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L2: Structures 2: Observational laws and proper theories. SSC: S2 (9-12), S12 (40)

• Nagel: intuitive distinction: +/- theoretical terms• Dynamic factor for explanatory programs and

between descriptive and explanatory programs• However: no theory-free/-neutral observation terms• Hence, explication to be based on a theory-relative

explication of theoretical and observation terms• Ex. the ideal gas law: first/second face

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Theory-relative explication

proper theory: terms laden with theory itselfobservational laws: improper theories

• epistemological distinction/stratification• byproducts:

– the hierarchy of knowledge and the long-term dynamics

– disentanglement “theory-ladenness of observations”:example: the periodic table of the chemical elements

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Fragment from the hierarchy ofknowledge

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Classification of observations in relation to theory X

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Ontological stratification

• Two essentially independent distinctions that frequently go together

• ontological: two (or more) kinds of entities, one kind being components of the other

• micro-level and macro-level• principles that only concern the micro-entities:

micro- or internal principles, • principles that connect: bridge principles• atomic theory: both stratifications

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Non-empirical theories• metaphysical theories are supposed to make claims about

reality without assuming any particular conceptualization or, equivalently, they make claims generalizing over conceivable conceptualizations of reality

• mathematical and logical theories deal with defined abstract objects, i.e., mental constructs, e.g., group theory

• conceptual theories concern ways of looking (perspectives) at a certain domain,

• normative theories deal with what is (supposed to be) ethically, legally, aesthetically (in)admissible

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The structuralist approach to (empirical) theories

Ex: the slide balance

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The naïve theory

------> contains <P,Pl,d,w> iff

1) P is a finite set (particles) and Pl a subset of P (particles left of S)2) d: P IR+ (d(p): distance p S)

SBp 3) w: P IR+ (w(p): weight of p) 4) the law of the balance

SB pPl d(p).w(p) = pP Pl d(p).w(p)

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Naïve claims

SBp SB empirical content:: non-empty

E SBp conceptual claim: the intended domain of

applications D can be represented as potential models, the naïve intended applications

E SB naive weak empirical claim the intended applications are equilibrium models

E=SB naive strong empirical claim

SBp

SB

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The refined theory <SBp,SBpp,SB, ,D,E>

------> contains <P,Pl,d,w> iff ---> contains <P,Pl,d>= <P,Pl,d,w> iff

1) P is a finite set (particles) and Pl a subset of P (particles of S)

SBpp 2) d: P IR+ (d(p): distance p S) SBp 3) w: P IR+ (w(p): weight of p)

4) the law of the balance

SB pPl d(p).w(p) = pP Pl d(p).w(p)

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Refined claims

SBpp SB empirical content without w-constraint empty, with w-constraint non-empty

E SBpp conceptual claim: the intended domain of

applications D can be represented as potential partial models, the refined intended applications

E SB weak empirical claim the intended applications can be extended to models

E= SB strong empirical claim

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<Mp, Mpp, M, , D, I> is an epistemologically stratified theory iff

Mp: potential models: a set of structures of a certain typeMpp: potential partial models: the substructures of Mp restricted to

non-theoretical componentsM models: the potential models (M Mp) satisfying all axioms : Mp Mpp: the projection function (from Mp onto Mpp)

X={ (x)/xX}, for XMp, hence X Mpp M: projected modelsMpp M: empirical contentD: intended domain of applicationsI Mpp: intended applications (non-theoretical):

conceptual claim: non-theoretical representation of D leads to the subset I of Mpp

I M: empirical claim (strong claim: I = M)

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Refined empirical claim: shaded area empty

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Mpp (potential partial models): NAMp (potential models): NA + TAMpart (partial models): NA + NSM (models): NA + TA + NS + TS

Decomposition of axioms by controversial distinction(s)

A/S: analytic / substantive axioms

N/T: non-theoretical / theoretical

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Absolute and relative empirical content

Mpp M: (absolute) empirical content AEC

Mpp Mpart: partial empirical content PEC

Mpart M: relative empirical content REC

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The set of intended applications I, and its determination

• “I is D seen through Mpp”• Determination of D, Mpp (hence I), Mp, M is a

‘dialectical process’• If Mpp is supposed to be fixed, 3 ways for I

– empirical determination: if interested in all nomic Mpp-possibilities To (or a well-defined subset of it)

– auto-determination: I = To M– paradigmatic determination, see below

• Always: two sides:conceptually relative & objective

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Definition: I is paradigmatically determined if there

are PAR and SIM such that 0. To : set of nomic Mpp-possibilities1. I is a subset of To

the intended applications2. PAR is a finite subset of I

the paradigmatic examples3. SIM is a binary relation on Mpp

a similarity relation

4. for all x in I PAR there is y in PAR such that SIM(x,y)

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Mpp

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Constraints of and links between theoriesDefinition: C is a constraint on the set S iff

1) C is a set of subsets of S2) the union of the sets in C exhausts S (UC=S)3) if X is in C and Y is a subset of X then Y is in C (subset-preservation)

Links• specialization: subsets of D and/or M • theoretization: (new) theoretical components• reduction: reproduction of one theory in another

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A theory net

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Hiërarchie van epistemologische posities

Q0: onafhankelijke natuurwerkelijkheid? Nee ontologisch idealisme Ja: ontologisch realisme

Q1: ware claims mogelijk? Nee epistemologisch relativisme - ervarings-scepticisme

Ja: epistemologisch realisme - inductief scepticismeQ2: voorbij waarneembaar? Nee observational realisme

- instrumentalisme Ja: wetenschappelijk realisme - constructief empiricisme

Q3: voorbij referentie? Nee referentieel realisme entiteiten realisme

Ja: theorie-realismeQ4: ideale conceptualisering? Nee constructief realisme

Ja: essentialistisch realisme

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Vier perspectieven voor theorie-realisme

ModusFocus

actueel nomisch

waarheids-waarde

standaard/traditioneel

Giere

waarheids-benadering

Peirce/Niiniluoto

Popper

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Soorten actuele en nomische waarheidsbenadering

• PM: het beste afleidingsinstrument: instrumentalist• observationeel: constructive empiricist• referentieel: referentieel realist• theoretisch: constructief realist• essentialistisch: essentialistisch realist

PM: “de waarheid”: de sterkste ware theorie over een gegeven domein in een gegeven vocabulair

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Conclusies ICRvooruitblik: How to approach the truth?

• goede redenen voor overstap:instrumentalist 1 constructief empiricist 2 referentieel realist 3 constructief realist, maar niet voor 4 essentialist

• 1,2 3 tbv lange termijn dynamiek: theorieën als waar accepteren levert nieuwe observatietermen

• instrumentalistische methode efficiënter voor waarheids-benadering dan falsificationistische methode

• hiërarchie van heuristische posities, geen dogma– everything goes sometimes– reculer pour mieux sauter