Felix qui potuit rerum cognoscere causas

Prolix introductions are often neglected. An excellent reason to be concise.

Many a symptom tells us that contemporary Logic is seriously ill. What credit could the common sense recognize to someone who assured the possibility to dissect an orange in such a way that with its pieces two oranges identical to the former could be recomposed? Neither Banach-Tarski's and Hausdorff's theorems (Skolem 1962, Lecture 11, or, more in details, Jech in Barwise 1977) are the sole manifestations of a severe disease. The situation of uncertainty determined by the fact that logical paradoxes are still waiting for a general and definitive solution compels the orthodoxy to nearly unbelievable contortions in order to save a merely apparent coherence.

Some examples. What about the theorem of the classical set theory according to which (Suppes, 1972 Theor.50) the set of individuals identical to themselves is empty? And what about the total elimination of variables (Schoenfinkel in V. Heijenoort 1967)? What about Lowenheim's Theorem? What about the truth functional analysis of conditionals? What about the theorization of truth?

Nowadays Logic is a freakish and esoteric doctrine far from our common sense, and the crumbling zones are too numerous to hope that the vice be superficial. Problems cannot be solved until we do not get out of the approach by which they have been born, says an old adage. Actually a radically new approach is needed.

For an unknown author, an almost infallible way to fall into ridicule is to begin by declaring that his results are important, My dilemma is then this: to lie or to face the charge of intellectual autolesionism? Someone says: My aim? To show the fly the way-out from the trap. and suddenly a chill casts over the gathering; yet the aphorism is not mine (Wittgenstein, 1953 p.309). It is a question of previous authoritativeness and mine, probably, entails a general inattention. Nevermind: the success is nearly always wrong, if Schopenauer is right. I am not so naive to think that history demonstrates the unavoidable success of meritorious works. History demonstrates only the unavoidable success of the meritorious successful works. What do we know about the rest? A bad destiny, yet not the worst: chronicles narrate that Hyppasus of Metaponto was put to death for having made public the existence of incommensurable quantities (hence my temptation to proceed apocryphally).

On the other hand already Locke (probably inspired by my contingent situation) realized that a simple and private writer cannot avoid being censured when pursuing the truth through an autonomous path (too many quotations? they are simply an awkward attempt to mask frightening cultural gaps).

Then to write with a serene irony, once the expositive clearness is assured. A really courageous aim, since an obscure text is the strongest defence against the Wildian terror of not being misunderstood.

Indeed an altruistic reason too induces me to publish this work: to put a new and fecund viewpoint at public disposal. Yet the main reason is egoistic: to establish a paternity. I confess that I would be proud to be considered as a great thinker; also because of the high social qualification which traditionally is recognized to the category; he is a stupid, he thinks too much, King Arthur admonished.

So to say roughly, the contemporary logic is crushed down by an intrinsically inadequate bidimensional approach: on one side the sign, on the other side the referent. But such an approach neglects the crucial protagonist of any reasoning, that is the information, the meaning, the mind. I agree that "information”, "meaning”, "mind" express difficult and dangerous notions, but to look elsewhere when they appear on the stage is a loosing ostrich strategy. The primigenial logic that allowed the animal evolution until the homo sapiens sapiens, cannot be a logic of the sign, since the sign appears millions of years later: it must be a logic of information, since information does exist wherever an even primigenial knower exists. No doubt that the sign and the referent too have an irrenunciable place in every realistic gnosiology, but to assume them as sole actors is like to reduce a cruise to the embarking and the landing.

As soon as a third dimension is granted to logic, its problems find a sequence of harmonious solutions. The evidences are too many to represent mere concomitances; only when the path is the right one the lifting of the fog reveals a landscape corresponding to the map we are following. In this sense I firmly believe that these same ideas, perhaps better proposed by other authors, but anyhow these same ideas, sooner or later, will enter into the history of Logic.

I spoke with absolute sincerity. Some smart spirit (Russell?) remarked that a reasonable private income is an indispensable requisite to practise the sincerity. Someone else (who?), not less smartly, remarked that to practise the sincerity is a rather dangerous behaviour if it is not coupled with a massive dose of dullness. Discouraging remarks for him who, like me, possesses a reasonable private income, shrinks from any danger and nevertheless thinks to be in the best conditions to practise the sincerity.