A fallacy of Observation (the first of the three fallacies of Proof) may be either negative or positive.

1. The former, which is called Non-observation, is a case, not of a positive mis-estimate of evidence, or of the proper faculties (whether the senses or reason) not having been employed, but simply of the non-employment of any of the faculties. It arises a ([Greek: a]) from neglect of instances. Sometimes this is when there is a stronger motive to remember the instances on the one side, and the observers have neglected the principle of the Elimination of Chance. Hence (the mind, as Bacon says, being more moved by affirmative than by negative instances) the belief in predictions, e.g. about the weather, because they occasionally turn out correct; and the credit of the proverb, that 'Fortune favours fools,' since the cases of a wise man's success through luck are forgotten in his more numerous successes through genius. But a preconceived opinion is the chief cause why opposing instances are overlooked. Hence originate the errors about physical facts (e.g. of Copernicus's foes, and friends, too, about the falling stone), and À fortiori, on moral, social, and religious subjects, where yet stronger feelings are involved.

The fallacy of Non-observation may occur ([Greek: b]) from neglect, not of the material instances wholly, but of some material facts in them, e.g. in cases of cures by quack remedies (such as Kenelm Digby's 'sympathetic powder'), of some attendant fact (as exclusion of air from a wound, rest, regimen, and the like) which really worked the cure. Sometimes the neglected fact is one ascertainable, not by the senses, but by reasoning, which has been overlooked. Thus, Cousin's argument that, if the sole end of punishment were to prevent crime by intimidating intending criminals, the punishment of the innocent, indiscriminately with the guilty, would have the same effect, ignores the fact that the innocent would then be equally intimidated, and so the punishment would be of no use as an example to criminals. So, in Political Economy, where the effects of a cause often consist of two sets of phenomena, the one obvious, the other deeper under the surface, and exactly contrary, the latter is often neglected. This was why the rapidly spent capital of the prodigal was supposed formerly to employ more labour than the invested savings of the parsimonious, and the purchase of native goods to encourage native industry more than the purchase of foreign.

2. The error in Mal-observation, which is the positive kind of Mis-observation, is not the overlooking facts, but the seeing them wrong. It arises from mistaking what is in fact inference (as much must be, whenever we try to observe or to describe) for perception, which is infallible evidence of what is really perceived. The Anti-Copernicans, when they appealed to common sense, made this mistake. So do untrained persons generally in describing facts, especially natural phenomena (e.g. apothecaries and nurses in stating symptoms), and that, too, in proportion to their ignorance. We might expect this, since usually the actual perceptions of the senses (e.g. the colour and extension) are not of interest, except as marks whence to draw inferences about something else (e.g. about the body, to which these qualities belong). Painters, therefore, to know what the sensation actually was, have to go through a special training. But this confusion of inference with perception is still more likely in highly abstract subjects; and, consequently, in these, mere, and often false inferences, have continually been regarded as intuitive judgments.