**CRITICISM** — In a general sense, the term designates any philosophical system or approach that, before constructing a metaphysics of the objects of knowledge (v.), first raises the problem of the value of knowledge itself, its possibilities, its conditions, and its limits. As such, it stands opposed both to dogmatism, which takes the value of knowledge as a presupposition, and to skepticism, which denies in principle the possibility of certain knowledge.
In a narrower and more proper sense, criticism is the formulation and resolution that KANT and the subsequent systems directly derived from Kantianism have given to the problem of knowledge and, consequently, to metaphysics. In relation to this meaning, the term is sometimes used to denote any philosophical system that leads to a subjectivist or idealist solution of the problem of knowledge; or, more broadly, any approach that, after Kant, grants to the critique of knowledge a preponderant and totalizing place in the construction of philosophy.
The fundamental lines of Kantian criticism, a historical outcome of the conflation of two antagonistic currents—Hume’s empiricism and Wolff’s rationalism—converge on the essential problem posed at the outset of the *Critique of Pure Reason*: How is scientific knowledge possible, or, in another formulation, how are synthetic a priori judgments possible—judgments in which the predicate adds something to the subject and which are at the same time universal and necessary? Kant reflects: while mathematics and physics have long been on the sure path of science, metaphysics, as evidenced by its endless internal disputes, has not yet enjoyed this fortune. It is therefore necessary for reason to examine itself anew and to determine whether the failure of all attempts to construct metaphysics may not stem from a radical methodological error. Indeed, Kant asserts, such a methodological error does exist: physics and mathematics advance because for a long time they have effected a revolution in the parts of knowledge that pertain to subject and object; in both, reason no longer seeks to conform to an object in itself but proceeds with its own constructions and principles, systematically ordering nature. A similar reversal must perhaps be effected in metaphysics, assuming that it is not our conceptual knowledge that conforms to objects, but rather that objects must conform to our knowledge. The necessity thus arises for a critique of pure reason that undertakes a complete analysis of reason in its a priori structure, in order to uncover all the elements, laws, and functions that are in it prior to any experience, as conditions of scientific knowledge and of experience in general (*Critique of Pure Reason*, Italian trans. by G. Gentile, 2nd ed., Bari 1940, p. 15 ff.). Kant carries out this investigation in the transcendental aesthetic, analytic, and dialectic, which respectively establish the a priori forms of sensibility (intuitions), the understanding (concepts), and reason (ideas). The result is a new conception of knowledge as a priori synthetic activity, whereby knowing is no longer a simple reception of a given standing over against the subject, but rather the objects of knowledge are constructed within the subject itself, according to formal elements derived from its transcendental structure, applied to the matter furnished by reality.
The solution of the *Critique* also resolves the problem of science: mathematics and physics are possible as sciences because the concepts of the understanding—formal elements of a priori synthesis and hence of the universal judgments that constitute these two sciences—have their own objective and universal field of application, namely, first, the pure forms of sensibility (pure mathematics and pure physics), and then the phenomena or sensible representations given to us in experience according to those forms (empirical physics). Metaphysics, however, as a science remains beyond the possibilities of human knowledge, because the ideas of reason (the World, the Soul, God), which metaphysics ought to treat, concern objects (things in themselves, the moment) that are not given and can never be given in experience, and about which, therefore, no science is possible: the Soul, the World, God, as objects of a possible metaphysics, are forever withdrawn from the domain of theoretical reason, which cannot pronounce either for or against them.
The final result of Kantian criticism, arising from an inexact and artificial formulation of the problem, thus expresses itself in a radical relativism, whose sole objectivity is the value universally valid for every human experience, and in a metaphysical agnosticism—which, however, in reality generates itself within Kantian criticism itself, which in its own way is a metaphysics of knowledge.
Post-Kantian criticism assumes manifold forms and directions according to the principles and methods that govern the solution of the problem of knowledge and the various philosophical systematizations born from the Kantian trunk. Alongside idealism in its various expressions—which may well be regarded as a form of absolute criticism for the totalizing role assumed by critique, transforming it into a logic or metaphysics of the transcendental Subject—Neo-Criticism will incline toward psychologism in G. F. Fries and F. E. Benecke; assume a physiological tendency in the founder of German Neo-Kantianism, Lange, and in Helmholtz; a metaphysical tendency in O. Liebmann; a realistic one in L. Riehl; an empiricist one in R. Avenarius; a logistic one in H. Cohen; develop into a theory of values with G. Windelband and E. Rickert; and finally accentuate itself in resolute voluntarism with C. Renouvier, who will attempt to overcome through the free act of faith the phenomenal subjectivism of theoretical reason, which remains almost the common legacy bequeathed to criticism by Kant. Recently in Italy, Neo-Criticism has been developed, in addition to the ontologism of P. Carabellese, by F. Masci and, in relation to pedagogical problems, by M. Maresca.
V. CONOSCENZA; KANT.
CRYPTOGRAPHY — CRIVELLI CARLO AND VITTORE
The simplest systems of transposition consist in writing the text in a rectangle, row by row, and then reading it column by column according to the order indicated by the normal sequence of the individual numbers that form the key-number. One then obtains:
| 2 | 3 | 4 | 5 |
| a | b | a | i |
| m | o | r | i |
| c | a | c | e |
| v | u | t | o |
| l | | | |
and thus the cryptogram BOVAM ELITA COBRU.
