Scientific Explanation

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Induction

The scientific method stems from inductive logic. The most basic form of induction is straight induction, which states that if you have a set of observed objects O, and all of the observed objects have a common property P, then one may conclude that all objects O that have not been observed will also have the property P.

O1 has property P
O2 has property P
O3 has property P
On has property P
All objects O have property P

Hume brought forth the dilemma concerning the justification of induction. If one uses induction to justify induction, then they make a circular argument. When using induction in reasoning, an implicit condition is that the future will not radically change from past future predictions. This resistance to change cannot be guaranteed in any way, so there should be no expectation that anything predicted to happen in the future will actually happen. The following riddle helps explain the problem of induction.

Something is grue if it is first examined before time t (any arbitrary time in the future) and is green, or is observed after time t, and is blue. All observed emeralds E1...En before time t are green. We can infer that all emeralds are green. We can also infer that all observed emeralds are also grue (they meet the criteria of being grue). Does one assume that an emerald observed after time t is green or blue?

A consequence of using induction allow for problems such as the grue riddle. One cannot justify future predictions with induction since the future is uncertain; one can only infer based on previous experience what may happen.

Scientific Theories

Various models of scientific explanation attempt to rigorize science and the methods of explanation. Among these are theories of explanation to best inference, explanation from law, and statistical explanation. One theory not mentioned above will be focused on - causality. In particular, Wesley Salmon's interpretation of causality.

Salmon's Causality

One theory of scientific explanation is offered by Wesley Salmon, who utilizes the idea of causality in order to account for scientific phenomena. Salmon, as well as most philosophers of science, agree that ‘why’ questions require some form of justification (Salmon, 51). Historically, science was never employed to answer questions of ‘why’ in science, that was handled by theology and metaphysics, rather, science was used to handle the ‘what’ and ‘how’ of science, as well as to make predictions (Salmon, 52). Salmon’s theory involves two components:

  1. First is the ‘causal conception’ – This involves locating and identifying the cause or causes of a phenomenon and arises more of less from common sense. (Salmon, 52 – 53)
  2. Second is the ‘inferential conception’ – This involves subsumption under laws which, to Salmon as well as other noteworthy authors such as Hempel, is essential for all scientific explanation. “A fact is subsumed under one or more general laws if the assertion of its occurrence follows, either deductively or inductively, from statements of the laws (in conjunction, in some cases, with other premises)” (Salmon, 53).

Salmon accepts these principles but sees that there is work to be done in order to allow them to provide a complete account of scientific explanation. He sees the causal conception as suffering from the fact that no adequate treatment of causation has yet been devised (Salmon, 53). He sees the inferential conception as problematic due to the fact that it, in his opinion, “seriously misconstrues the nature of subsumption under laws” (Salmon, 53). Furthermore, he argues that both principles have not taken the existence of a central explanatory principle into account (Salmon, 53). To date, the dominant view in scientific explanation has been the inferential view, of which Hempel is one of its strongest advocates. As Salmon describes Hempel’s account of the inferential view, anyone that knew all the nature/laws of the universe, all detail at a given moment and has infinite mathematical skill could predict any future event. “If determinism is true, then every future, every world thus be amenable to deductive-nomological explanation” (Salmon, 53). But Salmon sees an obvious problem arise from this treatment. Namely, it is when we consider past events, events before our initial conditions, that we see problems and disparity arise. “By applying known laws, we can reliably retrodict any past occurrence on the basis of facts subsequent to the event, our intuitions rebel at the idea that we can explain events in terms of subsequent conditions” (Salmon, 53 – 54). Salmon shows that inference and explanation both have preferred temporal directions and that these directions are opposite one another (Salmon, 54). The fact that these directions oppose one another is what makes Salmon doubt that explanations are, in fact, arguments though he does not believe that this requires us to abandon the concept of a covering law; it will simply be a different form of subsumption under laws. (Salmon, 54). Hempel allows both causal and non-causal laws, like mathematical functional relationships such as the ideal gas law, to both function as covering laws in scientific explanation. Salmon sees this as being too tolerant and cites two reasons that we cannot do this:

