Top Banner
“SEMIOTIC ANALYSIS OF EMPIRICAL CONVERGENCE AND AMPLIATIVE REASONINGby: Charls Pearson American Semiotics Research Institute [email protected] I. INTRODUCTION: Peirce asked how a concept, proposition, or argument could achieve empirical reality and suggested that the Cartesian single-chain mode of deductive reasoning, used by modern logic, be replaced by the multi-filament-cable mode of ampliative reasoning, for his postmodern logic. This was all the hint that Wendell Garner, a mid- twentieth century psychologist, needed in order to develop a concept of ‘operational convergence(Garner 1974). However, this still leaves unanswered the status of such important scientific signs as facts, laws, and theories. The Universal Sign Structure Theory, (USST), which is a theory within the Semiotic Paradigm, allows Garner’s approach to be completely generalized giving a satisfactory answer for the empirical reality of all scientific signs. A proposed fact that is justified by a single observation is nothing but an ad-hoc eduction from a concrete singular to a specific individual – nothing but a convenient shorthand for
31

Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

Nov 09, 2022

Download

Documents

Charls Pearson
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

“SEMIOTIC ANALYSISOF EMPIRICAL CONVERGENCEAND AMPLIATIVE REASONING”

by: Charls PearsonAmerican Semiotics Research Institute

[email protected]

I. INTRODUCTION:Peirce asked how a concept, proposition, or

argument could achieve empirical reality andsuggested that the Cartesian single-chain mode ofdeductive reasoning, used by modern logic, bereplaced by the multi-filament-cable mode ofampliative reasoning, for his postmodern logic.This was all the hint that Wendell Garner, a mid-twentieth century psychologist, needed in orderto develop a concept of ‘operational convergence’(Garner 1974). However, this still leavesunanswered the status of such importantscientific signs as facts, laws, and theories.The Universal Sign Structure Theory, (USST),which is a theory within the Semiotic Paradigm,allows Garner’s approach to be completelygeneralized giving a satisfactory answer for theempirical reality of all scientific signs.

A proposed fact that is justified by a singleobservation is nothing but an ad-hoc eductionfrom a concrete singular to a specific individual– nothing but a convenient shorthand for

Page 2: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

2 PEARSON

recording the data from that one observation.But a single fact that records and summarizes thedata from many different observations, each madeobjectively and fairly on different individualschosen by random sampling from the entirepopulation using experimental design theory,gains more empirical reality with each newobservation that justifies it. This gain inempirical reality is called “eductive phematicconvergence”. We say that the collection ofobservations converges to the empirical realityof the fact. Thus, eductive phematic convergencemeans that one fact converges to the recordingand summarization of the data from many differentobservations. The resulting fact is aproposition with a concrete singular denotation.

A proposed law that is justified by a singlefact or single kind of experiment is nothing butan ad-hoc induction from a concrete singular to ahypothetical general – nothing but a convenientshorthand for describing that one fact or theresults of that one kind of experiment. But asingle law that describes many different facts orthe results of many different experimentalparadigms gains more empirical reality with eachnew fact or kind of experiment that requires it.This gain in empirical reality is called“inductive phematic convergence”. We say that thecollection of facts or experimental paradigmsconverges to the empirical reality of the law.Thus, inductive phematic convergence means thatone law converges to a description of many factsor the results of many different experimentalparadigms. The resulting law is a propositionwith a concrete general connotation.

Page 3: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 3

A proposed theory that is justified by asingle law is nothing but an ad-hoc abductionfrom a concrete general to a hypotheticalabstraction – nothing but a convenient shorthandfor remembering that one law. But a singletheory that explains many different laws gainsmore empirical reality with each new law thatenters into its network of explanation. Thisgain in empirical reality is called “abductivedolemic convergence”. We say that the collectionof laws converges to the empirical reality of thetheory. Thus, abductive dolemic convergencemeans that one theory converges to an explanationof many different laws. The resulting theory isan argument with an abstract singularcognotation.

