tional sciences, depends upon the fact, that in them, preeminently, he who seeks the most certain truth may find it if he will only take sufficient trouble. As demonstrable truth partakes of the pure nature of God, it demands the highest degree of support and respect that man can give it, whilst doubtful or unprovable statements or hypotheses should not be exalted to the dignity of demonstrable truths.

The phenomena of consciousness are often adduced as being the most certain of truths, and doubtless we are compelled to believe, that when we recognise an impression we do experience something; but what that something is, our consciousness alone does not unerringly tell us. If we can perceive no cause for the impression, when the cause ought to be manifest, we doubt the reality of the impression, and sometimes ascribe it to a conception of our imagination. The simple consciousness of an idea or impression is not alone a complete proof of its truth, because as scientific knowledge advances we increasingly find that the ideas acquired by such means are often erroneous. Consciousness, therefore, does not excite in our minds truthful beliefs alone, but a mixture of truth and error, from which we have to eliminate the error by various processes. Appearances and realities are often opposite, or even contrary. There exists in some respects the greatest contrast between the human mind and external nature. Our minds are extremely finite; nature is nearly infinite. is law, and certainty, but our ideas are all uncertain and erroneous.

In nature all

more or less

The truthfulness of our ideas, and the real certainty of our knowledge, depend upon the accuracy with which the mind itself receives impressions, and this further depends upon mental state, which is itself a result of inheritance and experience, and varies with our physical

1 Such phenomena frequently occur in dreams.

L

health. The truthfulness of our ideas also depends upon the accuracy and completeness with which we reason upon our impressions, and draw conclusions from them. The less intelligent or truthful our minds, the greater is the proportion of impressions we receive in a false or distorted manner, and of false inferences we draw from them. As far as we know, the experience of all mankind, through all ages, confirms the conclusion, that all the operations of nature are absolutely certain. Uncertainty, therefore, exists not in the phenomena of nature, but in our mental reception and exposition of them. As nature itself is true, and we are very liable to transform truth into error in the act of receiving and interpreting it, our thoughts are not a test of the truthfulness of nature, but nature is the test of the truth of our thoughts, and our minds must be brought to agree with it.1

Another reason why our scientific knowledge is not infallible is because our inductions are never complete. We never make an exhaustive enumeration of all the instances, because it is either beyond our power, or the labour is too great. We also never know that undiscovered instances do not remain, or that we have not omitted some exceptional cases. Induction, therefore, never absolutely proves a general law, nor can we ever be absolutely certain that the next discovered instance will not be an exceptional one.

The strongest proof of the truth of a general law is usually considered to be the successful prediction of new results; but even in this case we are not absolutely certain, because our deductions also are never complete. Until we have predicted, and successfully verified every possible case, and that is beyond our powers, we are not certain we have not missed some exceptional one, and that our prediction may not be wrong. The extreme incom

1 For limiting exceptions see p. 23.

SCIENTIFIC KNOWLEDGE IS NOT INFALLIBLE.

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pleteness of our experience, the very limited and variable power of our senses, and the imperfect action of all our intellectual powers, weaken the entire fabric of our scientific beliefs.

But although the impressions we receive through our senses are often fallacious, and from this cause and from our defective intellectual powers, the conclusions we draw from them are more or less erroneous, we do still possess in science a means of arriving at the most certain truth. We are able by means of our faculties of comparison and reason, to compare those impressions or inferences with each other, detect contradictions and inconsistencies, eliminate error, and gradually impart an ever-increasing degree of truthfulness and certainty, even to our most fundamental scientific axioms and beliefs. It is by a laborious process of this kind, that much of our scientific knowledge has had imparted to it its present high degree of certainty; and as the process in itself appears to be a perfect one, we may reasonably hope, by a continuation of it through an immensity of time, to arrive at an extreme degree of certainty and completeness in scientific matters. By the same process as we have already arrived at what are termed 'axioms' in science, shall we be able to arrive at an everincreasing number of truths upon which we may rely reasonably with an equal degree of security. As an immense number of natural truths, probably including some of the greatest, remain still unknown, that which we suppose to be truth requires to be tested afresh by every accession of new knowledge, and in this way our beliefs are continually being purified; but in questions where no effectual test can be applied, the most certain truth cannot be obtained.

Notwithstanding, also, all the errors to which our senses and intellectual powers are liable, reason has in this way, during all human existence, proved itself a true rock

of ages; and it is usually those who least possess it who most doubt its power. And however sure we may feel of the facts of consciousness, and of any unprovable or undisprovable hypothesis in science inferred from them, we are morally bound to feel still more certain of the verified truths of the intellect, because they are themselves the facts of consciousness, corrected by the intellectual powers. However uncertain also the conclusions of the intellect may be assumed to be, those of uncorrected feeling and consciousness are much more so. • Greater liability to error on account of greater complexity does not necessarily render reason less trustworthy. True, it is not so easy to add up a long column of figures as it is to add five to five, but surely the result admits of as much correctness in the former instance as in the latter."1

CHAPTER XI.

TRUSTWORTHINESS AND ACCURACY IN SCIENCE.

THAT which is not to be depended upon is not science; assumptions and hypotheses are also not strict science, but only a means towards discovering it. Trustworthiness is the first object, and accuracy the perfection and final aim of science. Trustworthiness and accuracy may be regarded as not synonymous terms, the former representing a logical idea only, or one of matter of fact; the latter a quantitative one. Adopting this difference of meaning of terms, we may say that it is more important to be trustworthy than accurate, because the former affects the fact itself,

1 Rev. W. G. Davies on 'The Law of Certainty,' Psychological Journal, 1863, pp. 454, 455.

TRUSTWORTHINESS OF SCIENTIFIC KNOWLEDGE. 149

the latter only its degree or relative quantity. Experiments may be crude in a quantitative sense, and yet be trustworthy as qualitative tests; and a chemist may deserve trust, but yet not be accurate; for instance, he may obtain a pure and complete precipitate of a substance in analysis, and wash and dry it most perfectly, but failing to weigh it with exactitude, the result he obtains is not accurate; or he may be accurate and yet may err he may, for example, find a magnetic substance in tea, and may weigh it with the greatest precision, and set its weight. down as being that of metallic iron; but if he has not proved it to be iron, his result, although accurate in weight, is not to be depended upon. Strictly speaking, however, a man who may not be depended upon as to qualitative matter of fact cannot be accurate, because, if he cannot be relied upon for the fact itself, he cannot be certain in any of his quantitative statements, respecting it. It is of but little use to measure a thing, unless we know what it is we are measuring; and it is of less value to measure an effect without knowing and measuring the cause and conditions of it. Priestley was an example of a chemist who was trustworthy, but not accurate. He was a great qualitative investigator; he discovered many new substances, and his discoveries were real, as subsequent experience has proved; but his experiments were crude in a quantitative sense, he rarely made use of the balance, and was unable to make quantitative analyses.

In determining a qualitative fact, measurement is usually unnecessary, as we continually see in the art of qualitative chemical analysis. In other cases, however, by means of a measurement, we obtain both a qualitative and a quantitative result at the same time; and in a few cases the only method we know of obtaining a qualitative result is by means of a quantitative measurement, or under