As regards the negative side of these investigations, or the refutation of dogmatism, the attacks of Carneades were directed partly against the formal possibility of knowledge, and partly against the chief actual results of the knowledge of his day. In both respects he had mainly to do with the Stoics, [1452] though he did not confine himself to them. [(a) Denial of possibility of formal knowledge.] To prove the impossibility of knowledge in general, he appeals sometimes to experience. There is no kind of conviction which does not sometimes deceive us; consequently there is none which guarantees its own truth. [1453] Going then further into the nature of our notions, he argues, that since notions consist in the change produced on the soul by impressions from without, they must, to be true, not only furnish information as to themselves, but also as to the objects producing them. Now, this is by no means always the case, many notions avowedly giving a false impression of things. Hence the note of truth cannot reside in an impression as such, but only in a true impression. [1454] It is, however, impossible to distinguish with certainty a true impression from one that is false. For independently of dreams, visions, and the fancies of madmen, in short, of all the unfounded chimeras which force themselves on our notice under the guise of truth, [1455] it is still undeniable that many false notions closely resemble true ones. The transition, too, from truth to falsehood is so gradual, the interval between the two is occupied by intermediate links so innumerable, and gradations so slight, that they imperceptibly pass one into the other, and it becomes impossible to draw a boundary line between the two opposite spheres. [1456] Not content with proving this assertion in regard to impressions of the senses, Carneades went on to prove it with regard to general notions based on experience and intellectual conceptions. [1457] He showed that it is impossible for us to distinguish objects so much alike as one egg is to another; that at a certain distance the painted surface seems raised, and a square tower seems round; that an oar in the water seems broken, and the neck-plumage of a pigeon assumes different colours in the sun; that objects on the shore seem to be moving as we sail by, and so forth; [1458] in all these cases the same strength of conviction belongs to the false as to the true impressions. [1459] He showed further that this applies equally to purely intellectual ideas; that many logical difficulties cannot be solved; [1460] that no absolute distinction can be drawn between much and little, in short between all differences in quantity; and that it is the most natural course in all such cases to follow Chrysippus, and to avoid the dangerous inferences which may be drawn by withholding judgment. [1461] Arguing from these facts, Carneades concluded at first in regard to impressions of the senses,