The above explication has been sketched outfor propositions, or signs with phematicstructure. It could equally well have been donefor concepts, or signs with rhematic structure,and for arguments, or signs with dolemicstructure. Thus, we have a 2-dimensional, nine-way classification of empirical convergence asshown in Table 1. This makes it seem clear thatGarner’s concept of operational convergence isjust my inductive rhematic convergence.Nevertheless, Garner, who followed a line ofreasoning initiated by Peirce, provided thenecessary motivation for the above explication.II. GARNER’S EXPLICATION:

Wendell Garner was one of the earliestpsychologists to apply Shannon’s concept ofvariation measures in modal statistics(“information” – so called) to problems ofperception and other areas of experimental

Page 4: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

4 PEARSON

psychology (Garner 1954, 1962; Garner, Hake, &Eriksen 1956; Pearson 1978). Altho he came touse Shannon’s quantitative measure of informationless and less in later years, the basic idea ofinformation structure led him to develop severalinteresting concepts, such as the concept ofdimensional integrality, and the concept ofenergic vs. informational properties (Pearson1978). In applying his basic methodology of“Critical Realism”1, he had to ask himself howhis concepts could achieve empirical reality, andin doing so, he explicated his concept of‘operational convergence’ (Garner 1954, 1974;Garner, Hake, & Eriksen 1956; Pearson 1978).

The basic idea [of converging operations] is thatwe come to know things, usually described asconcepts, by carrying out two or more experimentaloperations that converge on the single concept. Aconcept that is synonymous with a single operationis nothing more than a restatement of anexperimental result. But a concept that arises asa consequence of converging operations has areality that is independent of any singleexperimental observation. … However, we must have avariety of inputs and outputs, differing in theirnature, to allow convergence to meaningful conceptsthat are in fact independent of any singleobservation or experimental result (Garner 1974:186f).Garner gave as an example several of his own

concepts. But one that will be more easilyunderstood by most readers, is that of the manyexperiments involving, and the many differentways of observing and measuring, the

1 Ironically, this is the same name that Peirce gave to his philosophy.

Page 5: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 5

observational temperature, all of which convergeto essentially the same result and play the samerole in the laws of thermodynamics, thus givingto the concept of ‘temperature’ an empiricalreality.

Table 1: Forms of Empirical ConvergenceConvergence Rhematic Phematic Dolemic

Eductive EductiveRhematic

EductivePhematic

EductiveDolemic

Inductive InductiveRhematic

InductivePhematic

InductiveDolemic

Abductive AbductiveRhematic

AbductivePhematic

AbductiveDolemic

One method of achieving convergence is toshow that the results of two or more experimentalresults based on two or more observationaltechniques are correlated. Garner claims thatsuch correlational techniques provide a form ofconvergence themselves (Garner 1974: 188). Thisprocess of establishing the existence and natureof a concept based on psychosemiotic andsociosemiotic research and then seeking thesemiotic basis for the concept is the very heartof the experimental research I have reported onover the last 30 years. It is, in fact, the verysoul of my Paradigm Inversion Principle and itsSemiotic Reinterpretation corollary (Pearson1981).

Since it is convergence, rather than theprecision of a single technique, that providesthe empirical meaning of a concept, we should befree to use techniques that are not as preciseand reliable as we might otherwise prefer. AsGarner says, “The ultimate validity of a concept

Page 6: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

6 PEARSON

does not depend on any single procedure, but on aconvergent result, so the importance of any oneprocedure is greatly diminished.” (Garner 1974:188)2.

Garner’s concept of ‘operational convergence’applies to inductive reasoning on a singleconcept. One can see here the influence of trothBacon, Mill, and Peirce. It thus falls somewherein the inductive convergence row of Table 1, butthe question is, just where.

Garner is nowhere clear on what he means bythe term “concept”. In fact, it is not evenclear that he realizes that ambiguity is presentin his explication. Does he mean ‘individualconcept’, ‘general concept’, or even ‘abstractconcept’? However, as shown in (Pearson 1990),induction always results in concrete generals.Hence, Garner obviously intends his concept ofoperational convergence to apply to generalconcepts, such as observable scientific terms.The semiotic generalization of ‘words’, ‘logicalterms’, etc. is ‘rheme’, and hence operationalconvergence is to be identified with inductiverhematic convergence. Since term conceptsestablished by induction are always concretegenerals, it is fair to say that concrete generalterms obtain their empirical reality by means ofinductive rhematic convergence.

Converging operations hold when manydifferent kinds of observations, measurements,experiments, etc. converge to a single generalconcept, which subsumes them all. The generalconcept arrived at always has a concrete generalconnotation.

