Before I show the application of this analysis of knowledge to the problem of error, let me try and clear up its obscurity, for undoubtedly it is difficult to comprehend. Its difficulty lies in this, that though all the ideas with which it deals are quite familiar--suppositions, real and unreal possibilities, fulfilled and non-fulfilled beliefs--yet it seems to run counter to all our notions of the extreme simplicity of the appeal to reality. It seems strange and paradoxical to our ordinary habit {87} of thinking to affirm that there are real things and real relations between things which though real yet do not exist, and also that non-existent realities are not things that once were real but now are nought--they are things that subsist. Yet this is no new doctrine. The most familiar case of such realities is that of numbers. The Greeks discovered that numbers do not exist--that is to say, that their reality is of another kind to that which we denote by existence. Numbers are realities, otherwise there would be no science of mathematics. Pythagoras (about 540-500 B.C.) taught that numbers are the reality from which all else is derived. And there are many other things of the mind that seem indeed to be more real than the things of sense. It is this very problem of error that brings into relief this most important doctrine. Now let us apply this theory of the supposition to the problem of error, and we shall then see how there can be an object present to the mind when we judge falsely, and also that the object is the same whether we judge truly or falsely. Suppositions are real possibilities; they are alternatives that may be fulfilled or that may never be fulfilled. These real possibilities, or these possible alternatives, are objects of thought; they do not belong to the mental act of thinking; they are not in the mind, but realities present to the mind. In mere supposing they are present as alternatives; in judging, we affirm of them or deny of them the relation to general reality that they are fulfilled. Judgments therefore are true or false accordingly as the fulfilment they affirm does or does not agree with reality. In this way, then, we may answer the perplexing question, How can there be an object of thought in a false judgment? The answer is, that the objects of thought about which we make judgments are suppositions, and our judgments {88} concern their fulfilment, and their fulfilment is a relation external to them--it is their agreement or disagreement with reality. CHAPTER IX CONCLUSION