Hesse: Models and Analogies in Science Chapter 1: The Function of Models: A Dialogue Broad examination of the role of analogies in scientific theories scientific explanation confirmation and growth of scientific theories meaning of theoretical terms Chapter 2: Material analogy preliminary analysis of nature of analogical reasoning and necessary and sufficient conditions for validity of analogical arguments
I. Background 1. Scientific explanation Scientific explanations are answers to why questions. Explanandum: the observation (data) to be explained Explanans: the account that does the explaining Three conceptions of explanation (Salmon, Scientific Explanation and the Causal Structure of the World): Erotetic: Explanations are arguments that the explanans was to be expected Leading example: Hempel s D-N model Why did the eclipse occur (E)? E follows deductively from laws L 1,, L n and initial conditions A 1,, A m. L 1, L 2,, L n A 1,, A m E van Fraassen fits in here Ontic: Explanations aim to describe the causal structure of the world. Causal structure is usually interpreted mechanically. Old idea: reduction to the familiar Leading example: Salmon s theory of causal processes and causal interactions Modal: Explanations aim to describe the modal structure of the world (explanation of why events had to happen in terms of necessary laws) Few advocates; no place for statistical laws Duhem vs. Campbell: continental = erotetic, English = ontic Question 1: Are models and analogies necessary for scientific explanation? Campbell: - requirement of intellectual satisfaction - ambiguity: the real causal story, or just any model? - ontic view gives weak support to the thesis that an analogy/model is always needed for an explanation: what it really supports is the thesis that a mechanical interpretation is needed. Hesse: - says very little about explanation
2. Confirmation/theory construction Confirmation is a relation between evidence E and theory or hypothesis H, relative to background knowledge K. Qualitative confirmation: E confirms H relative to K Relative confirmation: E confirms H 1 more than H 2, relative to K Quantitative confirmation: c(h, E & K) or prob(h / E & K) Models of confirmation: a) Popper: no confirmation - problem of induction - logic of science is falsification b) Hypothetico-deductive model E confirms H relative to K if E is entailed by H and K Example: Boyle s law Problems: - ad hoc hypotheses - multiple hypotheses - confirmation of statistical theories c) Probabilistic approach Theory construction Three phases: E confirms H relative to K if prob(h / E & K) > prob(h / K) Posterior probability is higher than prior probability. Problems: - how much of an increase? - subjective priors - technical objections i) Discovery (psychology, not logic) ii) Plausibility iii) Testing and confirmation Question 2: At which phases of theory development are models and analogies necessary (weaker: of some use)?
3. Meaning of theoretical terms Significance of distinction between theoretical and observational terms: - Parsimony: suspicion of hypotheses about hidden causes (and about causation) - Reductionism: to be meaningful, theoretical terms must be reduced to terms referring to objects with which we are acquainted (empiricist roots) - Anti-realism: block inference to literal truth of theories Objections: - Sellars: myth of the given - Maxwell: arbitrariness of the boundary Problem: how then do we explain the meaning of theoretical terms? Ex: operationalism define in terms of operations and observations (22) Objection: use of theoretical terms in new applications outstrips any such definition Duhem: define by role in context of the whole theory Campbell, Hesse: define via a model Question 3: Do models and analogies play an essential role in explaining the meaning of theoretical terms?
II. Hesse s introduction 1. English vs. continental approach Duhem: no need for models in mature theory (though useful in discovery) a) logic is enough (cf. erotetic view) b) elegance and simplicity favour the abstract approach c) models are just a distraction Campbell/Hesse: models are essential a) intellectual satisfaction b) dynamic character of theories: models play a crucial role in theory expansion 2. Problems for Campbell - Without a model, any theory extensions are arbitrary (cf. plausibility) a) restriction to mechanical models (e.g., theory of light) b) quantum mechanics (successful explanations; no model)
III. Chapter 1: The Function of Models Models and analogies are not distinguished 1. Meaning of model Example: billiard ball model of gases Model 1 = positive and neutral analogy Model 2 = positive, neutral and negative analogy 2. Model 1 vs. theory: Model 1 is more inclusive than theory in including the neutral analogy, which provides direction for change. Model 1 is less inclusive than theory in that theory can include uninterpreted, or only partially interpreted, deductive systems. 3. Models and theory construction Two bases for theory construction: - observables in the target domain (e.g., observable features of sound or light) - analogies: similarities between observables in the source (water) and target (sound or light), plus a developed theory in the source Analogy supports theory construction in two steps: i) Identifications/correspondences among observable properties in the two systems based on known analogy. ii) Target theory (e.g., sound) constructed on basis of developed theory of source (water waves). Duhem s challenge: - model has a causal (psychological) role in theory construction (discovery of the hypothesis) but no justificatory role in plausibility or confirmation
4. Duhemist objections Objection 1: Murkiness. The observable/unobservable distinction is too vague. Reply: Not crucial. Hesse settles for pragmatic contrast between theoretical (= novel) and (relatively) non-theoretical Objection 2: Dispensability. The model is dispensable when we come to justification. Argument: The logical connection between theory and observed evidence is the same in both cases: H-D (cf. Priestley). If this connection is sufficient for the source, then why not also for the target? Objection 3: Parsimony. The mathematical theory suffices for explanation and meaning; there is no point in introducing extraneous ideas from the model (e.g., motions of air particles ). Objection 4: Deception. There are important disanalogies between water and sound. Reply: - better analogues can be found (17-18) - chapter 2: No-essential-difference requirement Objection 5: Quantum mechanics. Modern physics shows that the logical connection is enough for theory construction to proceed; you don t need models.