2 Cf. Peirce’s multi-filament cable.

Page 7: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 7

Figure 1: Inductive Rhematic ConvergenceIII. EXPLICATION OF INDUCTIVE CONVERGENCE:A. Inductive Phematic Convergence:

Instead of asking for the source of empiricalreality for a general concept, we might haveasked how a general proposition, such as ascientific law, achieves empirical reality. Theexplication is a simple generalization ofGarner’s explication and is fully sketched in theIntroduction (Section I.), where I called it“inductive phematic convergence” because the semioticgeneralization of a sentence or logicalproposition is called a “pheme”. For example,the Law of Thermometric Equilibrium summarizesall of the results of a great many kinds ofthermometric experiments. This is just theclassical Theophrastian induction.

We can say that concrete general propositionsobtain their empirical reality by means ofinductive phematic convergence. InductivePhematic Convergence holds when many differentfacts, data, experimental paradigms, etc.converge by induction to a single generalproposition that describes them all. The generalpropositions arrived at always have a concretegeneral connotation.

ICON

INDEX INDEXINDEX . . .

. . .

General Concept Individual

Observations, Measurements,

and/or Experiments

ICON

INDEX INDEXINDEX . . .

. . .

General Propositio

nIndividual Facts,

Data, and/or Experimental Paradigms

Page 8: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

8 PEARSON

Figure 2: Inductive Phematic ConvergenceB. Inductive Dolemic Convergence:

There is not a whole lot of historicalguidance in the area of Inductive DolemicConvergence. There just does not seem to be muchinterest in the question of the empirical realityof particular arguments and/or proofs. And so itis that with Inductive Dolemic Convergence, wearrive at our first real difficulty. Do dolemeshave empirical reality? A negative answer tothis question precludes even asking theconvergence question.

Examples of dolemes include theories, books,arguments, proofs, etc. Theories cannot beestablished by inductive reasoning. Because oftheir abstract nature, they require abduction,and I will cover this under Abductive DolemicConvergence. Books only possess empiricalreality to the extent that their arguments do.So the question seems to boil down to theempirical reality of arguments and proofs, andtheir analyses are similar.

Philosophers have long known that the logicof proof and the logic of discovery aredifferent; almost opposite, in a way. Since thelogic of discovery is primarily abductive, thisexplication will concentrate primarily onanalyzing the notion of the empirical reality of

Page 9: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 9

proofs, for instance, the typical proof ofStokes’ Theorem as given in standard graduatetextbooks of physics.

Altho Stokes’ Theorem is of most interest tophysicists, it is strictly a mathematicaltheorem, and hence its proof is least likely tohave empirical reality as a proof in anysubstantive science. After all, a proof that twomagnets attract each other is very dramatic andtakes place in empirical reality itself, althosuch a proof is a rheme rather than a doleme.

First, it is well established that Stokes’Theorem holds under the stated conditions of thetheorem and that the proofs given in most, if notall, graduate physics texts are valid proofs.This, in itself, is an empirical fact, i.e.,empirically real. So the question no longer is“Do proofs have empirical reality?”, but, “Dothey have some interesting empirical reality?”.

A major purpose of a proof is to convince thereader of the truth of the theorem, or thevalidity of the proof. At least one proof mustconvince at least one person (at the very least,the person who claims it is a “proof”) for aproposition to actually be a theorem. ThatStokes’ Theorem has been proved and that theproof is convincing to most physicists (even ifnot to all physics students), is also anempirically real fact. So now, empirical realityis beginning to pile up for proofs. Since amajor purpose of a proof is to convince thetarget interpreter of its theorem, we ask next,“What is the most convincing proof for atheorem?”.

In order to answer this question, we mustexamine many more proofs. How many proofs are

Page 10: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

10 PEARSON

there? The blunt fact is that for any theoremthere are an infinite number of proofs, even ifonly a few of them are known. This is because wequickly arrive at a practical compromise betweensimplicity of a proof and its convincibility.Such a compromise is a practical approximation tothe most convincing proof of that theorem.

We are now in a position to ask what I thinkis the right question for this paragraph, “Whatis the empirical reality of the most convincingproof of a theorem?”. The answer to thisquestion requires only a simple generalization ofGarner’s explication to develop the concept of“inductive dolemic convergence”.

A proposed “most convincing proof” of sometheorem that is justified by exhibiting a singleargument, or single proof, is nothing but an ad-hoc induction from one example – nothing but aconvenient shorthand for repeating that oneproof. But a single argument for proving atheorem that is more convincing than any of themany other arguments for proving that theoremthat have been examined gains more empiricalreality with each new proof examined. This gainin empirical reality is an example of “inductivedolemic convergence”. We say that the collectionof proofs or arguments converges to the empiricalreality of the most convincing proof, even ifthis phraseology is awkward and contrived, and wewould most likely never use it. Thus, for thisexample, inductive dolemic convergence means thatone argument converges to the most convincingproof of a theorem out of the many differentproofs of that theorem discovered or examined.

