Various quantitative methods

It is necessary to distinguish between essentially different things, such as: the

use of quantitative considerations in general, the higher degree of rigour in

demonstrations, the use of mathematical methods in demonstrations and, in

particular, the use of analytical and geometric methods.V

* Not all quantitative sciences are also mathematical. With its atomic

theory, chemistry has become an almost entirely quantitative science, after

having already come close to becoming one with the theory of definite proportions,

but it is not yet a mathematical science. Statistics is definitely a

quantitative science and it is on the point of becoming mathematical as

well, but on this subject there are still treatises that make little or no use of

mathematical symbols.

An empirical quantitative method is already in use in the science of economics,

with the ever-increasing habit of verifying the propositions of this science

through statistically derived information. For example, one can no longer

simply state that a very heavy tax causes a decrease in the consumption of the

targeted goods, but one is also required to know of practical cases where that

effect of the law has actually been observed.

The treatise on Political Economy published in 1887 by Mr Yves GuyotVI

has nearly half of its pages taken up by diagrams and by numerical tables.

Quite rightly, Prof. Marshall states that ‘many of the faults, many of the

injustices that are the consequence of the economic policies of governments

arise from the lack of statistical information’.2

But this method, however excellent in verifying theorems found in other

ways, taken by itself could only lead to empirical propositions;3 consequently,

it is crucial to take advantage of the deductive method first. It is therefore

natural that many economists are turning to the most perfect form of the

latter, i.e. the quantitative method, and are looking for help in it.

As we all know, by acting in such a way other sciences obtained great

benefit. The path they followed was always the same. Some hypotheses were

put forward; from them, through logical or mathematical deductions – which

is the same thing, since mathematics is nothing but a type of logic – some

Considerations, I, May 1892 3

consequences were obtained; the latter were then compared with information

gathered from observation or from experience, and were acknowledged to be

true. Only from that, and nothing else, did the postulated hypotheses acquire

credit and authority.

To recall these things, when they are by now universally known, might seem

redundant, but we need these principles to help us wholly to understand some

of the statements of the new science of economics.4

For instance, after demonstrating how one can infer the way of achieving

price equilibrium from the principles of Pure Economics, Prof. Walras goes

on to say:

Quelques critiques se sont pourtant égayés du nombre de pages que

j’employais à démontrer qu’on doit arriver au prix courant en faisant la

hausse en cas d’éxcédent de la demand sur l’offre, et la baisse en cas

d’éxcédent de l’offre sur la demande.

Et vous, ais-je dit une fois à l’un d’eux, comment le démontrez-vous? –

Mais, me répondit-il, un peu surpris, et même assez embarassé, cela a-t’il

besoin d’être démontré? Il me semble que c’est une chose évidente. – Il

n’y a d’évident que les axiomes, et ce n’en est pas un.5

[Some critics, nevertheless, have laughed at the number of pages that I

found necessary to demonstrate that one must arrive at the current price

by making it increase in the case of excess demand relative to supply and

making it diminish in the case of excess supply relative to demand. And

you, I once said to one of these critics, how would you demonstrate it?

But, he responded to me a little surprised and also rather embarrassed; is

there a need to demonstrate it? It seems obvious to me. Only the axioms

are obvious and this is not.]

Now if, by saying that, Prof. Walras simply meant to attack those who have

the impudence of passing off as demonstrations the expression of their feelings,

then he was right. However, his words would rather seem to indicate a

wish to lead science on a metaphysical path, where reasoning dominates

experience; in this case we must confess that it was his interlocutor who was

right, only he did not defend himself well. He should have said that it is from

direct observation that we deduce the law about prices rising when demand is

greater than supply, and vice versa. And he should have added:

Since these are elementary, simple, direct observations, if you no longer

wish to take them as the basis of your reasoning, but as its consequences,

then you must show that the replacements are more elementary, simpler

and more direct.

We are not saying now whether this is true or not, but Prof. Walras does not

ask the question in these terms, and when he shows his belief 6 that the day will

come when ‘all sciences will blend together into a science that will be meta-

4 Considerations, I, May 1892

physics’, he sets off on a path that no follower of the experimental method

will be able to tread after him. He would therefore prove Dr IngramXIII right,

who in the new science of economics detects the fault ‘of restoring the metaphysical

entities that had already been purged from science’. As for us, if we

were convinced of this, we would side with the opponents of the new science,

such is the light we see radiating from the experimental method, from which

alone men have learned the few truths they now know. In fact, we prefer to

believe Prof. Edgeworth’s opinion to be true, according to which one should

deem mathematical economics to be as far from Dr Ingram’s interpretation

as it is from Gossen’s, who compares the new science to astronomy;7 these

considerations are indeed aimed at illustrating the opinion of that learned

English professor.

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