Reply to Objection 3 Without models, no explanation for meaning and new uses of theoretical terms (21) a) Duhemist: contextual account of meaning Meaning of a theoretical term is given by its role in a serious deductive system (that has observable consequences). Principal Objections: 1) Too rigid: does not allow the observational/theoretical boundary to shift Duhemist: shifts based on how term s role changes. 2) Tied to a static picture of theories. What motivates novel use of a term (e.g., electricity)? Only guesswork or direct link to observation. Duhemist: tu quoque argument. Why are the identifications in an analogy justified, rather than guesswork? Hesse: Scientists do reason in this way with models; model 2 is jettisoned if disagree is found in an essential property b) Hesse: meaning is defined by analogy Evaluation: Narrow conception: meaning = P + B Wide conception: meaning = P + B + Q (include neutral analogy), i.e., model 2 Ex: Air :: Ether Sound Light A. Pre-theoretic similarities among observables (sound, light) suggest identifications. Example: y = a sin ωx. a = amplitude for sound waves. A pre-theoretic analogy suggests that loudness is to properties of sound as brightness is to properties of light. (e.g., blinding vs. deafening ) B. Neutral analogy suggests further identifications. a) Importance of pre-theoretic similarities Positive: continuity between scientific and common-sense reasoning Difficulties: - does it fit any analogies besides water/sound/light? - reluctance to regard similarity as a serious problem: either resolved into identity and difference, or pre-theoretic similarity. Too sanguine? - why attach weight to ordinary-language predispositions? Proposal: - take the analogy as given, and evaluate the strength of the argument
Reply to Objection 2: (35 ff.) Claim: prediction (i.e., new hypotheses) can only be made using models (only valid for type B theories) Three types of falsifiability: a) Type G A theory is falsifiable if its observation statements are falsifiable Genuine falsifiability: leads to new, testable predictions b) Type A A theory is weakly falsifiable if it contains no statements involving P s: it makes testable predictions about the O s that aren t yet accepted, but goes no further. c) Type B A theory is strongly falsifiable if it does contain statements involving P s and makes testable predictions about the connection between O s and P s that are not yet accepted. Claim: for type B theories, models are essential. Where else do the P-statements come from? So the P-statements must be interpreted in terms of the theory; and this interpretation can only be given by a model. Example: let the P s be colour predicates, O s position and intensity of light. Our theory explains the O s; the analogy with sound suggests that f (frequency) be correlated with the P s: f corresponds to colour. Objection (Duhemist): There are other ways of extending theories to P-statements, without these pre-theoretic analogies; they are equally fallible. Ex: extension via similarity. Reply (Hesse): Isomorphism in disguise. Triviality of isomorphism in any rich theory (45). Deeper intuition: a purely syntactic analogy is useless, or at least not sufficient, for a justified analogy (hence the insistence on material analogy). Behind the intuition: idea that unification of theory must be possible.
