Logic, as a “logic of investigation” [Popper] or a “logic of science” [Carnap] is, in the history of logic, a recent development. Prior to the emergence of the empirical sciences logic had been associated with Aristotlean syllogisms. However, the rise of mathematics and the physical sciences demanded that logic no longer be equated with simple or syllogistic proof. Bacon, Descartes and Leibniz undertook the earliest development of logic as a logic of investigation which had as its essential purpose the discovery of new truth. This would fulfill logic’s commitment to science. Bacon, considered by Marx the founder of English materialism and of “contemporary experimental science,” looked upon scientific truth as emerging from inductive logic. Descartes and Leibniz, on the other hand, looked upon logic as a branch of mathematics and therefore chose deductive logic as the method of discovering truth. Both Descartes and Bacon looked upon logic as a means of studying objects of nature and therefore as a means of discovering truth. The logical-mathematical method was viewed by Descartes as a means of solving scientific problems. Leibniz, like Descartes, expressed profound optimism concerning the possibilities of logic facilitating discoveries in new areas of research. Descartes’ objective, to construct a single mathematical system within the limits of deductive logic, was attempted in the early twentieth century by Russell and Whitehead in their Principia Mathematica and by Wittgenstein in the Tractatus. These efforts, though failing to establish a single deductive system to explain reality, or to as Russell suggested confirm “the appearance of the anticipated sense data,” did spur on later efforts of logical empiricism.

On the side of inductivism Bacon and later John Stuart Mill made robust claims. Mill asserted that every process leading to scientific knowledge could be represented as an inductive process. Such an assertion brought forward its opposite. The earliest criticism of Mill’s Logic was based upon its being solely bound to the sense content of phenomena and its failure to address properties, aspects, relations or structures of the object that is empirically given.

William Whewell, not unlike much that has followed, argued that empirical laws–meaning in Mill’s sense the causal connections of sense perception –could not lead to the discovery of new scientific laws. His view was that the discovery of new scientific laws introduced new scientific abstraction, which thereby serve to discover new connections between empirical data and thus form new theoretical systems. For Whewell this process of discovery is founded upon the process of applying a priori ideas to empirical material. He sought to discover new scientific laws through the introduction of new levels of abstraction. Whewell argued that empirical connections alone did not in and of themselves suffice to establish scientific discovery. For Whewell the new level of abstraction necessary was identified with a priori conditions of knowledge. It was here that new empirical connections could be discovered. The substance of Whewell’s argument, and that which remains valid in the rejection of old type inductivism, is the need to go beyond that which is given in sensation and the method of identifying sense data with the real. Mill’s inductivism was undermined by its inability to go beyond sense datum which placed radical limitations upon the possibilities of knowledge. It was therefore at variance with the advances being made in the natural sciences.

The unsatisfactory results of Mill’s Logic along with the enormous achievements in the natural sciences created the demand for new logico-methodological approaches to the questions of scientific knowledge. Moreover, the structure of scientific knowledge was increasing in complexity occasioning the use of mathematics to explain the unobservable. Ernest Mach and the empririo-critics suggested a new positivism that based its outlook upon Hume’s epistemology. [See Lenin, Materialism and Empririo Criticism, David Hillel Ruben.] Empririo criticism, while enjoying some popularity, failed to provide the necessary logical apparatus to address the pressing needs of science. Problems of logic were assuming a daily presence in the activity of science. Under these circumstances the logical, and more specifically the logico-methodological apparatus of theory, assumed a place of practical necessity in the unfolding of research. Russell and Whitehead’s Principia Mathematica and Wittgenstein’s Tractatus sought to systematically address this situation. The formation of the Vienna Circle and the Society of Empirical Philosophy in Berlin attempted to construct upon the foundations of Principia and the Tractatus a consistent philosophy. They viewed past philosophy as a fetter to science. The objective then was to construct, based upon mathematics, a logical apparatus by which to determine the truth of the statements of science.