Transposition systems can be used with special grilles (such as the Cardano grille or the Sacco grille), can be complicated by double transpositions, and can yield cryptograms that are truly difficult to decipher.
Substitution systems replace each letter, syllable, word, or entire phrase of the plaintext with another letter, a group of letters, a numeral, or a group of numerals. In the 16th century, it was sometimes the practice to substitute signs of cabalistic appearance, soon abandoned because of their cumbersome use. These are the most effective in rendering the text obscure, but they have the drawback of requiring the existence of a written cipher key, which may fall into the hands of the decipherer. There are three types:
a) monoalphabetic substitution: each letter of the plaintext is replaced by another letter (the next one in the alphabet, the corresponding one in a reversed alphabet, etc.). If, instead of letters, pairs of numerals are used, each plaintext letter can be replaced by a two-digit number, and some homophones and nulls can be introduced.
With this system, if properly employed, cryptograms of difficult decryption are obtained;
b) polyalphabetic substitution (invented by DELLA PORTA, perfected by VIGENÈRE and DELASTELLE). To each letter of the plaintext is substituted another letter derived from alphabets that are always different, arranged in an order other than the normal one; in other words, if one must encipher the word ROMA, the R will be replaced by a letter taken from the 1st cipher alphabet; the O from the 2nd, the M from the 3rd, the A from the 4th. To employ these systems, special tables and keys are required. Modern cryptographic machines are based on the same systems, which they complicate with an enormous number of keys and cipher alphabets, yielding millions of different combinations;
c) repertories or codes; to each letter or word of the plaintext are substituted groups of letters or numbers chosen from a repertory that can vary greatly in size, from that of a pocket-sized booklet to that of a large dictionary.
Mixed systems result from the promiscuous use of transposition and substitution systems.
All systems can be infinitely complicated in various ways; one must only take care that the complication be substantial and not merely apparent, and that it does not create possibilities of errors in encipherment and decipherment.
Decryption — Whereas encipherment may be called a science, decryption may be called an art, for although it is based on certain mathematical and linguistic rules, it relies above all on the intuition and skill of the cryptanalyst. Decryption, as old as encipherment (a small treatise on decryption by Cicco Simonetta, secretary to Francesco and Galeazzo Sforza, who lived from 1410 to 1480, is cited), drives encipherment to continuous progress; so much so that today, in the secrecy offered by cryptographic systems, absolute indecipherability is no longer sought, but rather resistance to decryption for a more or less extended period, depending on the importance and nature of the dispatch.
Decryption is based on three notions that the cryptanalyst must possess: a) knowledge of the subject matter treated in the dispatch (if any); b) knowledge, therefore, of the type of language used (diplomatic, military, commercial) and of the formulas, words, or phrases that may recur; c) statistical knowledge of the language employed. By statistical knowledge of the language is meant, in our case, the frequency with which, in each language—or better still, in each type of language—letters and certain groupings of letters or certain words (conjunctions, auxiliary verbs, etc.) recur. In general, the longer the cryptogram, the more its statistical elements will approximate the language’s statistics, and the less difficult its decryption will be; for this purpose, several cryptograms enciphered with the same system may be considered as a single cryptogram. There are, however, systems whose decryption can be attempted even with only 30 or 40 elements.
Carlo Crivelli. Born in Venice around 1430–35, died between 1494 and 1500. He was the brother of Vittore Crivelli. He spent most of his activity in the Marches, where he took refuge after fleeing Venice due to a sudden condemnation (1457). In 1478 he is found in Ascoli Piceno; in 1488 he was in Camerino.
The development of his activity can be easily traced through a series of many signed and dated works, from 1468 (a political painting of the Urbino gallery) to 1493 (the Coronation of Brera, formerly in S. Francesco in Fabriano). From Mantegna and the Paduan school he drew incisive line, vigorous plastic sense, clear and firm coloring, and a love for decorations of garlands of fruits and flowers, fabrics, and precious marbles; but from the outset he modified these models with that decorative sense which, ever more refined, constitutes the principal attraction of his paintings. To it are subordinated the architectural details of the backgrounds, the garments of the figures, and even the features of their faces, contorted by suffering. The drawing is rigid and sharp, the sacred figures hieratically severe, the expression of affections—especially those depicted in sorrow—carried to exaggeration.
Among his principal works are: the political painting with the Madonna and saints (1481), the Madonna (1482), and the Pietà, all in the Vatican Pinacoteca; the Annunciation in the National Gallery in London (1486), delightful for its refined decorative realism; the Madonna of the Candle and the Coronation (1493) in the Brera Gallery, a complete example of what C.’s art could achieve.
Carlo C., not a great master, must be placed among the most sincere artists of all times and regions, and in his paintings he often attracts more than the very greatest. His models, together with those of other Venetians, played a large part in the formation of the Marchigian school.
VITTORE, his brother (b. in Venice ca. 1445, d. between 1501 and 1502), was a close imitator of him; numerous works of his, lacking originality, remain in the Brera Gallery, in various churches and collections of the Marches, and in Italian and foreign collections. — See pl. LX.