This explication, even tho modeled after theothers in the Introduction (Section I.), is still

Page 11: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 11

somewhat different. Inductive rhematicconvergence raised a singular concept to ageneral concept, or an indexical rheme to aniconic rheme. Inductive phematic convergenceraised a singular proposition to a generalproposition, or an indexical pheme to an iconicpheme. But as long as we look at the mostconvincing proof of a theorem from the aspect ofits being only one proof, it remains a singularargument. However, if we think of it from theaspect of it being “the most convincing proof ofthe theorem”, it gains a generality from itshaving competed against the infinitude of otherpossible proofs. From this standpoint we canbring this explication back into the generalscheme and say that inductive dolemic convergenceraises a singular argument to the level of ageneral argument, or an indexical doleme to aniconic doleme. The general argument thus arrivedat always has a concrete general connotation.

We are now also able to see the systematizingaspect of induction showing thru, i.e., that italways raises an index to an icon (Pearson 1990).We can also see now, that as contrived as thisexplication and the example it is based on is, itis suggestive of a whole host of other, perhapsmore empirically interesting, questions, withsimilar structure, see Figure 3.

Figure 3: Inductive Dolemic Convergence

ICON

INDEX INDEXINDEX . . .

. . .

General Argument, or Proof of a Theorem

Individual Arguments, or Proofs of a Theorem

Page 12: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

12 PEARSON

IV. EXPLICATION OF ABDUCTIVE CONVERGENCE:A. Converging Explanations:

Garner introduced the notion of convergingoperations as an empirical justification forgoing from the concrete individual to theconcrete general. The natural analog of Garner’sconcept is my concept of converging explanationsas an empirical justification for the step fromconcrete generals to an abstract singular – fromlaw to theory.

Converging operations hold when manydifferent kinds of observations, measurements,experiments, etc. converge to a single conceptwith one general description.

Converging explanations allow us to go to thenext level of scientific thinking. It isjustified when we have many different laws withmany different general concepts and theirattendant many different general descriptionsthat can all be explained by the assumption of asingle abstract theory.

As can be seen from the General AbductionDiagram of Figure 4, ‘converging explanations’ isnothing but ‘converging operations’ raised to thenext level.

Figure 4: General Abduction DiagramSince the individual abductive convergence

diagrams will deviate from Figure 4 only in the

Symbol

ICON ICONICON . . .

. . .

Page 13: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 13

appropriate systematic naming details, there isno need to repeat it for each of paragraphs B.,C., and D. below.B. Abductive Dolemic Convergence:

In the case of abduction, it is easier totreat the source of empirical reality for wholetheories first, before going on to explicate thesource of empirical reality for derivativeconcepts, such as principles and theoreticalconcepts. This explication is fully sketched outin the Introduction (Section I.), where I call it“abductive dolemic convergence” because the semioticgeneralization of arguments and theories iscalled a “doleme”3. For example, the Theory ofGeneral Relativity summarizes all of the knownlaws governing physical bodies moving under theinfluence of so-called “gravitational” forces.The resulting theory thus arrived at always hasan abstract singular cognotation.

We can say that abstract theories, and otherabstract dolemic symbols, obtain their empiricalreality by means of abductive dolemicconvergence. Abductive dolemic convergence holdswhen many different laws, general invariantdescriptions, etc. converge by abduction to asingle abstract theory that explains them all.C. Abductive Phematic Convergence:

Abductive phemes are abstract theoreticalprinciples, and abstract rules of inference, forexample, individual statements (phemes) that formthe essential pieces of a theory. One cannoteasily determine the source of the empirical3 Peirce’s actual term was “δελώμά”, but language design rules suggested that I transform this into “doleme” (Pearson 1977a).

