Their necessity is another way of stating this implication.We can show that to deny one theorem while admitting another is to be contradictory.The whole of physical science,however,from first to last,is a process of stating the changes of phenomena in terms of time and place,and therefore brings them all within the range of mathematical methods.Science is not fully constituted till it becomes quantitative or can speak in terms of definite relations of magnitudes.How,then,are its laws necessary?It is contradictory to say that the same thing has different space-relations at the same time;but there is no contradiction in saying that it is here now and somewhere else to-morrow.The formula of the 'uniformity of nature,'whatever may be its warrant,transfers the necessity of the geometrical theorem to the laws of phenomena.We assume that things are continuous or retain identity in change.We are no more permitted to say that the combination of the same elements may produce a compound of different properties,than to say that the product of two numbers may sometimes give one result and sometimes another.
Every change is regarded as regular,or as having a 'sufficient reason.'The same series of changes therefore must take place under the same conditions,or every difference implies a difference in the conditions.So far as we carry out this assumption,we resolve the shifting and apparently irregular panorama into a system of uniform laws.Each law may be,and if it be really a law must be,absolutely true,not in the sense that it states a fact unconditionally,but that it is stated so that the conditions under.which it is absolutely true are fully specified.If we could reach a complete science of all physical phenomena,we should have a system of connected laws as infallible and mutually consistent as those of geometry or arithmetic.But in order thus to organise our knowledge,we have to alter --not the facts --but the order of grouping and conceiving them.We have to see identities where there were apparent differences,and differences in apparent identities,and to regard the whole order of nature from a fresh point of view.
The fact remains just as it was;but the laws --that is,the formulae which express them --are grouped upon a new system.The questions remain,What is the precise nature of the scientific view?and What is our guarantee for a postulate which it everywhere implies?
The chapter upon causation(59)is a vigorous assertion of Mill's position.He accepts the traditional view of his school,that cause means invariable sequence;but he makes two very important amendments to the previous statements.A simple sequence of two events is not a sufficient indication,however often repeated,that they are cause and effect.We speak,he says,of a particular dish 'causing'death;but to be accurate we must also include,as part of the cause,all the other phenomena present,the man as well as the food,the man's state of health at the time,and possibly even the state of the atmosphere or the planet.The real cause must include all the relevant phenomena.
