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A Historical Introduction to the
Philosophy of Science

Ch. 9: Analyses of the Implications of the New Science for a Theory of Scientific Method

Book cover: A Historical Introduction to the Philosophy of Science by John Losee

The following is a summary of the ninth chapter of John Losee's book, A Historical Introduction to the Philosophy of Science (fourth edition), with some ancillary notes.

I. The Cognitive Status of Scientific Laws

Philosophers discussed in this section: John Locke (1632–1704); Gottfried Wilhelm Leibniz (1646–1716); David Hume (1711–76); Immanuel Kant (1724–1804)

Locke on the Possibility of a Necessary Knowledge of Nature

[p. 87] Locke specified two conditions for necessary a priori knowledge of nature:

  1. knowledge of configurations and motions of atoms
  2. knowledge of how motions of atoms produce primary and secondary qualities

[p. 88] For Locke, 1. is unachievable due to the minuteness of atoms, and 2. is unachievable because we are ignorant of how the power of atomic motions work (need divine revelation?)

Locke sometimes posited an unbridgeable epistemological gap between atomic motions and subjective ideas. Subsequently, he had no interest in hypothesizing about atomic motions, advocating instead Baconian inductivism.

At other times, Locke drew back from skepticism and posited a necessary connection between atomic motions in the external, mind-independent world and our subjective experience of secondary qualities.

Locke used his term, 'idea', to bridge the gap between the external and internal worlds.
[LA: Locke's 'idea' is synonymous with our term 'percept' where a 'perception' is had by a 'perceiver' standing in a causal relation to an object in the external world.]

[p. 89] Later, Berkeley and Hume demanded a justification for belief in this causal link to external objects.

Leibniz on the Relationship between Science and Metaphysics

Leibniz used his scientific contributions to inform his metaphysics, and vice versa.

Three examples:

  1. He used his metaphysical principle of continuity to correct Descartes' theory of motion after impact.
  2. His application of the differential calculus using extremum principles to cases of light refraction was motivated by his theological metaphysical principle of maximum simplicity/perfection.
    [LA: In calculus, an extremum is a point at which a value is a maximum or a minimum.]
  3. [p. 90] He sought a correlation for his metaphysics of monadic activity in the physical law of conservation of vis viva (mv2).
    [LA: In Leibniz's metaphysics, 'monads' are mind-like simple substances endowed with perception and active force/'appetite'. For a basic intro, see https://en.wikipedia.org/wiki/Monadology.  For a more technical treatment, see https://plato.stanford.edu/entries/leibniz/].

Leibniz saw the natural universe and its causal laws as the embodiment of the Perfect Being's teleological principles (e.g., extremum principles reflect natural processes' teleological striving for a minimum or maximum value).

Leibniz eschewed Locke's epistemological uncertainty over 'real essences' of things for the necessary truths revealed by his teleological metaphysics of perfection.

[p. 91] At one point, Leibniz used an analogy with the generation of an infinite series to argue that empirical laws could be derived from his metaphysical principles. Losee objects that analogy breaks down because the position in the series must be specified. Leibniz leaves unresolved the link between the metaphysical and physical realms.

Hume's Scepticism

Hume extended Locke's skepticism about formulating necessary principles of nature founded on atomic interactions.

[p. 92] Contra Locke, for Hume, even if we knew the internal micro-constituency of bodies, we would remain ignorant of necessary connections between phenomena. All we know is contingent constant conjunctions between physical events.

Hume denied necessary knowledge of empirical laws based on:

  1. an unbridgeable epistemic divide between 'relations of ideas' and 'matters of fact'
  2. all knowledge of matters of fact is based on sense impressions
  3. necessary knowledge of natural laws presupposes knowledge of necessary connections in nature
Book cover: A Treatise of Human Nature by David Hume

On 1., Hume thought relations of ideas are necessary truths because denying any one results in self-contradiction (e.g., Euclid's theorems in geometry). On the other hand, matters of fact are always contingent as it's not self-contradictory to deny any and all.