Page 14: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

14 PEARSON

reality for these kinds of propositions by asimple generalization of Garner’s explication.Instead, they mainly inherit their empiricalreality from their place in the conceptualnetwork of the theory of which they form a part,and the empirical reality of that theory. Thuswe might be tempted to call this “abductivephematic cohesion”, but I would rather keep themore systematic terminology for its usefulnesslater. And besides, we might think of the“convergence” part of the terminology asreferring to the abductive dolemic convergence ofthe overall theory of which it forms a part. Theabstract theoretical principles arrived at alwayshave an abstract singular cognotation.D. Abductive Rhematic Convergence:

Abductive rhemes are abstract theoreticalterms, etc. (rhemes), that refer to the essentialconcepts of a theory. The explication of thesource of their empirical reality mirrors thatfor abductive phematic convergence in IV.C.above. Likewise, the abstract theoretical termsarrived at always have an abstract singularcognotation.V. EXPLICATION OF EDUCTIVE CONVERGENCE:A. Converging Observations and the Elusive Nature of Eduction:

I have saved the row of eductive concepts forlast because of the difficulty philosophers ofscience have always had with these concepts.Reasoning by eduction has always been a veryelusive concept. Altho many philosophers havetried to find valid examples of it, all greatlogicians, from Aristotle to Peirce, have been

Page 15: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 15

unanimous in their claims that it cannot exist.Peirce, in fact, thought he had found out why.Reasoning from one individual to anotherindividual possesses no generality, and it isgenerality that makes inference possible.

It was Peirce, however, who began to suspectthat something was wrong. It was even Peirce, aswe shall see in just a moment, who solved most ofthe difficulty. But because Peirce was wedded toexactly three categories of reasoning by histheory of categories, he did not see the moreoverarching implications of his solution.Instead, he began to modify, or reinterprettraditional notions of induction.

In (Pearson 1990) I still accepted most ofPeirce’s approach, but even then, I preferred areturn to the standard interpretation ofinduction. However, by (Pearson 2002) I hadbegun to see the necessary role played byeduction in scientific reasoning, but hesitatedto perform the complete overhaul of the SemioticParadigm, including the Language of Menetics andthe Theory of Universal Sign Structure, that itwould have required to remain consistent. Todaythat overhaul still remains a promise, but manymore modes of semantic reasoning are nowrecognized and the need for making eduction anintegral part of the system more important thatever.

Eduction has traditionally been interpretedto mean reasoning from one individual to another.Peirce, who considered that the modes ofreasoning corresponded to the modes of semanticstructure of signs, evidently accepted theindividuality of the target of eduction. Onlythus can a lack of generality be shown.

Page 16: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

16 PEARSON

My contribution in (Pearson 1990) was to showthat reasoning should be considered as a signprocess, and as such, the modes of reasoningshould correspond to changes in the modes ofsemantic structure of signs. Thus, a theoreticalmaximum of three modes of semantic reasoningbecame instantly a maximum of nine modes.However, with the realization that other changesin sign structure could also affect the modes ofsemantic reasoning, an infinite number ofpossibilities opened up.

This change in interpretation of the semioticstructure of reasoning held unanticipatedimplications for eduction. Instead ofinterpreting eduction as reasoning from oneindividual to another, it should be interpretedas reasoning from one concrete singular toanother concrete singular, and this makes all thedifference in the world.

If we are testing a hypothesis, all swans arewhite, for instance, its subject is a concretegeneral which refers to an undistributedcollection of individuals. But in order to testour hypothesis we must observe some individualswans. By a single act of deduction we canselect one individual, this swan, and therebypartially convert the subject to a concretesingular. But this would be a biasedobservation. In order to have a chance at anunbiased observation, we must have available theentire population. Therefore, we must not stopwith a single act of deduction, but look at thegeneral act of deduction applied to the entireundistributed collection of individuals assumedin the hypothesis.

Page 17: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 17

By this means the undistributed collection ofindividuals is converted to a distributedcollection of individuals, a population, and theprocess of converting a concrete general into aconcrete singular is completed. Of course, ifthe undistributed collection contains an infinityof individuals so will the distributedcollection, but there is no need to actuallycarry out each individual act of deduction. Weonly need examine the general deductive process.

Now, the secret of obtaining enoughgenerality to obtain validity for the eductiveprocess is not to start from the one individualobtained by the single act of deduction but tostart with the entire distributed collection ofindividuals obtained by the general act ofdeduction and apply a protective screen developedby Peirce himself. We must apply the mathematicsof experimental design theory4 and then chooseindividuals for the experimental design from thedistributed collection by a process of randomselection5. If the process of observing theproperly chosen individuals converges to a fixedresult, again, a concrete singular, I call it‘converging observations’.

