12.3 Sophisms and the development of knowledge in logic

The "Covered" sophism can be reformulated in such a way that another side of the problem behind it will be revealed.

Suppose that, next to me, it is not Sidorov who, having covered himself, is standing by some other person, but I do not know about it. Do I know Sidorov? Of course I know. But next to me is someone unknown. And what if it is Sidorov?

Answering "I know," I am in some measure risking, for again I can find myself in a position where, knowing Sidorov, I did not recognize him until he was revealed.

You can even simplify the situation. Next to me, not hiding, stands Sidorov. Do I know him? Yes, I know and find out. Do I know that Sidorov has five children? No, I just do not know. But without knowing such an important fact, which most likely determines everything else in Sidorov’s life, what are my isolated information about him?

This simplified to the limit and naive-sounding examples hint, however, at important points concerning knowledge. It is always incomplete in a certain sense and never acquires a final, ossified outline. Elements of knowledge are diversely interconnected. Doubt in some of them without fail to other areas and elements, and ambiguity spreads evenly to the outskirts of the knowledge system in a light haze throughout the system. The introduction of new elements, especially if they look significant from the point of view of this system, often makes it necessary to rebuild it all.

The scientific theory as a statement system resembles in this plan a building that has to be rebuilt from top to bottom, adding a new floor each time it is revised.

All these hints of incompleteness, systemic and constant restructuring of knowledge can also be seen - with a great desire, however, - to be seen in sophistries like “Covered”.

Much of what is said here about scientific knowledge applies to all other forms of knowledge.

There is knowledge of Hamlet, the Prince of Denmark, described in the tragedy of William Shakespeare. But how many talented actors, so many different Hamlets. The well-known Russian actor V. Kachalov depicted in his Hamlet almost exclusively one filial love for his mother. Throughout the tragedy, he emphasized, above all, the words expressing this love. Other actors bring to the fore the loneliness, abandonment, helplessness, utter despair and complete impotence of Hamlet. Sometimes, on the contrary, will, strength and power are seen in him, and all his actions are given the character of a planned and predetermined evil. There were Hamlets-philosophers, abstract thinkers, not so much acting and feeling, as reflecting over everything and analyzing weight. There were Hamlets lost in the palace surroundings.

Hamlet in the description of W. Shakespeare is only a literary character, so to speak, a theoretical, “unpresented” Hamlet. Hamlet in the play of Shakespeare is the "objectification" of literary Hamlet. Full knowledge of Hamlet requires the unity of the theoretical and the substantive, literary and scenic. With a very bad performance of the play, you can say: “I know Hamlet, but I do not recognize him.”

The considered sophisms involve, in addition to general issues, logical problems as well. In particular, they draw attention to the distinction between extensional and intensional contexts, which is important in modern logic. The peculiarity of the second is that they do not allow replacing each other with different names denoting the same subject. The form "Electra knows that X is her brother" is just a special case of intensional expressions. Substituting into this form instead of the variable X the name Orest gives a true statement. But, substituting the name “this covered person”, denoting the same person as the name “Orest”, we will get a false statement.

Of course, this distinction is now well known in logic. But in gray antiquity, when even logic as a science did not exist, it was possible, nevertheless, if not to express it clearly and distinctly, then at least to feel it. This was done by “Electra” and “Covered”. They indicated, moreover, the dangers of neglecting this distinction.