At the stage when the practical tasks of logic are to be found in the construction of the methodological apparatus of scientific knowledge that logical empiricism assumes centrality. What Suppe calls “The Received View” is an attempt to discover the “given” content of knowledge and the empirical significance of its elements. Logical empiricism, therefore, makes robust claims both from the standpoint of its negative and positive objectives. On the positive side it seeks a precise analysis of the cognitive significance of the concepts and statements of science in order to disclose their empirical or given content. Its negative function is to eliminate speculative philosophy from scientific discourse. This objective is best described as removing from statements of science all which is not reducible to that which is given in sensation. These objectives establish the reductionist and non-realist dimension of logical empiricism. Simply put, the logical empiricist program constitutes the reconstituting of the system of existing knowledge. Whereas for Bacon and Descartes the logic and methodology of science was directed to giving priority to searching for methods and techniques for discovering new knowledge, the logical empiricist seek to confirm existing knowledge.

Logical empiricism presents the primacy of empirical knowledge, what they have called the “directly given” based upon the reduction of knowledge to what is considered its primary empirical elements. Such a reduction ipso facto eliminates the possibility of levels of knowledge in the formation of knowledge, and literally collapses the theoretical into the empirical.

Logical empiricism has attempted various logical means of addressing the problem of levels of knowledge, while simultaneously maintaining their reductionist posture. For example, Russell proposed an extensional logic based upon the idea of nomological statements. Herein is reflected a change in the fundamental principles of methodology and logic of the eighteenth and nineteenth centuries. The roots of this change are to be found in the enormous complication of scientific knowledge and the development of the mathematical apparatus of science, the decline in the role of direct visualization or observation in scientific experimentation. The objective is to order and organize in a rigorous manner the exact meaning of scientific assertions and concepts. One would find it difficult to disagree with this objective if it is properly contextualized. However, to absolutize such an objective occurs at the expense of the creative and emergent characteristics of knowledge. Thus Russell and Whitehead’s Principia developed a mathematical logic that is extensional, the logic of truth functions. The truth value of each statement capable of being subdivided into component statements is determined unambiguously by the truth value of these components or, in other words, each component statement is a truth function of its components. If knowledge of reality requires reconstruction into a language whose grammar is extensional logic, the result of this reconstruction would be a set of statements interrelated by truth values. In order to rigorously define the “significance” of any statement, under this concept of logical structure, it is necessary to examine the connection of the given statement with other statements in terms of their truth values, that is to demonstrate of what statements the given statement is a truth function. It is, however, obvious that such a reductionist strategy cannot proceed endlessly. Such a system must contain ultimate statements, representing the limits of reducibility. Since the truth value of ultimate statements is not based upon the logical connection between them, they may only be postulated by some extra-logical means. It is at this point that purely logical procedures are of little value. The solution must be discovered at the level of epistemology. Thus the logical apparatus of the Principia finally rests upon certain epistemological and philosophical foundations. Russell rests upon an idealist, neo-Platonist epistemology, holding that sense perception is the ultimate source of experience. [See Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy, p. 363.] For Russell all knowledge is reducible to a set of atomic statements or assertions, which are empirically verifiable by sense perception. Therefore, for logical atomism, all knowledge is a set of statements about sense data and the cognitive meaning of the set of fundamental statements is revealed in the last analysis through the empirical sense-perceived conditions of truth. Therefore, to understand an assertion or statement consists in knowing its empirical conditions, the sense datum which verifies them. Russell formulated this relation thusly, “Verification always consists in the appearance of the anticipated sense-data.” Schlick used the phrase “The meaning of a proposition is the method of its verification.” Obviously, the verification principle of logical atomism relies upon observation or sensation. But what of non-observable statements? Wittgenstein’s answer in the Tractatus held that logical and mathematical propositions do not constitute knowledge of reality, they are contentless and empty. They are basically guidelines indicating the permissible transformations of modes of linguistic expressions, but in no way bear upon their meaning. Logical propositions are tautologies which are true under any and all combinations. Such tautologies convey no knowledge of the actual world or bring forth no new information [see Suppe on the Received View]. Carnap later on took up this same view. [The Logical Structure of the World.] According to this view the world assumes the structure of mathematical logic and therefore proposes that the world is in a one to one correspondence with logic. [Russell, The Structure of the External World.]