In the example used above, the subject, allswans, was a rheme, i.e., a single word orphrase, but not a clause or complete thought.But the subject might also have been a pheme,i.e., a clause, proposition, or other completethought, or it might have been a doleme, i.e., acomplete argument meant to convince, entertain,

4 A branch of statistics developed by Peirce and one of his students.5 Another concept developed by Peirce.

Page 18: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

18 PEARSON

or satisfying any other purpose of the intendedmessage. In sections B., C., and D. below, Iexamine this concept of converging observationsin turn for rhemes, phemes, and dolemes. But ineach one, the concrete singulars arrived atalways have concrete singular denotations.

As can be seen from the General EductionDiagram of Figure 5, ‘converging observations’ isnothing but the foundational level of scientificthinking. Since the individual eductiveconvergence diagrams will deviate from Figure 5only in the appropriate systematic namingdetails, there is no need to repeat it for eachof paragraphs B., C., and D. below.

Figure 5: General Eduction DiagramB. Eductive Rhematic Convergence:

A proposed observation that is justified by asingle examination, in an idiosyncratic way, ofsome individual is nothing but an ad-hoc eductionfrom an unexamined population to an arbitraryconcrete singular – nothing but a convenientshorthand for remembering the operational detailsof that single idiosyncratic examination. Thisis the false step that possesses no generality,and thus justifies no valid eduction. But asingle observation that records and summarizesthe operational details from the many differentexaminations of concrete singulars all chosen by

INDEX

INDEX INDEXINDEX . . .

. . .

Page 19: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 19

random selection from the entire population ofconcrete singulars according to an appropriateexperimental design, gains more empirical realitywith the examination of each new concretesingular that justifies it. This gain inempirical reality is called “eductive rhematicconvergence”. We say that the collection ofexaminations converges to the empirical realityof the observation. Thus eductive rhematicconvergence means that one observation convergesto the summarization of the operationalizeddetails of the examination of many differentconcrete singulars from the entire population.For example, the observation that the temperature of thissample of water is 32.04 °F.C. Eductive Phematic Convergence:

Instead of asking for the source of empiricalreality for a singular observation, we might haveasked how a singular proposition, such as ascientific fact, achieves empirical reality.This explication is fully sketched in theIntroduction (Section I.), where I call it“eductive phematic convergence” for reasons alreadyexplained. For example, the fact that this sampleof water froze at 32.04 °F summarizes the data from manydifferent observations.D. Eductive Dolemic Convergence:

Again, there are few existing examples forthe analysis of eduction on dolemes. I thinkthat the analysis of an experimental paradigm, orwhat is often called “a lab procedure”, willserve to illustrate the general result.

A proposed lab procedure that is justified byperforming a single trial is nothing but an ad-hoc eduction from the unexamined population of

Page 20: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

20 PEARSON

trials to an arbitrary procedure – nothing but aconvenient rehearsal of that procedure. But asingle lab procedure that has been proven to bereliable, precise, and accurate, over a largenumber of trials, gains more empirical realitywith each new trial performed. This gain inempirical reality is an example of “eductivedolemic convergence”. We say that the collectionof trials converges to the empirical reality ofthe lab procedure.VI. SUMMARY OF THE GENERAL CONCEPT OF CONVERGENCE:

Four things have become obvious fromperforming this systematic analysis of the sourceof empirical reality for scientific concepts.First, the concepts with empirical reality fittogether systematically into a diagrammaticsystem very similar to the ampliative half of theLadder of Scientific Reasoning (Pearson 1990).This is shown in Figure 6: Empirical Convergenceand Ampliative Reasoning. Eductive convergencemay also be called observational convergence.Inductive convergence may also be calleddescriptive convergence, altho one particularform of it, inductive phematic convergence, wascalled operational convergence by Garner (1974).And abductive convergence may also be calledexplanatory convergence.

Second, the diagrammatic system of Figure 6may be factored into the product of two vectors.One vector along the semantic dimension refers tothe nature of ampliative reasoning: eduction,induction, and abduction. Let us call it Ŝ, forsemantic, so that

Ŝ = <Eduction, Induction, Abduction>.

Page 21: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 21

The other vector lies along the pragmaticdimension and refers to the grammaticalcomplexity of the scientific sign. Let us callit Ĝ, for pragmatic, so that

Ĝ = <Rheme, Pheme, Doleme>.Then the convergence of ŜTΧĜ gives the 3 by 3matrix that abstracts Table 1 and yields back allof Figure 6. Thus, we can see that scientificconcepts are composed of two, more elementary,semiotic concepts; one involving pragmaticcomplexity and lying along the pragmaticdimension, while the other involves the nature ofampliative reasoning required to give empiricalreality to the concept, and lying along thesemantic dimension. As is inherent in semioticstructure, each vector consists of exactly threecomponents and each is also in exactly the orderdictated by the Universal Sign Structure Theory(Pearson 1977b, 1981).