On 2., for Hume, the necessary truth of the relations of ideas is independent of empirical evidence and is either (1) known intuitively from meanings of terms (e.g., Euclid's axioms), or (2) known demonstratively (e.g., Euclid's theorems).

[p. 93] Truth of matters of fact about events, on the other hand, are not determined by reflecting on the meaning of words alone.

Hume sharpened Newton's distinction between an axiomatic system and its application to experience, and posed a problem for naïve Pythagoreanism.

Contra Descartes, Hume argued there are no innate ideas, such as of mind, body, God, world. Mirroring Aristotle, all ideas come from antecedent sense impressions (both internal and external). Hume allowed for operations of the mind on impressions: compounding, transposing, augmenting, diminishing.

Hume's thesis is both a psychological hypothesis and a theory of empirical significance. Hume excluded from empirical significance: 'vacuum', 'substance', 'perduring selfhood', 'necessary connectedness of events'.

[p. 94] Hume was not a naïve Baconian inductivist. Although Hume recognized Newton's axiomatization of physics from creative insight, he denied it the status of necessary truth.

Whereas Bacon and Locke discussed necessary connections among properties, Hume focused on events. He argued that event B following event A is never necessary as it is not self-contradictory to deny the causal proposition.

Hume concluded that our knowledge of 'causes' does not extend beyond a de facto conjunction of two types of event. Our feeling of causal 'necessity' results from habit and is unjustified.

[p. 95] Hume defined 'causal relation' as both:

  1. a constant conjunction between two kinds of events (objective)
  2. the mind leading to anticipate a second type of event following an event of a different type (subjective)
Book cover: Enquiries Concerning the Human Understanding and Concerning the Principles of Morals by David Hume

However, in his An Enquiry Concerning Human Understanding, Hume offered in addition a counterfactual definition of an objective causal relation (i.e., if A had not been, B would not exist). Losee offers a counterexample to Hume describing two synchronous pendulum clocks; that if the first clock is stopped, the second will not stop. Hume's two definitions pull apart.

Hume's uneasiness with his definition is also shown in his A Treatise of Human Nature where he includes versions of the Methods of Agreement, Difference, and Concomitant Variations.

Losee notes that the Method of Difference establishes a causal connection on the basis of just two observations, contra Hume's definition. [LA: For the Method of Difference, see Losee pp. 30–1.] Hume responded that the belief is still based on custom.

[pp. 95–6] Having demolished proof of necessary causal connections, Hume maintained a confidence in science as giving probable knowledge and saw 'custom' as a legitimate guide to knowledge.

Kant on Regulative Principles in Science

[p. 96] Kant accepted Hume's conclusion that sense experience cannot justify belief in causal necessity. Contra Hume, he argued the mind provided structure to experience.

Kant specified three stages in knowing about physical reality (see diagram on p. 97):

  1. 'Forms of the Sensibility' structure 'sensations' with respect to Space and Time → 'perceptions'
  2. 'Categories of the Understanding' relate the ordered 'perceptions' to each other via concepts of Unity, Substantiality, Causality and Contingency → 'judgements of experience'
  3. 'Regulative Principles of Reason' organize the 'judgements of experience' into a single system of knowledge
Book cover: Critique of Pure Reason by Immanuel Kant

[p. 97] Kant charged Hume with ignoring the importance of the organization of scientific knowledge into deductive systems. Kant's 'Regulative Principles of Reason' function to prescribe how scientific theories ought to be organized.

[pp. 97–8] Kant prescribed criteria of acceptability for:

  • empirical laws – must be incorporated into higher-level deductive systems (e.g., incorporation of Kepler's laws into Newtonian mechanics)
  • theories – must be testable with power to predict novel experience via binding together empirical laws using new entities or relations

[p. 98] For Kant, an important mark in a scientific theory's favour is its fertility for extending knowledge to new experiences and connecting previously thought disparate phenomena.

