) evident unforeseen and unnoticed relation of velocity and mass ... and plausibly, vagueness ( in many forms ) is as endemic to abstract thinking as heat dissipation entropy and hysteresis are to physical technology ... whereby, vagueness plays ( in thinking ) a role remarkably similar to such ... f) european grammars ... a simple, effective ontology based on grammatical structure of european languages ... has served, profoundly, as the basis of philosophical study of abstraction, as well as scientific reality models ( and formalized logic ) ( at least ) since time of aristotle ... at basis of this model are individuals ^^^^^^^^^^^ ( substance, etc. ) rooted in grammatical form of noun ^^^^ ... then, related to individuals are properties ^^^^^^^^^^ ( which may be primary ( essence, essential ) ( related to existence ( being ) ) or secondary ( accidental, variable ) ) ... properties are related to grammatical form of adjective ^^^^^^^^^ ... relations ( e.g. taller, shorter, longer ) are closely associated with properties ( e.g. tall, short, long ) whereby what ( modernly ) may be termed a relational operator associates relational operands ( or ) relata ( generally in an ordered form ) ... such are commonly seen in programming as, e.g. ... /* pseudocode */ if( joe_height >= fred_height ) { /* ... */ } else { /* ... */ } ... and arithmetic operators and arithmetic operands , similarly as comparative relations, e.g. ( + - * / ) ( and others ... ) ... and in common computer programming ( general purpose algorithmic languages ) as, e.g. fortran_iv algol_60 pascal the 'c' programming language modula_2 etc. variable ^^^^^^^^ serves role similar to individual ... rooted in noun ... value of variable ^^^^^^^^^^^^^^^^^ is similar to property ^^^^^^^^ which may be compared in relations or serve as arithmetic operand, etc. type ^^^^ of variable is similar to essence ^^^^^^^ e.g. long double char char* etc. /* ... from 'c' programming language */ g) translation and emergence two forms which have 'emerged' in higher level languages, >=1960s are; -- ( if else ) form ... -- generalized loop form 1) ( if else ) form as, e.g. if ( /* ... */ ){ /* ... */ } else { /* ... */ } /* pseudocode */ 2) generalized loop form as, e.g. do{ /* ... */ }while( /* ... */ ); /* pseudocode */ while( /* ... */ ){ /* ... */ } /* pseudocode */ such forms do not have analogues in traditional assembler, as, e.g. a86 ( eric isaacson ) chasm etc. but may effectively be reduced to such like, as commonly is done automatically by compiler systems ... problems of abstraction aa) non-decidability ... suppose: a policy to divide assets by two when challenged ... in circumstances where assets are 'granular'; such may be effective if assets are of even number ... however, if of odd number ... policy leaves non-decided ^^^^^^^^^^^ how to proceed ... rules based on generalization and abstraction frequently will encounter non-decidables when applied without restriction ... bb) subtlety ... supposing a rigid response model then ... either ---lockup or ---inappropriate response is likely outcome ... however, subtle response to 'unforeseeable' non-decidables and paradoxes, well may be possible to engineer ... if reasonable objective study of abstraction and generalization is made ... cc) vagueness, paradox and the arbitrary if vagueness is not banished from a domain; then, generally, difficulty ( e.g. paradox ) results ... however ... generally, banishment of vagueness requires rules and/or distinctions more or less arbitrary ... as instanced in ( very ancient ) sorites paradox ... recently, ( march 31, 1998 ) in ( local newspaper printing of ) dilbert following comic dialogue was found ... ************************** dilbert ... is it my imagination, or is your necktie getting shorter every day? wally ... heh heh... [new frame] i'm gradually moving toward casual cloths. in six months this necktie will be gone and no one will notice. [new frame] dilbert ... everyone noticed when you went bald. wally ... i'm bald? ************************** here subtlety of thought is related to sophistication in method of reasoning about abstraction, vagueness and the arbitrary ... dd) map analogy ... analogy may be made between abstraction and mapping ... while a complete model of world might be useful where globe or map is used ... such is not feasible ... reasonably, similarly ... limited capability of human nervous system renders unfeasible model of entire universe as simple 'look up' means ... ( also, perhaps, paradox of 'set inclusion' ... related to self-reference ... ) ... thus ... abstraction may serve similarly as 'simplified' map or model as basis for generalized thought ... if effectiveness of e.g. world mapping in e.g. navigation were to make this basis of 'reality model' then much could be learned about basis of geography from mapping ... however ... if physical foundations of map are taken simply as foundations of geography ... then paper and ink might similarly be taken as foundational reality ... of course, such would be a mistake ! possibly ... grammar based ontology .... which so well has served ... may also have limits ... e.g. in very large application e.g. cosmology or in very small applications e.g. micro-physics ... ee) paradox types arguably, 'paradoxes' which seriously threaten stability of ai system may be classified in two categories ... 