The ‘empirical concept’, or scientiﬁc method of determinate abstraction, is the bridge whereby della Volpe passes from the 1950 Logica to the 1956. The concept, the logos, is a feature of both versions and its importance is indicated in the original (1942) work. However, in the 1956 version, the ‘concrete’ is semantic fusion of thought and language. In the ﬁrst, the concrete is a fusion of the multiplicity of the real and the semantic unity of the concept. In the ﬁrst version, the unity of logic contains the multiplicity of the real, but does so in thought. In the second, language-thought is revealed by scientiﬁc abstraction to be a semantic representation of multiplicity. The ﬁrst version strives for a materialist theory of cognition — the second for a theory of determinate semanticity. The logos is a common element, but in the ﬁrst as a gnoseological instance, in the second as semantic key to gnoseology: in other words, in the ﬁrst, language is the key to experience (a gnoseological problem) and in the second semantic determinacy is the key to knowledge (a theory of historical epistemology).
The immediate political context of the second version is 1954-5, the lectures prepared for the Istituto Gramsci in Rome, on ‘La struttura logica della legge economica nel marxismo’.  The publication of the new edition of the Logica (the Preface is dated March 1956) coincided coincidentally with attempts by members of the review Ragionamenti to strengthen della Volpe’s critical stance vis-à-vis the PCI’s orthodoxy. Ragionamenti reviewed his Poetica del cinquecento in September-October 1955, and Il verosimile filmico in the November-December issue.  In the January-February 1956 number, della Volpe contributed a review.  In the November 1956 supplement, the journal, whose political complexion was left-socialist, condemned Soviet action in Hungary by a judicious but ultimately damning analysis. The connections, based on personal respect and friendship, were lost in the Socialists’ drift to the right, their attempts to split the PCI, and della Volpe’s rallying to the defence of the Party.
The second, 1956, version of the theory of determinate abstraction runs:
From the preceding one can already infer that the logical, which is to say gnoseological, structure, of the Marxist economic law is well symbolized by the above-mentioned methodical circle of concrete, abstract and concrete, or circle of the reciprocal functionality of matter and reason (induction which is deduction and vice versa): this is equivalent to the determinate or historical abstraction in economics, which is substituted for the indeterminate, or a prioristic and imperfect, abstraction used by bourgeois economics. It is equivalent, sub specie logicae, to the historico-sociological method of Marxist economics or the critique of political economy. Avoiding metaphor, the logical structure of the law of economics in the Marxist sense comprises: (a) the problematized concrete or datum (historico-material instance); (b) the hypothesis or setting up of normative, non-absolute means (tr. — in the mathematical sense) of the antecedents or conditions of the given consequent (historico-rational instance); (c) the criterion of practice which validates, or veriﬁes, the hypothesis, turning it into a law (last instance of the historical reciprocal functionality of given and hypothesis, matter and reason, induction and deduction).
But this also means that the above three logical aspects are effectively common to all knowledge worthy of the name, that is, to all knowledge as science, and hence no longer mere knowledge or contemplation: it means that ultimately there is only one science, because there is only one method or one logic: the materialist logic of Galilean or modern experimental science, hence, broken out from that implicit, more or less mathematized, platonism, which is the philosophical setting of the science of all bourgeois scientists from Galileo to Einstein. It follows that, from physical to moral law and thence to economic, the techniques which constitute laws certainly vary according to the variation of experience and reality. For example, mathematics enter with their calculations as an essential constitutive element in the elaboration of physical laws in general, while on the contrary they can be applied only occasionally and then only as an auxiliary, statistical, element, in, for example, the elaboration of moral (social) laws, and also in the elaboration of economic laws, where, for example, the pure or abstract mathematical-economic curve is destined to have substituted in Marxist analysis a kind of historized curve; but the method, the logic, whose symbol is the concrete-abstract-concrete circle, does not vary. ‘History itself [says Marx in the Philosophic manuscripts] is a real part of natural history — of nature developing into man. Natural science will in time incorporate into itself the science of man, just as the science of man will incorporate into itself natural science: there will be one science.ʼ 
Della Volpe goes on in a footnote to criticize the Soviet philosopher Eval’d Il’enkov for associating the abstract with the simple, concrete with the complex. Things would be clearer if Il’enkov had realized that scientiﬁc abstraction was historical abstraction, part of a continuous logical process. Della Volpe wishes here to assert the equivalence of historical and logical. Where Marx, however, uses the future tense to argue for the unity of science, della Volpe uses the present.