The Theory of Correspondence

This unique theory of correspondence brings together the reductionist and anti-realist positions of logical empiricism. While later rejecting the earlier atomist ontology [Suppe, p. 67] it sacrificed nothing in terms of its logic and methodology. It merely separated analytical and synthetic truths [Suppe, p. 67]. Hindess goes so far as to suggest that neo-positivism treats all ontology as strictly meaningless [p. 239] Carnap as well argues in this direction [Schlick, 1963, p. 868] this constituted an abandonment of ontology by Carnap and the Vienna Circle. This constituted a solipsistic turn, and as V. S. Shvyrev suggests, the universalization of formal logic and the effort to build a theory of knowledge resting exclusively upon concepts of formal logic. Shvyrev finally makes the following point: “. . . abandonment of ontological presuppositions such as the theory which constitutes reality as a set of atomic facts does not in any way influence the essence of epistemological logic. . . . Therefore, by disregarding the pluralist ontology of logical atomism, the neopositivists of the Vienna Circle were able to borrow the fundamental characteristics of the conception of the epistemological logic of Russell and Wittgenstein: the view of knowledge as a system of extensionally related statements, the understanding of the truth of ultimate statements as empirical truth, and the fundamental opposition presumed to exist between the logical character of the propositions of both logic and mathematics on the one side, considered as procedures for symbolic transformations, and, on the other side, the propositions of the rest of science considered as empirical knowledge of reality” [pp. 15-16]. Thus the problem now becomes that of cognitive significance of statements. Statements therefore, either have formal meaning–i.e. synthetic significance, or empirical meaning–i.e., analytic significance. Finally, logic and mathematics and later semantics are contrasted to all other sciences as a formal science.

However, the problems of observation and empirical significance are seen as problems of the relations of logical knowledge to sensory knowledge–of tautological statements to sense datum [quote Carnap and Schllip].

Assertions containing empirical conditions of truth are contrasted to those which contain formal meaning. This synthetic-analytic distinction first appeared in Kant’s Critique of Pure Reason [Suppe]. This distinction can be characterized as the observation-theoretical distinction. It is crucial to logical empiricism’s attempt at carrying out a logical analysis of knowledge directed at disclosing its empirical significance. Shvyrev suggests that logical empiricism’s concept of empirical significance reduces the logical and in particular the intellectual content of knowledge to sensory knowledge, to the expression of given sensations in speech, thereby depriving thought of its distinctive quality as the highest stage of reflection [p. 16]. Suppe [p. 80] draws attention to the untenability of the observation-theoretical distinction as developed by logical empiricism. Using the findings of Putnam-Achinstein Suppe argues that logical empiricism onesidedly develops the distinction. Moreover, he argues that logical empiricism artificially presents the distinction.

Underlying the concept of empirical significance is the conclusion that the cognitive meaning of an assertion about the world consists of the expression of an immediate site of things. Joergensen quotes Carnap as saying, “The meaning of a statement consists in its expressing a (thinkable, not necessarily also an actual) state of affairs. If an alleged statement expressed no (thinkable) state of affairs, it has not meaning and hence is only apparently an assertion. If a statement expresses a state of affairs, it is at all events meaningful, and it is true if that state of affairs exists and false if it does not.” [p. 29] The point is that for a statement to be factual it must be grounded upon experience. For Carnap the use of logistical concepts allows for the statements of various sciences being transformed into statements about immediate experiences having the same truth-values as original statements. Therefore, all scientific statements are capable of being verified or falsified by means of immediate experience. This method of achieving empirical significance came to be known as the principle of verification. For logical empiricism in general the meaningfulness of reality-sentences is connected to their verifiability.