1) physical 'paradoxes' ... representative of physical 'paradoxes' is ancient 'paradox' of zeno known as flying arrow paradox ... arguably, this 'paradox' has defied solution until development of quantum theory and relativity theory in 20th century ... however ... evidently, modern thinking in physics renders flying arrow paradox tractable ... 2) philosophical paradoxes ... evidently, most important philosophical 'paradoxes', fall into three major types ... ---liar 'paradox' ---russell 'paradox' ---sorites paradox ... -- liar 'paradox' ... liar 'paradox' is ancient. modernized version is presented ... *** statement A) statement A is false. *** to appearances, circumstances that make statement A true also make statement A false ... and circumstances that make statement A false also make statement A true ... and hence; liar 'paradox' does not settle on truth value ... -solution of liar 'paradox' ... statement A above is in form of 'truth claim' or assertion ... any true statement is compatible with assertion of truth of same as e.g. statement B) joe is in the room. statement C) statement B is true. truth of statement C is necessary for truth of statement B ... hence for any statement ( e.g. statement B ) a 'and' form developing such should preserve truth value ... as ... statement B [modified]) joe is in the room AND statement B is true. similarly developing statement A reveals this to be a simple contradiction ... statement A [modified]) statement A is false AND statement A is true. **** ... russell's paradox evidently is attributable to cantor zermelo and russell understanding of russell paradox may best be rooted in older paradox of barber ... --barber paradox suppose regulations intended to assure that all men shave ... rules --- rule A) all men will shave ( exclusive )or be shaved. rule B) all and only those men not shaving themselves will be shaved by the barber. rule C) the barber must be a man. end rules --- problem here ... does the barber shave himself ? if he does shave himself ... then ( rule B ) is violated ... if he does not ... then ( if ( rule A ) is not violated ... then ( rule B ) is violated ... ) barber 'paradox' may rest on some faith in infallible applicability of rules ... because ( if appropriately stated ), certainly, no such barbers are found ... --russell paradox ... russell paradox relates to set theory however, from experimental period; where modern form of such was not yet determined ... modern set theory, as taught in schools, is of very nominalist form ... set name is simply notation form representing unordered collection of members ^^^^^^^ ( individuals ) and is not reified ; ( set is not an individual or 'thing' ). thus, in such modern set theory, a set may not be a member of a set and a ( set of sets ) is not possible ... and ( instead ) similar seeming forms e.g. superset subset proper subset are used ... to represent such set relations as applicable ... --statement of russell 'paradox' *** supposing a set ( S ) such that the members of ( S ) are all and only sets which are not members of themselves ... is ( S ) a member of ( S ) ? either response is unsustainable ... and question will not settle ... *** in russell 'paradox' much similarly as with barber 'paradox' ; rules determine specification of 'entity' which can not be actual ... so, evidently, russell 'paradox' simply manifests deficiency of such rules ... and not some profound 'paradoxical' feature of human language and thought ... --sorites paradox statement of sorites paradox ... *** rule 0) suppose a man ( S ) is rich ... then loss of one cent ( of man's fortune ) is insufficient to make ( S ) not rich ... end rule 0) problem) but if applied recursively ... ( rule 0 ) may result in ( S ) poverty ... whereby ( S ) has no money ... thus ( S ) may be rich and also have no money if ( rule 0 ) is valid and recursively applicable ... *** ( of course, sorites paradox may be applied in many domains; also sorites paradox is very ancient ... ) strangely, at this time, evidently, sorites paradox ( type ) is the most intractable known and evident simplicity of sorites masks a profound basis ... metalanguage aaa) intractability of sorites --arbitrary determination ... possible resolution tactic is arbitrary borders of e.g. rich poor large bald etc. --truth problem ... however ... if borders are arbitrary ... then truth of judgements, statements ... which result from such determinations is jeopardized ( at least in borderline areas ) ... such error might accumulate ... --reduction response ... argument might be made that such ideas are vague and reduction to fundamentals is effective ... however ... e.g. in case of rich, not rich, penny ( as earlier described ... ) precise specification of fundamental level also generally is questionable by similar means and ontological regress may be inescapable ... thus ... retreat from truth and resolution of paradox on higher level 'borrows' credibility from faith that lower level is immune ... but such should be established with care ... bbb) type ... token a 1960s analytic philosophy interest was in type-token distinction ... e.g. question "how many characters in document ?" might relate to types e.g. 65 (e.g. (a A c C ... @ ... * ... y ... )) or tokens e.g. 5439 ... such distinction is reflected in computer programming practice ... where data_types and individuals of such types are used widely in practice ... as e.g. long id; /* as 'c' pseudocode */ char *name; etc. an intermediate form of type is found widely in common ( and scientific ) language which is tokenized in relation to a more general type, yet, at least arguably, not actually an individual ... 