This version attenuates those elements of the earlier version which are retained. Earlier in the footnote, a reference (to orthodoxy refers to Lenin’s technical ‘criterion’ of practice. In this second version, the problem of practice is reformulated in this way: if practice closes the c-a-c circle, that is, closes the scientiﬁc-logical moment, it is a logical instance of a philosophical dualism — of matter and reason. Thus, the fusion undertaken by orthodoxy is not materialist but dualist, a fusion of materialism and rationalism in which the latter is subordinate. In the ﬁrst version, della Volpe tried to overcome the problem of orthodoxy’s dualism rather than, as he was later to do, criticize it. In the second version, science resolves the dualism of materialism and rationalism — but the test, the veriﬁcation, is one-sidedly scientiﬁc — experience itself must conform to the principle of non-contradiction (whence the argument for della Volpe’s alleged dogmatism!) Materialism is shown to be unequivocally the method of scientiﬁc reason — not a metaphysical theory of the activity of ‘matter’. The intellect resolves the political schism between matter and reason, dogmatism and negative criticism, by means of hypothesis, innovation.
The earlier version reads:
Therefore, that the determinate abstraction, the method of economic science, is the same thing as the speciﬁc conception or method of the philosophic sciences is shown on the one hand by the fact that they share as presupposition the materialist rejection of the a priori, and on the other hand by the fact that they are both resolved in sociology (the critique of political economy is itself sociology: Marxist sociological economics), or in history-science, the (materialist) science of history: in short, both are experimental conceptions or testing (tauto-heterological identity). This means, as we have seen, that ultimately there is only one science, because there is only one method or one logic: the materialist logic of Galilean experimental science. Hence, from physical to moral law and to economic law and so forth, the techniques which constitute laws vary according to the variation of experience and reality, and, for example, mathematics which provide in their processes of ‘transformation’ only structures gnoseologically neutral in themselves (the contemporary mathematizing philosophy of logical positivism, for example, is only, we repeat, a modern scholasticism), (mathematics) enter with their calculations and functions as an essential constitutive element in the elaboration of physical laws, but on the contrary can only be an auxiliary (statistical) element in the elaboration of moral (social) laws and so forth; but the method, the logic, whose symbol is the concrete-abstract-concrete circle, does not vary: the circle shows us the three logical-gnoseological aspects common to all knowledge in so far as it is scientiﬁc — and hence no longer mere knowledge or contemplation: (a) the problematic given or historico-material instance; (b) the hypothesis or historico-rational instance (setting-up of hypothetical means (tr. — in the mathematical sense) of the antecedents of the problematized datum); (c) the experiment or closing of the circle of reciprocal functionality of datum and hypothesis or matter and reason. 
SOURCE: Fraser, John. An Introduction to the Thought of Galvano Della Volpe (London: Lawrence and Wishart, 1977), p. 83-87. The endnotes refer to the Italian sources. See also:
Della Volpe, Galvano. Logic as a Positive Science, translated by Jon Rothschild. London: NLB, 1980.
Logica come scienza positiva was originally published in 1950. A second, revised edition was published in 1956. The 1956 edition was reissued under a new title in 1969, which is English would be Logic as a Historical Science. The English translation is based on the second, definitive edition. Frasers book is the only book-length study of Della Volpe in English.
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