The question of how to verify reality sentences is of utmost importance. Popper establishes falsification as the criterion of the meaningfulness of statements. Using this criterion of meaning Popper proposed to sort out empirical-scientific sentences from a priori analytical sentences (logical and mathematical) as well as from nonfalsifiable reality sentences (metaphysics). Popper is, therefore, suggesting rather than an absolute concept one that argues for “degrees of testability (Prufbarkeit)” (Joergensen, p. 73). Empirical testability is identified not with verification, but with falsification–i.e., the possibility of empirical refutation of statements. The principle of falsifiability is regarded by Popper as the “criterias of demarcation,” the distinction between scientific empirical knowledge of the world and “metaphysical systems” [V. S. Shvyrev, p. 21). Carnap in the essay “Testability and Meaning” (Philosophy of Science, Vol. 3] argues that truth and confirmation must be distinguished. Truth he says is an absolute concept, independent of time, confirmation, on the other hand, is a relative concept, the degree of which varies with the development of science. Carnap differentiates directly testable reality-sentences from those that are indirectly testable. Directly testable reality sentences are those based directly upon observation. Indirectly testable reality sentences consists in directly testing other sentences that have certain relationships to it. Concerning verification and confirmation and thus the basis of establishing empirical significance Carnap says,

If by verification is meant a definitive and final establishment of truth, then no (synthetic) sentence is ever verifiable, as we shall see. We can only confirm a sentence more and more. Therefore, we shall speak of the problem of confirmation rather than of the problem of verification.

Carnap, finally, proposer that logic, rather than a fact for verification is directed to confirming sentences. As such, as with further developments in analytic philosophy, logic and methodology are primarily tools for formalizing given knowledge.

With this overview I will proceed to the works of Mill, Russell and Carnap.

Mill’s Logic, Scientific Inquiry and Deduction
In his System of Logic Mill sought to separate the empirical foundations of natural science from Humean causality. As such, he wished to demonstrate that the philosophy of experience could be the epistemological foundation of scientific inquiry. Although his epistemology remained bound to the sense content of phenomena and remained traditional and empiricist, his logical approach was innovative. His Logic is essentially a discussion of inferential knowledge and the rules of inference. His final object was to establish the superiority of inductive reasoning. As far as deduction is concerned he held it could never be the source of new knowledge. Mill equated deductive reasoning with its most common syllogistic form and argued that the syllogism cannot contain more than is in its premises. As he posited, “no reasoning from generals to particulars can, as such, prove anything since from a general principle we cannot infer any particulars, but those which the principle itself assumes as known.” However, Mill defends deduction on the limited grounds that deductive and inductive reasoning proceeds “from particulars to paraticulars.” Syllogistic reasoning proceeds, “All men are mortal; Jones (not yet dead) is a man; therefore, Jones is mortal.” Our evidence that Jones wil die and therefore is mortal (a particular truth) is based upon our evidence that Smith, Johnson, Harris have died and others who in significant ways are like Jones have died. We, therefore, infer from thier deaths to his. We infer from one set of particulars to another. Finally, it is experiential evidence upon which prediction rest. Experience is the real foundation of inference. Deduction is a manner of interpreting our initial inference. The value of deduction rests, therefore, upon its capacity to prevent misinterpretation. However, no new information is brought forward. Syllogisms merely recover from general statements particular ones that were previously assumed. Deductive or syllogistic reasoning is tautological. Mill refers to deductive inference as apparent inference. The propositions that arise from deductive logic are called verbal propositions.

Induction, on the other hand, is that method of logic which gives non-verbal general proposition that go beyond apparent observation. Real inference comes only from induction.

Inductive Reasoning and Scientific Explanation in Mill’s Logic

Induction is for Mill the source of substantive general propositions. He uses the term induction in two ways: (a) as inference and (b) as investigation. Mill is here proceeding in a Baconian manner. He held that the cannons of the experimental method have the same function for induction as the cannons of syllogisms have for deduction. [O. A. Kubitz: 39] Mill’s definition of induction is classic and significant. Of induction he states: it is

the operation of discovering and proving general propositions. It is true that . . . the process of indirectly ascertaining individual facts is truly inductive and that by which we establish general truths . . . But it is not a different kind of induction; it is a form of the very same process: since on the one hand, generals are but collections of particulars, definite in kind but indefinite in number; and on the other hand, whenever the evidence which we derive from observation of known cases justifies us in drawing inference respecting even one unkown case, we should on the same evidence be justified in drawing a similar inference with respect to a whole class of cases. The inference either does not hold at all, or it holds in all cases of a certain description, in all cases which in certain respects resemble those we have observed. [Logic: 208]