Reply to Objection 5: - classical physics serves as the model - examples: electrons as billiard balls vs. money in the bank; positrons as holes Duhem s objections: a) QM does not always use such models b) further, the formalism may be interpreted in terms of contradictory models (particle and wave): how can Hesse account for this, if models are essential to the logic of the theory? Hesse: Conclusion of discussion: - no reply to objection a) - to b): each of particle and wave models has some positive and some negative analogy (complementary) and no better model exists - models clearly needed - we won t be content until we have a model incorporating both positive analogies, without contradiction. - theory construction MAY occur without models - There is a need for a logic of analogy: distinction between descriptive and justificatory logic is interesting (cf. descriptive vs. normative ethics) - distinct from Hume s problem of justifying induction
II. Chapter 2: Material Analogy 1. Questions What is an analogy? When is an argument from analogy valid? 2. Classification - horizontal and vertical relations - vertical are usually causal: at very least, tendency to co-occurrence - Hesse introduces a classification of types based on the horizontal relations. Type A: feature matching. Example: Earth-moon (Reid). - Horizontal relations are (pre-theoretical) identity and difference of properties. Type B: feature similarity. Example: sound-light. - Horizontal relations are (pre-theoretical) correspondence of similars. Identifying the corresponding pairs is now more difficult: defining the analogy relation requires justification. Type C: relational similarity. Example: homologies and analogies in biology. - Horizontal relations are (pre-theoretical) identity or similarity of relations. Type D: similarity of the vertical relation. Example: father-children :: state-citizens - the only horizontal relation is similarity of the vertical relation. In the other three types, the horizontal relations were independent of the vertical relations. 3. Comparison with mathematical proportion - in common: reflexive, symmetrical, invertible, logical sum (?), and most interestingly, the idea that the fourth term may be determined by the third term plus the vertical relation R. - differences: - uniqueness: the fourth term may not be unique in an analogy fish tails: bird tails or bird legs triangles: tetrahedra or pyramids - alternation: because the vertical and horizontal relations are not the same kind, can t alternate b and c. - transitivity: fails because similarity is not transitive. (Pizza :: quarter :: dollar bill)
4. Similarity Relation Formal analogy: correspondence between different interpretations of the same formalism Material analogy: pre-theoretic similarities between observable properties *Claim: only material analogy licenses prediction from models Argument: If you have only formal analogy as in case D, then the isomorphism may be accidental. Claim: to license prediction, there must be observable similarities that don t depend upon a theory of the target. - Not argued for here? Main argument is that we have no theory of the target. But often we do have a partial theory. Claim: A regress argument that similarity must resolve into identity and difference: you stop where differences can be ignored (70-71). - Justification? The regress argument, plus convenience! Not very convincing - gets around this by grouping the characters - Literature: extensive criticism of idea that all similarity can be reduced to possession of common properties (e.g., Goodman) - Alternative ways to represent similarity are as precise as identical shared features (e.g., generalization in mathematics) Redundancy argument: (attributed to Mill) Either causal conditions are known independently of the two domains, and then we have no need for the source domain; Or we have no knowledge of the causal conditions and are proceeding from one instance of co-occurrence, hence by single-case induction. Response: In general, we don t know the causal relations of the properties separately, but only in groups. Claim (interesting): Analogical argument is weak, but does justify hypothesis selection. (chap. 3) Pointless to seek degrees of similarity: it would not strengthen the justification of the argument according to any philosophical account.
5. The Causal Relation claim: the vertical relations must be causal = at least a tendency to co-occurrence Argument: Examples lacking such a relation support no analogical inference (e.g., homologies based on part-whole relation). Different analyses of the causal relation are possible (Humean, modal, counterfactual, etc.): not part of the theory of analogy. ***Argument carries over the same sense of causal relation to target ***Argument starts with observables Explains why there are two sorts of attacks on analogical arguments: i) The causal relation is not there (superficial) (Ex: ideal type theory of organisms) - also: there has to be some probability that if there is a causal relation between AB and D, then there is one between A and D. ii) Causal relations of source inappropriate to target - different ontological levels : e.g., cosmology, theology
6. Conditions for a Material Analogy Summary: 1) Horizontal relations are similarities which can be reduced to identities and differences. 2) Vertical relations are causal relations in some acceptable scientific sense. Counterexamples: A. Conceptual models. A wholly imaginary model that satisfies 1), but not 2) (not derived from a causal theory). It might suggest new ideas, etc. Hesse: might be helpful, but provide no plausibility to the conjectures. B. Models associated with false theories. Ex: Fluid model of heat. Some positive analogy. Negative analogy: heat was weightless, and not conserved. But it seems to satisfy 1) and 2). Criterion: Essential properties defeat an analogical argument; non-essential may be relegated to the negative analogy. Essential: - causally related to the positive analogy (conservation) - causally related to the neutral analogy (so that if it were shown to be part of the negative analogy, most of the neutral analogy would also become negative) - so long as there is some neutral analogy, may use the model, if there are no better alternatives In sum, we need a third condition: 3) The essential properties and causal relations of the model have not been shown to be part of the negative analogy.
7. Critique/Assessment: limitation to causal vertical relation is too restrictive. - rules out mathematical analogies (logical relations) - strong correlation may be persuasive, even if no known causal connection in the source. (Franklin) (strong correlation) Just requiring that there be some sort of causal relation is not sufficient: need a more finegrained analysis. (Reid s argument) Hesse s No essential difference condition. a) inadequate basis for judging when unstated similarities and differences are relevant (background relevance). b) inadequate basis for judging when stated similarities and differences are irrelevant (foreground irrelevance) There are many essential differences between rectangles and boxes, but don t reject all uses of this analogy in mathematics on such a basis. Key problem: Hesse s conditions apply to the analogy relation, independently of particular inferential context; so it s not possible to evaluate relevance of similarities and differences.