Kant pointed to three 'analogies of experience' as necessary conditions for objective empirical knowledge:

  1. Conservation of Substance – substance is conserved throughout all changes
  2. Principle of Causality – a rule specifies the antecedent circumstances for every event
  3. Community of Interaction – substances perceived as coexistent in space interact with one another

Kant thought his three 'analogies of experience' translate respectively to the three principles of mechanics:

  1. Conservation of Matter
  2. Principle of Inertia
  3. Equality of Action and Reaction

[p. 99] Kant held that his three principles of mechanics ('Regulative Principles of Reason'):

  • ought to guide the search for empirical laws, and
  • set the criteria for adequate scientific explanation and objective empirical knowledge

[LA: Note how here Kant attempts to elevate Newton's Three Laws of Motion into necessary a priori knowledge in a vein similar to Descartes' Rationalist project.]

Kant promoted the Principle of Purposiveness as a further regulative principle not borrowed from experience and without which the systematization of knowledge is not possible.

[p. 100] The Principle of Purposiveness is the presuppositions of (1) parsimony of paths, (2) continuity, (3) parsimony of interaction types, (4) comprehensible hierarchies, (5) ascending hierarchies.

Kant suggested three other regulative principles for taxonomic ordering:

  1. Principle of Homogeneousness – disregard specific differences so species are grouped into genera (to prevent explosion of species and genera)
  2. Principle of Specification – emphasize specific differences so species are divided into subspecies (to prevent hasty generalization)
  3. Principle of the Continuity of Forms – assume a gradual transition from species to species (to balance first two principles)

Against naïve empiricism, Kant also supported the use of idealized entities in scientific theories (e.g., 'pure earth', 'pure water', 'pure air') to aid systematic organization and scientific explanation.

[p. 101] Kant saw his Principle of Purposiveness as regulative (i.e., investigate as if laws of nature were arranged by a super-human 'understanding') and not as genuinely teleological.

For Kant, teleological explanations are useful for:

  • their heuristic value in the search for causal laws
  • supplementing available causal interpretations

Kant was doubtful that causal explanations could be given for all life processes because they show a reciprocal dependence of part and whole.

For Kant, purposiveness is a regulative principle only that aids the systematic organization of empirical laws.
[LA: This is unclear. How can it be a regulative principle only helping to find causal laws when explanations pointing to 'purpose', for Kant, may be an unavoidable supplement to causal explanations?]

By making teleology a regulative principle only, Kant achieved the integration of teleological and mechanistic emphases that Leibniz wanted.

Questions to Consider:

  1. How much do you think proper explanations of physical phenomena depend on metaphysical principles?
  2. How convinced are you of Hume's argument that the Method of Difference does not contradict his definition of 'causal relation' based on 'constant conjunction'?
  3. Is there another type of 'necessity' other than logical necessity that can account for necessity between cause and effect?
  4. What role does experience play in Kant's theory of knowledge?
  5. Did Kant successfully integrate teleological and causal explanations in his theory of scientific explanation?

II. Theories of Scientific Procedure

Philosophers discussed in this section: John Herschel (1792–1871); William Whewell (1794–1866); Émile Meyerson (1859–1933)

[pp. 103–4] Major works were:

Herschel:   A Preliminary Discourse on the Study of Natural Philosophy (1830)
Whewell:    History of the Inductive Sciences (1837)
                  Philosophy of the Inductive Sciences (1840)
Meyerson: Identity and Reality (1907)

John Herschel's Theory of Scientific Method

[p. 104] Herschel's Preliminary Discourse on Natural Philosophy was the most comprehensive work to date. He distinguished between the 'context of discovery' (induction/wild guess?) and the 'context of justification' (criteria for acceptability), with the former irrelevant to the later.

For Herschel, scientific discoveries of laws come from: (see diagram on p. 105)

  1. induction (Baconian method); or
  2. hypotheses formulation

Step 1: Subdivide complex phenomena into their parts/aspects and focus on those properties crucial for explanation. (Examples: for motion of bodies, focus on force, mass, velocity; for sound, focus on vibration, transmission, reception, production).

