Discuss how some authors have critically established that objectivity, certainty and individualistic knowledge

40 What i.s this thing called Science?

deflected, the reading on the ammeter may or may not in- crease. Ye cannot make the oytcomes conform to our theorie~ .. It was because the h sical world is the way i · that the

rimen con ucted by Hertz yie ed no e ection of cath· ode ra sand the modified expenment con ucte Thomson ~- It was the mclterial i erences m e experimental arrangements of the two physicists that led to the differing outcomes, u ot. the differences in the theories held by them. It is the sense in which experimental outcomes are determined by the workings of the world rather than by theoretical views about the world that provides the possibility of testing theo- ries against the world. This ig not to say that significant results arc t’asily achievable and infallible, nor that their significance is always straightforward. But it does help to establish the point that the attempt to tes t the adequacy of scientific theories against experimental results is a meaning- ful quest. What is more , the history of science gives us exam- ples of caRes where the challenge was successfully met.

Further reading

The second half of Hacking (1983) was an important early move in the new interest philosophers of science have taken in experiment. Other explorations of the topic are Franklin (1986), Ji~ranklin (1990), Galison (1987) and Mayo (1996), although th~se detailed treatments will take on their full significance on ly in the light of chapter 13, on the “new experimentalism”. The issues raised in this chapter are dis- cussed in a little more detail in Chalmers ( 1984).

CHAPTER 4

Deriving theories from the facts: induction

Introduction

In these early chapters of the book we have been considering the idea that what is characteristic of scientific knowledge is that it is derived from the facts. We have r eached a stage where we have given some detailed attention to the nature of the observational and experimental facts that can be consid- ered as the basis from which scientific knowledge might be derived, although .. we hav~ seen that those facts cannot be established as stntghtforwardly and securely as is commonly supposed. Let us assume, then, that appropriate facts can be established in science. We must now face the question of how s~-ientific knowledge can be derived from those facts.

“Science is derived from the facts” could be interpreted to mean that scientific knowledge is constructed by first esta~ lishing the facts and then subsequently building the theory to fit them. We discussed this view in chapter 1 and rejected it as unreasonable. The is~ue that I wish to explore involvC’s interpreting “derive” in some kind of logical rather than temporal sense. No matter which comes fi~~, the facts or the theory, the question to be addressed is the ~t{int to which the theory is borne out by the facts. The strongest possible claim would be that the theory can be lo,brically derived from the facts. That is, given the facts, the theory can be proven as a c~nsequence of them. Thi!’! strong claim cannot be substanti- ated. To see why this is so we must look at some of the basic features of logical reasoning.

Baby logic

Logic is concerned with the deduction of statements from

42 What is this thing called Science?

other, given , statements. It is concerned with what follows from what. )To a ttempt will l.w made to give a detailed account and appraisal of logic or deductive reasoning here. Rather, I will make the points that will be sufficient for our purpose with t he aid of some very simple examples.

Here is an example of a logical argument that is perfectly adequat e or, to use the technical term used by logicians, perfectly valid.

Example 1 1. All books on philosophy are boring. 2. This book is a book on philosophy. 3. This book is boring.

In this a rgument, (1) and (2) ar.e the premi~:>es and (3) is the conclusion. It i,s evident, I take it, that if (1) and (2) are true then (3) is rl~uncf to be true. It i:s not possible for (3) to be false once it is given that (1) and (2) are true. To assert ( 1) and (2) as true and to deny (3) is to contradict onesdf. This is the key feature of a logically valid deduction. If the premises are true then the conclusion must he true. Logic is truth pre- ~~rving.

A slight modification of Example (1) will give us an in- stan ce of an argument t hat is not valid.

Example 2 l. Many books on philosophy arc boring. 2. This book is a book on philosophy. 3 . This book is boring.

In this example, (3) does not follow of necessitv from (1) and (2). Even if (1 i and (2) arc truf:!, then this book-might yet t um out to be one ofthe minority of books on philosophy that a re not boring. Accepting ( lJ and (2) as true and holding (3) to be fa lse does not involve a contradiction. The argument is invalid.

