Updated:    03 March 2000


EXPLANATION – beside intrinsic interest


goal of science ?


theories that have truth or high verisimilitude because they are needed for explanations


instrumentalism vs realism



Duhem - science does not explain



contemporary instrumentalism seeks account of explanation that permits explanation without truth





EXPLANATION : what is it?



Answer to a “why” question.


Why did Adam eat the apple?

Why is the sky dark at night?

Dewey’s story

Why is the balloon expanding?





answer depends on the context

audience - questions


information available to audience

(why does sodium turn yellow ?)        





specification of question

(why do you rob banks?)

apprentice robber of some naivety

ernest young social worker


supposed to give understanding


OED: explanation - “statement or

circumstance that explains”



explain: “to make clear or intelligible”

              “to give understanding”




? Explanation = any story that gives understanding


Real vs apparent understanding


Margaret Lawrence


The seven heavenly bodies


add in background belief

why – God – mirror - cosmos


Philosophical theory of explanation - an account of what constitutes genuine explanation in a context.


All things being equal, we seek a single unified account




Covering Law Model

Deductive-Nomological Model

Hempel’s Model


Dewey’s puzzle


In his book, How We Think, John Dewey describes a phenomenon he observed one day while washing dishes.  Having removed some glass tumblers from the hot suds and placed them upside down on a plate, he noticed that soap bubbles emerged from under the tumbler’s rums, grew for a while, came to a standstill and finally receded into the tumblers.


Why did this happen?  Dewey outlines an explanation to this effect: Transferring the tumblers to the plate, he had trapped cool air in them; and thus to an expansion of the soap film that had formed between the plate and the tumblers’ rims.  But gradually, the glass cooled off, and so did the air inside, and as a result, the soap bubbles receded.


The explanation here outlined may be regarded as an argument to the effect that the phenomenon to be explained, the explanandum phenomenon, was to be expected in virtue of certain explanatory facts.  These fall into two groups: (I) particular facts and (ii) uniformities expressible by means of general laws.  The first group includes facts such as these: the tumblers had been immersed in soap suds of a temperature considerably higher than that of the surrounding air; they were put, upside down, on a plate on which a puddle of soapy water had formed that provided a connecting soap film, and so on.  The second group of explanatory facts would be expressed by the gas laws and by various other laws concerning the exchange of heat between bodies of different temperature, the elastic behaviour of soap bubbles, and so on.  While some of these laws are only hinted at by such phrasings as ‘the warming of the trapped air led to an increase in its pressure’, and others are not referred to even in this oblique fashion, they are clearly presupposed in the claim that certain stages in the process yielded others as their results.




Mill System of Logic 1843

      ? Newton


Received View - in empiricist tradition

      uses relatively unproblematic ideas


      social sciences vs natural sciences


remains point of departure for discussions of explanation


      can you solve Hempel’s problems ?



See that what happened, had to happed given other things (the particular facts) because of the laws


      See why it had to happen





An explanation is an argument !!!




      Initial Conditions:         C1, C2,...Ck


      Laws:                   L1,L2,...Lr


      Explanadum              \    E



      1. Argument valid

      2. Laws enter essentially into derivation


Potential explanation

True explanation




      explains importance - prediction

      simple ideas

      particular events and to laws




But explanations don’t look like this !


Hempel : “models” … “a useful reminder … explanation as characterized constitute ideal types or theoretical idealizations and are not intended to reflect the manner in which working scientists actually formulate their explanatory accounts”



Elliptical Formulations


Why did the butter melt? The pan was still hot.


      “an account of this kind omits mention of certain laws of particular facts which it tacitly takes for granted, and whose explicit citation would yield a complete deductive-nomological argument”




Partial Formulation



explanans not detailed enough to entail the specific explanadum



more work needed



Freud explains his slip of the pen due to unconscious desire


has laws

need more detail




Explanatory Sketch



      Why did anyone go to Canada?


      Because of the fur trade



      general outline to be developed


area to look for laws



Non-Pragmatic Ideal


concept of proof in mathematics


“an argument Y is a proof of a given sentence X without making any mention of persons who might take cognizance of Y”


“… constructing a nonpragmatic concept of scientific explanation - a concept which is abstracted, as it were, from the pragmatic one, and which does not require relativization with respect to questioning individuals any more than does the concept of mathematical proof.”



But is there any such thing?

Idealized audience of Nobel prize winners ?




Better to acknowledge that it is pragmatic



Handle certain objections



All crows are black

Icabod is a crow

Therefore, Icabob is black



fall about laughing at poor old Hempel



Or imagine telling quantum chemistry story to school kids








Logical Space of Explanation



-  Hempel avoid subjectivity in explanation



All meet the conditions, pragmatic factors dictate which one it is appropriate to give



Henry the mad bird painter




Statistical Inductive Explanation


smoking - lung cancer


high probability replaces proof   


syphlis – paresis






1The American Objection

            flag pole

            sky dark at night


Explanation is asymmetrical

DN Model does not guarantee this.


So not a sufficient condition for explanation.


Accidentally true generalizations do not explain.


What makes a true generalization a law?


But this is a common problem







      Icabod fails to get pregnant

      Sugar dissolves in holy water



DN Model fails to exclude irrelevancies.



Common Cause


      barometer falls, bad weather





Can it be done? Dewey’s problem again.



Dewey understood without knowing the laws. Cannot match the laws with the initial conditions.



Try to fit your favourite explanations into DN form



accept claims as explanatory without checking to see if we can transform them to DN model



Explanation by models and analogies

plate techtonics





Causal Relevance



for a wide class of cases, to explain is to cite a causally relevant factor


      explanations are not argument


to explain is to cite a feature of the world which is causally responsible (partially) for what you want to explain



But what is causation?


      must be more than Humean regularity ?





Explanation by identification



      Water is H2O



      Temperature is mean molecular motion



      Geometrical explanations




Why did DN seem so good?



Tradition of deductive presentation of knowledge


      Models as idealizations


Much of physics - stipulating ideal systems (ideal gases).  Derivations (if temperature goes up, so does pressure).


Understanding provided if world is sufficiently like the idealization.


      Derivation confused with explanation.


Models explain by drawing attention to the causal mechanisms.