10. The best way therefore of describing our position in Probability is as follows:--We are _entertaining a conception_ of some event, past, present, or future. From the nature of the case this conception is all that can be actually entertained by the mind. In its present condition it would be incorrect to call it a fact, though we would willingly, if we could, convert it into such by making certain of it one way or the other. But so long as our conclusions are to be effected by considerations of Probability only, we cannot do this. The utmost we can do is to _estimate_ or _evaluate_ it. The whole function of Probability is to give rules for so doing. By means of reference to statistics or by direct deduction, as the case may be, we are enabled to say how much this conception is to be believed, that is in what proportion out of the total number of cases we shall be right in so doing. Our position, therefore, in these cases seems distinctly that of entertaining a conception, and the process of inference is that of ascertaining to what extent we are justified in adding this conception to the already received body of truth and fact. So long, then, as we are confined to Probability these conceptions remain such. But if we turn to Induction we see that they are meant to go a step further. Their final stage is not reached until they have ripened into facts, and so taken their place amongst uncontested truths. This is their final destination in Logic, and our task is not accomplished until they have reached it. 11. Such language as this in which we speak of our position in Probability as being that of entertaining a conception, and being occupied in determining what degree of belief is to be assigned to it, may savour of Conceptualism, but is in spirit perfectly different from it. Our ultimate reference is always to facts. We start from them as our data, and reach them again eventually in our results whenever it is possible. In Probability, of course, we cannot do this in the individual result, but even then (as shown in Ch. VI.) we always _justify_ our conclusions by appeal to facts, viz. to what happens in the long run. The discussion which has been thus given to this part of the subject may seem somewhat tedious, but it was so obviously forced upon us when considering the distinction between the two main views of Logic, that it was impossible to pass it over without fear of misapprehension and confusion. Moreover, as will be seen in the course of the next chapter, several important conclusions could not have been properly explained and justified without first taking pains to make this part of our ground perfectly plain and satisfactory. CHAPTER XII. _CONSEQUENCES OF THE FOREGOING DISTINCTIONS._ 1. We are now in a position to explain and justify some important conclusions which, if not direct consequences of the distinctions laid down in the last chapter, will at any rate be more readily appreciated and accepted after that exposition.