'animal kingdom' | | ^^^^^^^^^^^^^^^^^^ | | | bird mammal ... | | ... | | ^^^^^^^^^^^^^^^^^^ | | | horse dog cat a small set of operating system ( os )level commands allow creation, traversal, access of device directory systems ... in e.g. unix os, ( ms pc )dos ( >= version 2.* ), os/2, dr_dos ... ( though command particulars may somewhat differ among such systems ... ) in such systems a set of files situates within a directory one top level directory for each device is allowed ... ( though 'physical device' may optionally be partitioned into various 'virtual' devices ... ) top level directory is termed root directory directories may be 'tokenized' ( subordinated to ) directories as ... subdirectories ... ( when fully formatted such device commonly has single, 'root' directory created as default directory ... ) commands as ... make subdirectory command as e.g. mkdir delete subdirectory command as e.g. rmdir ( commands for directory traversal ... ) as e.g. ( to change 'working directory' ) as e.g. cd and such command with 'special argument' to traverse to 'parent directory' as e.g. cd .. and such command with argument to traverse to 'root directory' as e.g. cd / ( generally, unix ) cd \ ( generally, ( ms pc dr )dos >= v2.* ) and command for removing file as e.g. del rm ... interestingly, generally, such systems have been found workable and effective in computer applications since <= 1980 and are well proven ... such are not particularly provocative of operational 'paradox' and have proven tractable ... ccc) ken thompson ontology ... tree structured file-directory device organization of unix operating system reflects capabilities of organization of information similar to biological classification system ... similarly ... organization chart etc ... such reflects widespread form of abstraction whereby classifications ( types ) are tokenized relative to higher level classifications ... modern set theoretic model is nominalist, and such relations are entirely extensional there ... ( reasonably, 'proper subset' is form reflecting such ... ) ... ddd) nominalism ? philosophical movement of first half 20th century ... logical positivism and also developments in set theory symbolic logic transfinite mathematics have profoundly advanced nominalism ... such developments respond to efforts to generalize set theory ( and the like ) as a general model of abstract thinking, ( e.g. work of g. frege ) ... such efforts to generalize set theory then generated problems related to 'paradox', ( e.g. russell 'paradox' ) ... why should a generalized model of abstract thinking attempt the 'paradoxical'; and what, if anything, is deficient re. nominalism ? -- 'table and chairs' ontology ... truth-functional and ( integer ) arithmetic bias of early 1900s thinking ... might seem to justify nominalism in schematization of thinking ... basis of thinking in individuals arguably is supported in ( integer ) number theory and common thought ... however ... -- in ordinary thinking ... subjects frequently are not presently in being ... but are components of plans ... and common use of abstraction system for such purpose is critical to thinking ... also ... use of abstraction system to test plan performance and to evaluate results of such ... 'nominalist' abstraction model makes most mysterious such ( planning ) uses ... which uses would seem, generally, as important at least an application of abstraction system as is truth assertion ... shall radically different abstraction systems be inferred for use with plans and such; and ( alternatively ) with truth assertion ? -- roots of 'table and chairs' ontology in aristotle ... long and widely criticized feature of aristotle ontology ... teleology relates to realization of concrete circumstances through purpose and, reasonably, such relates to abstract thinking: whereby generalized, even, vague, idea is realized ... 'tokenized' or 'realist' abstraction model far better serves such purpose ... -- nominalism is aristotle's 'grammar based' ontology ... with foundation removed ... with 'high level' abstraction capabilities removed and nominalism remaining ... 'common sense' foundation of aristotle ontology is gone also ... ... individuation within phenomenal world has proven problematic over long period ... as ... parmenides heraclitus plato spinoza hume and modern micro-physics relativity theory ... ( also, arguably individuation is problematic re. 