[p. 105] Laws of Nature include:

  1. correlations of properties (e.g., Boyle's Law and law of doubly refracting substances)
  2. sequences of events (e.g., Galileo's laws of free fall and trajectory of projectiles)

and are not boundless (e.g., Boyle's Law applies only where temperature is constant).

[p. 106] Laws of nature are discovered by:

  1. induction from experimentation (e.g., Boyle's inverse law for gases)
  2. hypotheses formulation (e.g., Huygens' postulation of elliptical propagation of light ray)

Step 2: Construct a theory that incorporates previously unconnected laws either by:

  1. inductive generalization (i.e., Bacon's hierarchy of scientific generalizations); or
  2. hypotheses formulation (e.g., Ampère's postulation of circulating electric currents in magnets)

Creative theories, although not inductively derived, are tested by their experimental consequences.

[p. 107] An experiment is a severe test for a law or theory when an observation is:

  1. an extreme case of a law (e.g., falling coin and feather as test for Galileo's law of falling bodies)
  2. an unexpected result not within the original design of the law or theory (e.g., elliptic orbits of binary star, discrepancy between calculated and observed velocities of sound systems)
  3. a decider between competing hypotheses ('crucial experiment') (e.g., between attraction to Earth and internal mechanism theories of acceleration; between atmospheric pressure and 'abhorrence of a vacuum' theories of mercury rise)

Losee points out that an experiment is truly a 'crucial' decider between hypotheses only if every possible alternative hypothesis is inconsistent with the observed results. This oversimplification led scientists to accept Foucault's conclusion in support of Huygens' wave theory of light against Newton's theory.

[p. 108] Herschel rightly pointed to the methodological significance of scientists searching for falsifying instances of their theories.
[L.A.: Herschel's emphasis on falsification as a test for theories was a prelude to Karl Popper's philosophy of 'Falsificationism' in the mid-twentieth century.]

Whewell's Conclusions about the History of the Sciences

In writing his history of science, Whewell developed a sophisticated historical methodology focused on polarity of 'facts' and 'ideas'.

For Whewell, a 'fact' is an item of knowledge used for the formulation of laws and theories.

[pp. 108–9] A 'fact' includes both:

  1. report of a perceptual experience of individual objects
  2. scientific law or theory incorporated into a more general theory (e.g., Kepler’s Laws)
How the World Thinks: A Global History of Philosophy by Julian Baggini

[p. 109] For Whewell, an 'idea' is a rational principle that binds together 'facts'. He affirmed Kant's thesis that 'ideas' are not derived from sensations, but prescribe to them (e.g., space, time, cause, 'vital forces').

There is no 'pure fact' divorced from all 'ideas' as all 'facts' involve ideas of space, time and number. When we label a 'fact', we are ignoring how it integrates a sense experience with theory (e.g., the 'fact' that one year is 365 days integrates ideas of time, number, recurrence).

Theory is a conscious inference while Fact is an unconscious inference. The Fact/Theory distinction is still useful as a psychological distinction and for interpreting the history of science.
[L.A.: This entanglement of fact and theory in observation later came to be termed the 'theory-ladenness' of observation statements.]

Whewell's Pattern of Scientific Discovery consists of three overlapping stages: (see diagram on p. 110)

  1. prelude: collection/decomposition of facts; clarification of concepts
  2. inductive epoch:  conceptual pattern is superinduced on the facts
  3. sequel: consolidation/extension of the integration of the facts

[p. 110] Stage 1: Decomposition of Facts and Explication of Conceptions

Decomposition of facts is clearly and distinctly reducing to relations among 'elementary' facts (e.g., space, time, number, force) and measuring quantitatively.

[pp. 110–11] Explication of conceptions is the progressive clarification of concepts showing their logical relations to fundamental ideas.