The reader may by now be feeling bored. Experiences of that kind certainly have a bearing on the truth of statements (1) and (3) in Example 1 and Example 2. But a point that

Deriving theories from the facts: induction 43

needs to be stressed here is that logical deduction a lone cannot establish the truth of factual~~tatc~.~~ts-o.f.(he kir~d­ f~ring .. in oure~ampies. All_ _t~-at logic-can offer in thil:l connection is lhat· £1 the premises are true and the argument is valid then the conclusion must be trw~ .. But whether the ~s ~;;··t~ue ~;-not is .not~ q~e;oon that can be settled by an appeal to logic. 1n argument can be a perfectly valid deduction even if it involves a fa lse premise. Here is an __ …. — — ·. ·· -· …. example.

Example3 1. All cats have five legs. 2. Bugs Pussy is my cat.

3. Bug::i Pussy has five legs. This is a perfectly valid deduction. If (1) and (2) are true

then (3) must be true. It so happens that, in this example (1) and (3) are false. But this does not affect the fact that the ar~:,TUment is valid.

There is a strong ~ense, then, in which lo1,ric alone is not a so~~-ce of new truths. The truth of the factualstat.em~nte.that ·constitute th e pre~~es of arguments cannot be established ·by appeal t o logic. Logic can simply reveal what follows from, or what in a sense is al re-ady containeJ in, the statemer)ts we ·already: have to hand. Agclinst this limitation we have the great st~ength oflogic, namely, its truth-preserving character. I( we .can be sure our premi~es are true then we can be cquaUy ~ure that everything w.e logically derive from them will also be true.

Can scientific laws be derived from the facts?

With thi8 discussion of the nature oflogic behind us, it can be straightforwardly shown that ss_!ent~~c knowledge ~annot be derived from the facts if “derive” is interpreted as “logically deduce”.

Some simple examples of scientific knowledge will b~ suf- ficient for the illustration of this bask point. Let us consider

“71”’ -~ ‘1r . . . · :

I ,I :!

·i

44 What is this thing called Science?

some low-level scientific laws such as “metals expand when heated” or “acids turn litmus red”. These are general state- ments. They are examples of what philosophers refer to as universal statements. They refer to all events of a particular kind, all instances of metals being heated and all instances oflitmus being immersed in acid. Scientific knowledge invari- ably involves general statements of this kind. The situ~~~ is quite otherwise when it comes to the_~~rvation state- ments that con!:ititute the facts that provide the evidence for general scientific laws. Those observable facts’Ot- experimen- tal results are specific claims about a state of affairs that obtains at a particular time. They are what philosophers call singular statements. They include statements such as “the length of the copper bar increased when it was heated” or “the litmus paper turned red when immersed in the beaker of hydrochloric acid”. Suppose we have a large nwnber of such facts at our disposal as the basis from which we hope to derive some scientific knowledge (about metals or acids in the case of our examples). What kind of argument can take us from those facts, as premises, to the scientific laws we seek to derive as conclusions? In the case of our example concerning the expansion of metals the argument can be ~chematised as follows:

‘ Premises 1. Metal x1 expanded when heated on occasion t 1. 2. Metal x2 expanded when heated on occasion t~. n. Metal Xu expanded when heated on occasion tn. Conclusion All metals expand when heated.

Thi~Js..n~t a l~__gic~lly _yalid argument. It lacks the basic features of such an argument. It is simply not the case that if the statements constituting the premises are true then the conclusion must be true. However many observations of ex· pan ding metals we have to work with, that is, however great n might be in our example, there can be no logical guarantee that some sample of metal might on some occasion contract when heated. There is no contradiction involved in claiming

Deriuing theories from the facts: induction 45

both that all known examples of the heating of metals has re~uited in expansfon and that “all metals expand when heated” is false. – ·This straightforward point is illustrated by a somewhat ~oiiie e~ample attributed to Bertrand Russell. It con- cerns a turkey who noted on his first morning at the turkey farm that he was fed at 9 am. After this experience had been repeated daily for several weeks the turkey felt saf~1in draw- ing the conclusion “I am always fed at 9 am”. Ala8, this conclusion was shown to be false in no uncertain manner when, on Christmas eve, instead of being fed, the turkey’s throat was cut. The turkey’s argwnent led it from a nwnber of true observations to a false conclusion, clearly indicating the invalidity of the argument from a logical point of view.