Third, all concepts in Table 1 involve finitesampling from an infinite population. Can thisstatistical process be restricted to either Ŝ orĜ, and which one, or must it involve both? Ithink it is clear that the sampling process is afunction of only the kind of reasoning involvedin developing the empirical reality of theconcept and is independent

.

.

.

Symbol

Icon

Index

Index

Abductive

Inductive

Convergence

Convergence

Eductive Convergence

Page 22: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

22 PEARSON

Figure 6: Empirical Convergence andAmpliative Reasoning

of the pragmatic complexity. This is easiest tosee in connection with the inductive modes ofreality convergence. Whether it is inductiverhematic convergence (Garner’s operationalconvergence), inductive phematic convergence(classical Theophrastian induction), or inductivedolemic convergence (my descriptive convergence),the explication of the concepts above should havemade it clear that the nature of the finitesampling from an infinite population remains thesame.

In the case of the abductive modes of realityconvergence, this is a little more difficult tosee, because of the questions of network cohesionand inheritance from the primary convergenceconcept (that of abductive dolemic convergence toa theory), but not very much more. In theabductive process, the theoretical scientistconsiders a finite sample from an infinitepopulation of laws to abduce one abstractexplanatory theory. The principles and otherpropositions of the theory and the terms andother rhematic concepts of the theory theninherit their empirical reality from theircohesiveness in the theory and the empiricalreality of the theory itself.

I think this may be most difficult to see inthe case of the eductive modes of reasoning.This is because traditionally, logicians andphilosophers have been conditioned to thinking ofeduction as did Aristotle: as reasoning from one

Page 23: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 23

individual to another. Instead, we must reasonfrom the infinite population of concretesingulars, the distributed collection thatresults from applying deduction to every one ofthe undistributed members of the concretegeneral. We extract a finite sample on thisinfinite population using the Peirceanmethodology6 and reason to an observation, fact,or procedure.

For this reason, it may be well to considerthe introduction of a new logical operator, @,that converts an undistributed collection into adistributed collection. Thus, we would have:

xP(x)formalizes the concrete general pheme “Every x is(a) P”, which refers to the whole undistributedcollection,

@xP(x)formalizes the concrete singular pheme “Each x is(a) P”, which refers to all of the individualdistributed members of the collection,

xP(x)as usual formalizes the concrete general pheme“Some x is (a) P”, which refers to any x ingeneral which happens to be P, and

¡xP(x)formalizes the concrete singular pheme “This x is(a) P”, which refers to an individual x which isP.

However, the implication S(x) P(x) isambiguous. Does it mean xSP(x) or @xSP(x)?Therefore, the implication notation is onlyappropriate when the question of singularity vs.

6 Combining random selection with the appropriate experimental design.

Page 24: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

24 PEARSON

generality – indexical symbol vs. iconic symbol –is irrelevant. This has helped to hide the truenature of eduction for nearly two and a halfmilleniums. We can rectify the implicationalnotation by combining it with the appropriatequantifier as either

x:[S(x) P(x)], or @x:[S(x) P(x)].We thus would have

xSP(x) @xSP(x), and@xSP(x) S ≠ Φ xSP(x).

The extra assumption, S ≠Φ, is required to raisethe singular @ back to the general . This isalso an example of a noninductive method ofraising an index to an icon.

All men are mortal and Socrates is a man, therefore Socratesis mortal. is the classical example of deduction.However, in testing a scientific hypothesis,whether inductive or abductive, we must think interms of a deduction that takes us from All men aremortal. to Each man is mortal. in order to provide aninfinite population from which to sample so thatvalid eduction may take place.

Thus we can now see that all forms ofampliative reasoning require finite sampling froman infinite population, and that this isrepresented within the semantic vector Ŝ.

Fourth and last, all scientific conceptsinvolve the asymptotic approach of an infinitepossibility of vague proposals to a more or lessprecise fixed limit concept as the appropriatesample size increases7, i.e., as our confidencein the knowledge of the sampling process and thenature of the infinite population increases.

7 As small as one in the case of a good guess at a theory.

Page 25: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 25

This is consistent with Peirce’s asymptoticconcept of truth and its twin concept of reality,which breach the distinction betweencorrespondence theories of truth and reality andcohesive theories of truth and reality.