[p. 111] Fundamental ideas are expressed by a set of axioms, with derivative conceptions (e.g., 'accelerating force') helping to understand their 'necessary cogency' 'clearly and steadily'.

Recognizing an idea 'clearly and steadily' is only done in hindsight following the historical success of a theory (e.g., the progressive clarification of the concept of 'inertia' by Galileo, Descartes and Newton).

Useful scientific conceptions are also 'appropriate' to the facts. Some conceptions can be ruled out a priori as not 'appropriate' (e.g., use of mechanical/chemical principles in physiology). Other conceptions are admitted when the laws and theories in which they are embedded are confirmed.

Stage 2: Colligation of Facts

The scientist superinduces (inductive 'binding together') a conception upon a set of facts (e.g., Kepler's Third Law binds planets' periods of revolution and distances from the sun using the mathematical relations of squares and cubes).

[p. 112] For Whewell, 'induction' is not the application of rules to generate hypotheses, but the use of creative insight. Induction is framing several tentative hypotheses and selecting the right one.

Whewell did recognize certain regulative principles in selecting hypotheses (simplicity, continuity, symmetry) and specific inductive methods in formulating quantifiable laws (e.g., least squares, residues).

Stage 3: Tributary—River Analogy

Thinking and Reasoning: A Very Short Introduction by Jonathan St. B. T. Evans

Whewell saw the history of science as a progressive incorporation of earlier successes into more comprehensive theories—as tributaries flow into a river (e.g., Kepler's Laws, Galileo's Law of Free Fall, motions of tides, etc., into Newton's theory).

[pp. 112–13] Even rejected theories (e.g., Phlogiston Theory) contributed to the progressive development of their successors.

[p. 113] Whewell's Inductive Table illustrates how a 'consilience of inductions' leads from a myriad of specific facts to progressively increasing levels of generalization.

[pp. 113–14] But this increasing level of generalization is not simply a summation/enumeration of lower-level generalizations. Incorporation is via conceptual integration using new concepts (e.g., force, inertial motion, Absolute Space, Absolute Time).

[p. 114] For Whewell, this 'consilience of inductions':

  • only happens when the theoretical concepts attempting the binding are up to the task; and
  • is a test for the acceptability of a  scientific theory

Example of successful consilience: Newtonian elastic collisions in a gas bind together the empirical laws of Boyle, Charles and Graham.

In sympathy with Kant, Whewell distinguished the form from the content of knowledge. Hence, he regarded some physical laws as necessarily true. [L.A.: Recall Kant's three a priori principles of mechanics on p. 99.]

Along with Hume, Whewell thought it not contradictory for a conjunction of events to be otherwise. [L.A.: See p. 94 for Hume's skepticism over necessary causal connections.]

[p. 115] Whewell tried to resolve this paradox by holding that Newton's laws of motion exemplify the form of the Idea of Causation. As the Idea of Causation is a necessary prerequisite for objective knowledge, this necessity flows to Newton's laws.

The experimental confirmation of Newton's laws specifies the content of the three axioms implicit in the Idea of Causation; viz.: (1) universality, (2) proportionality, (3) reciprocity.

The content provided by Newton's laws is:

  • matter has no internal cause of acceleration
  • forces are compounded in certain ways
  • certain definitions of 'action'/'reaction' are appropriate

For Whewell, this exemplification of the a priori Ideas by the fundamental laws of nature is a gradual clarification as the history of science progresses. Although certain about the necessity of Newton's general laws of mechanics, he was less certain about other general laws.

Meyerson on the Search for Conservation Laws

Meyerson credited Whewell for being the first to explain the a priori necessity of the fundamental laws of motion (Newton's laws).

For Meyerson, there are two types of scientific laws:

  1. empirical laws – specify how system changes when conditions are modified
  2. causal laws – apply Law of Identity to specify what does not change in an interaction

[p. 116] Empirical laws allow prediction while causal laws allow understanding.

As causal laws state an identity, they imply a necessary truth.
As causal laws are empirical, they imply a contingent truth.