'real' number system ... ) ... eee) historic trends in ontology prior origins of pre-socratic philosophy remain mysterious ... however ... prior most secretive pythagorian brotherhood is known ... as well as some features ... metaphysical trends of pre-socratic philosophy and philosophy of plato aristotle etc. suggest 'overarching' trend of thinking ... --mathematical - geometrical - harmonic standard ... evident interest in mathematics topics as 'unchanging' basis of thought served as foundation of pythagorian world view ... similarly as ... frege whitehead russell wittgenstein in 20th century ... attempts to apply such standard to generalized thinking ( including re. world of phenomena ... ) lead to 'interface problem' whereby fitting of 'precision' language to world of phenomena lead to paradox vagueness non-determinacy reference problems along various routes ... two major trends in pre-socratic philosophy ( re. metaphysics ) ... are ... parmenides - zeno heraclitus each reflecting ( evidently prior ... ) recognition of such misfit ... --parmenides school of parmenides ( and related ) views power of ideas as primary and denies 'common sense' view of world of phenomena ... especially in relation to dynamics of such ... --hearclitus school of heraclitus ( and related ) views dynamics of reality as primary ... denies features of 'common sense' ... view of world of phenomena ( e.g. substance, 'thing', referents of common nouns ... ) thereby initiating opposition played out repeatedly over thousands of years ... ( e.g. spinoza hume ... ) --data discipline ... related data_structure fundamental algorithms may be termed data discipline as, e.g. stack binary tree etc. ... data discipline resembles ontology through topology ( much as set theory resembles symbolic logic ) ... thinking about topology of an ontology _as though_ such were a data discipline is useful ... particularly through nature of topology of such ... e.g. re. idea of set of sets implicit in russell 'paradox' ... especially idea of self-membership ... suppose set ( C ) is a member of set ( B ) set ( B ) is a member of set ( A ) set ( A ) is a member of set ( C ) such topology resembles cycle of network theory known, generally, to provoke operational problems ... ( similar problem infects system suggested in russell 'paradox' ... ) recognizing such ... reasonably, russell 'paradox' system would seem not to reflect common model of abstraction, and trouble with such is intuitive probability ... topology of such systems is studied much in software engineering ... thus ... "ken thompson" ontology ( derived from operational data discipline ) might provide topological form of more acceptably intuitive ( and workable ) ontology ... fff) sense and reference ( --heading after g. frege ) ... abstraction system of language used for thought and speech, generally, is useful primarily when effective in representing reality ... in ordinary ( speech ) assertion truth of assertion is taken as standard of effectiveness ... ( and, certainly, is standard in philosophy, historically ) ... truth is thought as a relation between language entity ( statement utterance sentence and/or etc. ) and reality ... which ( relation ) is a kind of fitting correspondence parallelism and/or etc. ... phrases and words used to identify individuals, e.g. this sign this the cat the third person from the left joe ( a name ) ... are used to refer ( make reference ) to individuals ... commonly, such is the basis of the relation between language ( abstraction system ) and reality ... ( in the 'c' programming language as traditionally described, certain forms are identifiers ( as e.g. int counter; /* pseudocode */ ( here 'counter' is an identifier ... ) ) and such forms similarly serve a 'noun-like' role ... ) --objectivity ... evident ancient program leading to thinking of parmenides zeno heraclitus plato aristotle ... is rooted in high valuation of objectivity ... prototypic 'scientific method' was hoped to 'close' abstraction system and lead to 'true', 'objective' world perspective ... rooted in number theory ( and the like ... ) while such research well may have originated, largely, secretly ... evident early publications ( parmenides, zeno, heraclitus ) plainly outline problem ... evident failure of early efforts result in multi-faceted approaches ... ongoing into present ... science, mathematics, philosophy, electronic and computer engineering ... as we know these today ... are outcomes of such ... similar fundamental problems abound still in this area ... and solution today evidently is as remote as in time of zeno ... --roots of objectivity from time of flourishing of newton physics ... until down-fall of same ... in 20th century ... three related fundamental ideas have predominated ... objectivity causation determinism today ... none of these three stands untouched in scientific world view ... foundation of program to solve problems of abstraction system through natural science is gone ... though ( in some degree ) such ideas remain viable partially, or probabilistically, usefulness of such ideas as firm foundation of abstraction evidently now is untenable ... ggg) language games ... great progress in approximative and adaptive software ... for optimization of response in circumstances such that potential alternative situations and responses are unfeasible to list ... e.g. financial program trading game playing ( e.g. chess ) diagnostic system logic analysis scientific, engineering modeling typography space utilization in two and three dimensions time optimization route optimization generalized resource allocation adaptive communication network language translation tactical system etc. such capabilities now are well established ... reasonably, study, modeling and operation of abstraction system might be approached by such methods ... much as a game ... also, ( in various ways ) suggestive of automated representation of abstraction system in works of philosophy ... from ancient to recent ... as e.g. plato philebus aristotle organon metaphysica ... philosophical investigations ( l. wittgenstein ) . -- Ralph Silverman z007400b@bcfreenet.seflin.lib.fl.us -- Ralph Silverman z007400b@bcfreenet.seflin.lib.fl.us