_Ar.gym.ents9f.the k_ind I have illustrated with the example concerning the expansion of metals, which proceed from a finit~-~~mber of specific facts to a general conclusion, are cal1ed i~ductive argwnents, as distinct from logical, deductive argu111.ents. A characteristic of inductive arguments that dis- t~guishes them from deductive ones is that, by proceeding as they do from statements about some to statements about all events of a particular kind, they go beyond what i~ con- tained in the premises. 9-.!!neral_scientific la~sj,nvariably go ~eiQr~~ ~he finite amount of observable evidence that is avail- ~~Je to support them, and that is why they can never be P.!:£>Y.e!l in the sense of being logically deduced irom that evidence.

What constitutes a good inductive argument?

We have seen that if scientific knowledge is to be understood as being derived from the facts, then “deriv~Il!:lS~ be under· stood in an inductive rather than a deductive seJ!S.~- But what -are the characteristics of a good inductive argument? The question is of fundamental importance because it is clear that not all generalisations from the observable facts are war- ranted. Some of them we will wish to regard as ~~e~hasty or

I !’

46 What is this thing called Science?

based on insufficient evidence, as when, perhaps, we condemn the attribution of some characteristic to an entire ethnic group based on some unpleasant encounters with just one pair of neighbours. Under precisely what circumstances is it legitimate to assert that a scientific law has been “‘derived” from some finite body of observational and experi~ental evidence?

A first att(‘mpt at an answer to this question involves the demand that, .if an inductive inference from observable f~ct’$ to laws is to be justified, then the following conditions must

c satisfied: The number of observations forming the basis of a gener- alisation must be large.

2. The observations must be repeated under a wide variety of conditions.

3. No accepted observation statement should conflict with ·the.derived law.

.,

Condition 1 is regarded as necessary because it is dearly not legitimate to conclude that all metals expand when heated on the basis of just one observation of an iron bar’s expansion, say, any more than it is legitimate to conclude that all Australians are drunkards on the basis of one observation of an intoxicated Australian. ~large number of independent observations would appear to be necessary before eith!:r generalisation can be justified. A good inductive argument does not jump to conclusions. ·

One way of increasing the number of observations in the examples mentioned would be to repeatedly heat a single bar of metal or to continually observe a particular Australian getting drunk night after night, and perhaps morning after morning. Clearly, a list of observation statements acquired in such a way would form a very unsatist~’lctory basis for the respective generalisations. That is why condition 2 is neces- sary. “~!1_ J:!letals expand when heated” will be a legitimate generalisation only if the observations of expansion on which it is based range over a wide variety of conditions. Various kinds of metals should be heated, long bars, short bars, silver

Deriving ilworit~s (rom the facts: induction 47

bars, ~~pp~r bars etc. should be heated at high and low pressures and high and low temperatures and so on. Only if on all such oc(:asions expansion results is it legitimate to generalise by induction to the general law. Further, it is evident that if a particular sample of metal is observed not to expand when heated, then the generalisation to the law will not be justified. Condition 3 is essential.

‘l’he above can be summed up by the following statement of the principle of induction.

v .•. ·-· •’.. …–· …….. ·”···-· -· .•

l . If a lar~e number of A’s have been observed under a wide variety ~f conditions, and if all those A’s without exception possess the

. !1roperty B, then all A’s have the property B.

There are serious problems with this characterisation of induction. Let us consider condition 1, the demand for large numbers of observations. One problem with it is the vague- nc·ss of”large”. Are a hundred, a thousand or more observa- tions required? If we do attempt to introduce precision by introducing a number here, then there would surely be a great deal of arbitrariness in the number chosen. The problems do not stop here. There are many instances in which the demand f(Jr a large number of instances seems inappropriate. ‘l’o illustrate this, consider the strong public reaction against nuclear warfare that was provoked by the dropping of the first atomic bomb on Hiroshima towards the end of the Second World War. That reaction was based on the realisation of t.he extent to which atomic bombs cause ~idC”~pr~’ad destruction and human suffering. And yet this widespread, and surely reasonable, beH,ef was based on just or~e drarnatk observa- tion. In similar ~ei’n, it would be a very stubb~m investigator who insisted on putting his hand in the fire many times tJef(Jre concluding that fire burns. Let us consider a less f,~~cifui example related to scientific practice. Suppose I reproduced an experiment reported in some recent scientith: journal, and sent my results offfor publication. Surely the editor of the journal would reject my paper, explaining that the