So, a particular causal law may turn out to be false (e.g. conservation of mass, conservation of parity). But the Law of Identity remains intact.

Losee points out that the Law of Identity is a tautology [A = A] that entails nothing about the real world. But Meyerson thought it a 'significant' tautology that serves as an essential directive principle that leads to understanding nature. Exemplars are atomic theory and the conservation laws of mechanics.

Example of a challenge to this directive principle is Carnot's Principle (Second Law of Thermodynamics) in which entropy (disorder) increases in a closed system. Meyerson concluded entropy is not a 'substance' and Carnot's Principle is not a law of nature.

Questions to Consider:

  1. In Herschel's system, how crucial is a 'crucial experiment' really?
  2. How important is it for a scientist to try to falsify their theory?
  3. Is there a substantive distinction between a 'fact' and a 'theory'? If so, what is it?
  4. How useful is Whewell's three stage Pattern of Discovery?
  5. Can you see Whewell's 'consilience of inductions' happening across scientific disciplines as well?
  6. Did Whewell resolve satisfactorily the paradox of the necessity of the fundamental laws of nature?
  7. Did Meyerson explain successfully how causal laws are a priori necessary using the Law of Identity?

III. Structure of Scientific Theories

Philosophers discussed in this section: Pierre Duhem (1861–1916); Norman R. Campbell (1880–1949); Mary B. Hesse (1924—); R. Harré (1927—)

[pp 118] Major works were:

Duhem:     The Aim and Structure of Physical Theory (1906)
Campbell:  Physics: The Elements (1919)
                  Foundations of Science (1957)

Pure Geometry and Physical Geometry

[p. 118] Non-Euclidean geometries in the 19th Century drew attention to the distinction between an axiom system and its application to experience.

[p. 119] Lobachevsky and Riemann's non-Euclidean geometries had differing axioms about points and lines and entailed theorems that the sum of angles in a triangle is greater/less than 180 degrees.

For Helmholtz, a priori axioms of 'pure geometry' only become empirically significant when conjoined with specific principles of mechanics showing how 'point', 'angle', etc. are to be measured.

Duhem on the Binding Together of Laws

Book cover: Ideas That Matter: The Concepts That Shape the 21st Century by A. C. Grayling

Duhem agreed with Whewell that successful scientific theories bind together various experimental laws, but insisted that theories are not explanatory (i.e., they do not point to reality behind phenomena).

[p. 120] For Duhem, a scientific theory is exhausted by its axioms and the 'rules of correspondence' that link some of the terms in the axioms with experimental measures. The theory is not arrived at by inductive inference from particular observations/empirical laws. Also, the picture/model plays no part in the deductive system.

Example: kinetic theory of gases links the theoretical 'molecule', 'velocity', 'mass' and root-mean-square velocity to measured gas pressure and temperature. The theory binds together and deduces Boyle's, Charles' and Graham's empirical laws.

For Duhem, the model of elastic collisions between point-masses may serve as a heuristic for future research.
[LA: How can the model be a heuristic for future research if the model is a fiction?]

Duhem agreed with Whewell that there are no facts devoid of theory. All experiments are interpreted using a theory (e.g., a pointer reading of 3.5 is interpreted as a particular amount of current in a circuit).

[p. 121] For Duhem, unavoidable experimental error means a given measurement is consistent with indefinitely many 'theoretical facts'. He rejected Newton's dictum that theory be arrived at by inductive generalization from observation statements.

Campbell on 'Hypotheses' and 'Dictionaries'

(pp. 121–2) For Campbell, a physical theory comprised of:

  1. hypothesis – non-empirical set of axioms and theorems
  2. dictionary – relates terms in hypothesis to empirical truths

(p. 122) Campbell agreed with Duhem that not every theoretical term requires a dictionary link to an empirical measure in order for the theory to have empirical significance (e.g., in the kinetic theory of gases, there is no entry for mass and velocity of an individual molecule).