In addition, the analysis of eduction,motivated by this examination of the empiricalreality of scientific concepts, has solidifiedthe need for an overhaul of the Language ofMenetics, the linguistic and philosophicalsubparadigm of the Semiotic Paradigm, asmentioned in paragraph V.A.VII. BIBLIOGRAPHY:Garner, Wendell R.

1954 “Context Effects and the Validity ofLoudness Scales”, Jour. Exp. Psych.48, p218-24.

1962 Uncertainty and Structure asPsychological Concepts. New York:Wiley.

1974 The Processing of Information andStructure. Potomac, Md.: LawrenceErlbaum Associates; ExperimentalPsychology Series.

Garner, Wendell R.; Hake, H.W., & Eriksen, C.W.1956 “Operationism and the Concept of

Perception”, Psych. Rev. 63, p149-59.Pearson, Charls

1977a Towards an Empirical Foundation ofMeaning. In partial fulfillment of therequirements for the degree Doctor ofPhilosophy, Georgia Institute ofTechnology; Atlanta: June, 1977. AnnArbor, MI: University Microfilms.

Page 26: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

26 PEARSON

1977b Semiotic Foundations of InformationScience. Atlanta: National ScienceFoundation.

1978 “The Processing of Information andStructure”, Computing Reviews, 1978.

1981 “The Semiotic Paradigm”, SIG/FISProceedings 1(1981). Washington:American Society for InformationScience.

1982 “The Cognitive Sciences: a SemioticParadigm”, Chapter 15 of Language,Mind, and Brain. T.W. Simon and R.J.Scholes (eds.); Hillsdale: LawrenceErlbaum Assoc. p 225-240.

1990 “An Application of the Universal SignStructure Theory to Understanding theModes of Reasoning”, Semiotics 1991.John Deely and Terry Prewitt (eds.),New York: University Press of America,p297-311.

2001 “Summary of Advantages of RecentlySuggested Changes to the UniversalSign Structure Theory”, Semiotics 2001Scott Simkins (ed.), New York:University Press of America, p325-39.

2002 “The Role of God in ScientificReasoning”, to appear in Semiotics2002. Terry Prewitt (ed.).

Peirce, Charles S.i.1866-1913 The Collected Papers of Charles

Sanders Peirce, vols. I/VI ed. CharlesHartshorne and Paul Weiss (Cambridge,MA: Harvard University Press,1931/1935), vols. VII/VIII ed. ArthurW. Burks (Cambridge, MA: HarvardUniversity Press, 1958).

Page 27: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 27

1982-2001 Writings of Charles S. Peirce: aChronological Edition. Peirce EditionProject (Bloomington: Indiana U.P.).

Page 28: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

28 PEARSON

Table 1: Forms of Empirical ConvergenceConvergence Rhematic Phematic Dolemic

Eductive EductiveRhematic

EductivePhematic

EductiveDolemic

Inductive InductiveRhematic

InductivePhematic

InductiveDolemic

Abductive AbductiveRhematic

AbductivePhematic

AbductiveDolemic

Figure 1: Inductive Rhematic Convergence

Figure 2: Inductive Phematic Convergence

ICON

INDEX INDEXINDEX . . .

. . .

General Concept Individual

Observations, Measurements,

and/or Experiments

ICON

INDEX INDEXINDEX . . .

. . .

General Propositio

nIndividual Facts,

Data, and/or Experimental Paradigms

ICON

INDEX INDEXINDEX . . .

. . .

General Argument, or Proof of a Theorem

Individual Arguments, or Proofs of a Theorem

Page 29: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

PEARSON 29

Figure 3: Inductive Dolemic Convergence

Figure 4: General Abduction Diagram

Figure 5: General Eduction Diagram

Symbol

ICON ICONICON . . .

. . .

INDEX

INDEX INDEXINDEX . . .

. . .

.

.

.

Symbol

Icon

Index

Index

Abductive

Inductive

Convergence

Convergence

Eductive Convergence

Page 30: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

30 PEARSON

Figure 6: Empirical Convergence and AmpliativeReasoning

Page 31: Semiotic Analysis of Empirical Convergence and Ampliative Reasoning

“SEMIOTIC ANALYSISOF EMPIRICAL CONVERGENCEAND AMPLIATIVE REASONING”

by: Charls PearsonAmerican Semiotics Research Institute

[email protected]

Semiotics 2003, (Ottawa: Legas Press), 137-56.