180 Dr. WHEWELL, ON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY. 



reeled so as to be true instead of false. And thus we still say, that if in any department of 

 science a man can conceive distinctly at all, there are principles the contrary of which he cannot 

 distinctly conceive, and which are therefore necessary truths. 



27. But on this it may be asked, whether truth can thus depend upon the particular state of 

 mind of the person wlio contemplates it ; and whether that can be a necessary truth which is not 

 so to all men. And to this we again reply, by referring to geometry and arithmetic. It is plain 

 that truths may be necessary truths which are not so to all men, when we include men of confused 

 and perplexed intellects ; for to such men it is not a necessary truth that two straight lines cannot 

 inclose a space, or that li and 17 are 31. It need not be wondered at, therefore, if to such 

 men it does not appear a necessary truth that reaction is equal and opposite to action, or that the 

 quantity of matter in the world cannot be increased or diminished. And this view of knowledge and 

 truth does not make it depend upon the state of mind of the student, any more than geometrical 

 knowledge and geometrical truth, by the confession of all, depend upon that state. We know that 

 a man cannot have any knowledge of geometry without so much of attention to the matter of 

 the science, and so much of care in the management of his own thoughts, as is requisite to keep his 

 ideas distinct and clear. But we do not, on that account, think of maintaining that geometrical 

 truth depends merely upon the state of the student's mind. We conceive that he knows it because 

 it is true, not that it is true because he knows it. We are not surprized that attention and care and 

 repeated thought should be requisite to the clear apprehension of truth. For such care and such 

 repetition are requisite to the distinctness and clearness of oiu- ideas: and yet the relations of these 

 ideas, and their consequences, are not produced by the efforts of attention or repetition which we 

 exert. They are in themselves something which we may discover, but cannot make or change. The 

 idea of space, for instance, which is the basis of geometry, cannot give rise to any doubtful proposi- 

 tions. What is inconsistent with the idea of space cannot be truly obtained from our ideas by any 

 efforts of thought or curiosity ; if we blunder into any conclusion inconsistent with the idea of space, 

 our knowledge, so far as this goes, is no knowledge: any more than our observation of the external 

 world would be knowledge, if, from haste or inattention, or imperfection of sense, we were to 

 mistake the object which we see before us. 



28. But further : not only has truth this reality, which makes it independent of our mistakes, 

 that it must be what is really consistent with our ideas ; but also, a further reality, to which the 

 term is more obviously applicable, arising from the principle already explained, that ideas and 

 perceptions are inseparable. For since, when we contemplate our ideas, they have been frequently 

 embodied and exemplified in objects, and thus have been fixed and modified; and since this compound 

 aspect is that under which we constantly have them before us, and free from which they cannot be 

 exhibited ; our attempts to make our ideas clear and distinct will constantly lead us to contem- 

 plate them as they are manifested in those external forms in which they are involved. Thus in 

 studying geometrical truth, we shall be led to contemplate it as exhibited in visible and tangible 

 figures; — not as if these could be sources of truth, but as enabling us more readily to compare the 

 aspects which our ideas, applied to the world of objects, may assume. And thus we have an addi- 

 tional indication of the reality of geometrical truth, in the necessary possibility of its being capable 

 of being exhibited in a visible or tangible form. And yet even this test by no means supersedes 

 the necessity of distinct ideas, in order to a knowledge of geometrical truth. For in the case of 

 the duplication of the cube by Hobbes, mentioned above, the diagram which he drew made two 

 points appear to coincide, which did not really, and by the nature of our idea of space, coincide; 

 and thus confirmed him in his error. 



Thus the inseparable nature of the Fundamental Antithesis of Ideas and Things gives 

 reality to our knowledge, and makes objective reality a corrective of our subjective imperfec- 

 tions in the pursuit of knowledge. But this objective exhibition of knowledge can by no means 

 supersede a complete development of the subjective condition, namely, distinctness of ideas. 

 And that there is a subjective condition, by no means makes knowledge altogether subjective, 



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