(p. 123) Campbell distinguished between:

  1. mathematical theories – every term correlated directly with an empirical measure (e.g., physical geometry)
  2. mechanical theories – some terms only correlated via functions (e.g., kinetic theory of gases)

(pp. 123–4) Contra Duhem, Campbell held that extended analogy (positive-plus-neutral) plays a crucial role in scientific explanation (e.g., van der Waals extension of the kinetic theory of gases to volume of and forces between particles).

(p. 124) Campbell draws an example from the mathematical relationship between electrical resistance and temperature to show that deduction of an empirical law is necessary for a theory but not sufficient as:

  1. the hypothesis-plus-dictionary was constructed only to deduce the empirical law
  2. indefinitely many such hypothesis-plus-dictionary can deduce the same law/s

(p. 125) But for a mathematical theory, the analogy is where the theory from which the experimental laws are deduced is of the same mathematical form as the laws (e.g., Fourier's theory of heat conduction).

For Campbell, constructing successful analogies requires imagination and not simply induction from experimental laws. A successful theory must be:

  1. internally consistent
  2. able to deduce experimental laws
  3. heuristically useful

(p. 126) Hempel rejected Campbell's insistence on analogical explanation with the example of an ad hoc theory (analogous to Ohm's Law) that also deduced the mathematical relationship between electrical resistance and temperature.

Hempel argued that this ad hoc theory has no explanatory power as it deduces only one empirical law—it fails in conceptually integrating a number of empirical laws. Although the analogy may be heuristically useful in guiding future research.

(p. 127) Losee points out that Hempel's counterexample of an analogical theory with no explanatory power does not refute Campbell's claim that a successful analogy is necessary for scientific explanation.

Hesse on the Scientific Use of Analogies

Book cover: Philosophy of Natural Science by Carl Hempel

Hesse proposed two types of independent relations between an analogue and what is explained:

  1. horizontal – similarity relations between the properties of the analogue and what is explained
  2. vertical – same causal/functional relations for the analogue and what is explained

Example: properties of sound and properties of light (see diagram on p. 127). Each type of relation may be challenged.

(p. 128) But this example is different to Hempel's counterexample in which the horizontal and vertical relations are dependent ('formal analogy'). On the other hand, a 'material analogy' with independent relations invites reasons for accepting the analogy beyond mere formal identity.

Harré on the Importance of Underlying Mechanisms

(p. 129) In contrast with the formal, deductive Duhem–Hempel view, Harré put scientific models (such as Copernicus') at the centre. Harré noted three components of a scientific theory:

  1. statements about the model – postulates existence of theoretical entities and theorizes their behaviour
  2. transformation rules – comprises causal hypotheses and modal transforms
  3. empirical laws (e.g., PV/T = constant)

A model's existential hypotheses (e.g., there exists capillaries, radio waves, neutrinos) drives scientific progress.

(p. 130) For Harré, trying to confirm a model's existential hypothesis can either:

  1. lead to demonstration (e.g., Mendeleef's prediction of Scandium, Gallium, Germanium), or
  2. fail demonstration (e.g., planet interior to Mercury, the ether), or
  3. fail recognition (e.g., Galen's pores occupied by continuous muscle in heart), or
  4. lead to recategorization (e.g., 'caloric' substance reinterpreted as average kinetic energy)

For Harré, advances in understanding underlying mechanisms comes from analogies that generate existential hypotheses. To that extent, Campbell's and Hempel's deductive systems for electrical resistance versus temperature are inadequate as explanations.

Questions to Consider:

  1. How does the distinction between pure geometry and physical geometry impact Kant's 'Forms of the Sensibility' that structure our perception of space?
  2. Is Duhem right in thinking that scientific theories are not explanatory?
  3. What is the role of analogical thinking in science? Do analogies serve an explanatory function?
  4. Must a scientific theory posit an existing theoretical entity to drive progress?
  5. From the work of these philosophers of science, is induction by simple enumeration dead?

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