  1. “Failure to require covering laws to be causal laws leads to a violation of the temporal requirement on explanations” (Salmon, 54)
  2. “Non-causal regularities, instead of having explanatory force which enables them to provide understanding of events in the world, [need] to be explained” (Salmon, 54 – 55)

From this Salmon concludes that we must give equal attention to the causal explanations of regularities and particular facts (Salmon, 55). At this point, Salmon only requires one further point before he can give the explicit detail of his account of scientific explanation. Given science today and that knowledge is incomplete, Salmon foresees that “some of our scientific explanations will have to be statistical” (Salmon, 55). “By employing a statistical conception of causation along the lines developed by Patrick Suppes and Hans Reichenbach, it is possible to fit together harmoniously the causal and statistical functions in explanatory contexts” (Salmon, 55), in other words, Salmon sees no conflict between statistical and causal factors. Now Salmon believes he has set up everything he needs to for his account of scientific explanation. First he makes the distinction between causal processes and causal interactions. For example, a billiard ball in motion is an example of a causal process; a collision between two billiard balls is a causal interaction. Salmon believes it is “important to distinguish them from such pseudo-processes as a shadow moving across the landscape” (Salmon, 56). In order to accomplish this Salmon decides to invoke Reichenbach’s mark criterion in that only a true “causal process has the capability of transmitting a causal influence” (Salmon, 56). In Salmon’s account, if one considers the “cause as one event and of an effect as a distinct event, then the connection between them is simply a spatio-temporally continuous causal process” (Salmon, 57). Now that Salmon has established the difference between causal processes and causal interactions as well as introducing the mark criterion, which will serve to show the difference between pseudo-processes and true causal processes (Salmon, 57) he moves onto the next step of establishing his causality. It is time to turn our attention towards the principle of the common cause, another important piece of Salmon’s causality first described by Hans Reichenbach. The Principle of the common cause states that, “if two or more events of certain types occur at different places, but occur at the same time more frequently than is to be expected if they occurred independently, then this apparent coincidence is to be explained in terms of a common causal antecedent” (Salmon 57 – 58). Drawing on Reichenbach’s theory once again Salmon uses the idea of a conjunctive fork to articulate common cause. Specifically:

“In order to satisfy the conditions for a conjunctive fork, events of the types A and B must occur independently in the absence of the common cause C… furthermore the probabilities of A and B must each be increased above their overall values if C is present… finally, the dependency between A and B is absorbed into the common cause C, in the sense that the probability of A and B given C equals the product of the probability of A given C and the probability of B given C” (Salmon, 58).

Salmon further discusses his conjunctive fork use stating that a common cause E can also be part of a conjunctive fork with A and B, however there must be a common cause C. The reason for this is to accommodate for a principle first described by Russell that “symmetrical patterns emanate from a central source – they do not converge from afar on a central point” (Salmon, 59). Salmon not expands on Reichenbach’s conjunctive fork to define a new type of causal fork to handle a different type of causal interaction, the interactive fork. In a conjunctive fork, the common cause screens-off one effect from the other, in an interactive fork, it does not (Salmon, 60). Making an explicit description of the difference of the two, Salmon states that:

“In the conjunctive fork, the common cause C absorbs the dependency between the effects A and B, for the probability of A and B given C is equal to the product of the probability of A given C and the probability of B given C. In the interactive fork, the common cause C does not absorb the dependency between effects A and B, for the probability of A and B given C is greater than the product of the two separate conditional probabilities.” (Salmon, 60)

“When two processes interact, and both are modified in such ways that the changes in one are correlated with changes in the other we have a causal interaction (Salmon, 60). To illustrate the interactive fork, Salmon gives an example of a Compton scattering:

Consider an incident photon hitting an electron; “the probability of getting a photon with energy E1 and an electron with the energy E2, where E1 + E2 is approximately equal to E (the energy of the incident photon), is much greater than the product of the probabilities of each energy occurring separately. Assume… that there is a probability of 0.1 that a photon of energy E1 will emerge if a photon of energy E impinges on a given target, and assume that there is a probability of 0.1 that an electron with kinetic energy E2 will emerge under the same circumstances. In this case the probability of the joint result is not 0.01, the product of the separate probabilities, but 0.1, for each result will occur if and only if the other does.” (Salmon, 59)

Salmon does believe that intersection without interaction is possible such as the crossing of two light beams with no photonic collision. Salmon uses his new account for a special subset of causal interactions to add two new points to the principle of the common cause: He reiterates points one to three and adds his two as points four and five thus forming the covering law his wishes to use to subsume causal processes and interaction under. According to Salmon the principle of the common cause now:

  1. “supplies a schema for the straightforward explanations of everyday sorts of otherwise improbable coincidences” (Salmon, 61)
  2. is “the source for the fundamental temporal asymmetry of causality, and it accounts for the temporal asymmetry we impose upon scientific explanations” (Salmon, 61)
  3. “provides the key to explication of the concept of causal interaction” (Salmon, 61)
  4. “plays a fundamental role in the causal theory of perception… various observers arranged around a central region… have perceptions that correspond systematically with one another in the customary way, we may infer, with reasonable reliability, that we have a common cause” (Salmon, 61)
  5. “can be invoked to support scientific realism… [and applies] directly to the explanation of observable regularities by appeal to unobservable entities… in this instance… the common cause is not some sort of event, it is rather a common constant underlying structure which manifests itself in a variety of different situations” (Salmon, 61)

As mentioned before, Salmon does admit that any occurrence will require subsumption under statistical regularities but states that the causal explanation of the occurrence will also be required (Salmon, 63). As a final point in light of this admission of statistical dependency Salmon concludes that:

“If we can have events of two types, A and B, whose respective members are not spatio-

temporally contiguous, but whose occurrences are correlated with one another, the causal

explanation of this regularity may take either of two forms. Either there is a direct causal connection from A to B or B to A, or there is a common cause C, which accounts for the statistical dependency. In either case those events which start in the cause-effect relation to one another are joined by a causal process.” (Salmon, 63)

Problems with Causality

Bas Van Fraassen refutes this view of causality. He states that the first difficulty with this view "is that to be a causal process, the sequence of events must correspond to a continuous spatio-temporal trajectory" (Van Fraassen, 70). Causality fails to explain microcausal events, such as quantum mechanics. The second problem is that "many scientific explanations certainly do not look as if they are causal explanations in Salmon's sense" (Van Fraassen, 70). Van Fraassen states that there are also 'laws of coexistence', that describes interactions between objects that are not results of any causal processes. Frassen suggests the theories like Pauli's exclusion principle, Boyle's gas law, and Newton's law of gravitation are laws of this type. "In some cases we can say that they (or their improved counterparts) were later deduced from theories that replaced "action at a distance (which is not action at all, but a constraint on simultaneous states) with "action by contact" (Van Fraassen, 70). Van Fraassen asks if these laws of coexistence were not so replaceable, if they could be used for explanation. Salmon attempts to explain this with his idea of 'common cause', where events can be traced back to a common cause. This is not necessarily the case, as Van Fraassen suggests events with similar outcomes have come about from "the similarity in the physically independant causal processes" (Van Fraassen, 70).

Notes

  • Induction (Explanation of) Account. Discussion with Dr. Richard Zach
  • Haack, Susan. The Justification of Deduction p.112. In: Phil 409.02 McKerlie & Zach (ed.) University of Calgary, Calgary. 2006.
  • Hume, David. §IV - Sceptical Doubts Concerning the Operations of the Understanding. An Enquiry Concerning Human Understanding. pp.15-39. In: Phil 409.02 McKerlie & Zach (ed.) University of Calgary, Calgary. 2006.
  • The Grue problem (Description) Account. Discussion with Dr. Richard Zach
  • Salmon, Wesley C. Why Ask, "Why?"? An Inquiry Concerning Scientific Explanation pp.51-64. In:Phil 565/667. M. Ereshefsky (ed.) University of Calgary, Calgary. 2006.
  • Van Fraassen, Bas The Pragmatics of Explanation pp.65-75. In:Phil 565/667. M. Ereshefsky (ed.) University of Calgary, Calgary. 2006.
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