Herein we discover Mill’s dual usage of induction. The first is the collection of facts–here MIll is wedded to the Baconian experimental method. Secondly, induction is used to infer from particular observation. [Kubitz: 144]

Causality in Mill’s System

Mill, in order to propose the possibility of inference from particulars to general truths, assume dregularity and constancy in nature. Such an assumption is rooted in Newtonian mechanics. Newton argued that the movement of solid particles occurs in an absolute spatial and temporal framework. Their movements, moreover, are governed by immutable laws. The method of finding these laws was characterized by Newton as a process of analysis and synthesis. Analysis included the experimental operations; synthesis the mathematical and deductive operations Mill, however, gave primary to the analytic or experimental. For Mill it is evident that the “uniformity of the course of nature is . . . itself a complex fact, compounded of all the separate uniformities which exist in respect to single phenomena.” [Kubitz: 48, quoted from Mill’s Definition of Political Economy] Mill says of this method,

“the method of the practical philosopher consists . . . of two processes; the one analytical, the other synthetical. He msut analyze the existing state of society into its elements, not dropping or losing nay of them by the way. After referring to experience of individual man to learn the law of each of these elements, that is to learn what are its natural effects, and how much of the effect follows from so much of the cause when not counteracted by any other cause there remains an operation of synthesis; to put all these effects together, and from what they are separately, to collect what would be the effect of all the causes acting at once. [Early Essays: 152-153]

General laws are general regularities emerging from the synthesis of particular regularities. As he states in the Logic, “what happens once, will under a sufficient degree of similarity of circumstances, happen again.” [quoted from Nagel: 317] The assumption of constancy in nature makes this possible. Thus an effect has a constant cause given constancy of circumstance. Thus Mill argues, causality is an “unconditional invariable antecedent” [Logic: 326] Inductive logic has as its principle purpose to discover nature’s regularities–i.e., the “unconditional invariable antecedents.” Mill suggests that the problem of induction is to discover, “the fewest and simplest assumptions, which being granted, the whole existing order of nature would result.” This search for atomic truths, as it werre, will be rediscovered by Russell. Mill places this matter in the follwoing words, “What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred?” [Logic: 317] Mill locked upon this as a long process which occurs over generations.

Newtonian Macrophysics and Millsean Causality

It is helpful, I believe, in understanding Mill’s concept of causality to look at the basic assumptions of Newtonian Macro-physics. Professor Horz and his colleagues have written on Newtonian causality. If the state of a physical system, i.e., the position coordinates and momenta, and the forces affecting it are known with absolute precision at a given moment of time, the state of the system at any other time can be predicted with absolute accuracy. Characteristic of this classical-mechanical form of causality is the assumption of precise predictability.

According to this and the Millsean conceptualization law and causality are identical. Its power rests with its mathematical elegance and systematic construction which is based upon experimentally verified knoweldge and fully tested in practice [Horz]. Mill’s assumption that law-likeness or regularity in nature reflect invariance and precision are rooted in Newtonian mechanics. Moreover, Kubitz suggests that Mill’s understanding of analysis and synthesis was similar to Newton’s. According to Kubitz Newton and Mill adopted Stewart’s position on analysis and synthesis. Stewardt reversed the Greek foundation holding that the mathematical or geometric was distinct from that of the physicist. Mathematics begins from hypothetical assumptions and the object is to arrive at a known truth or datum by reasoning synthetically–a path that allows us to later on retrace our steps. The synthetic process is obtained by reversing the analytic process. Since both processes have in view the demonstration of the same theorem or the solution of the same problem, theyt form in reality different parts of one and the same investigations. [Kubitz: 173] Stewart states the problem in the follwoing manner,

Our analysis necessarily sets out from known facts, and after it has conducted us to a general principle, the synthetical reasoning which follows consists always of an application of this principle to phenomena, different fromm those comprehended in the original induction. [quoted in Kubitz: 263]

Both Newton and Mill appear to have adopted this process. Analysis is to be understood as the experimental and observational stage, while the formalization of the results into law is considered the synthetic stage. The discovery of cause results from the formalization of observation and experiment.

* Hilary Putnam poses the question in the manner which asks, “How does the mind access the world.” Putnam, rather than transcendental idealism, argues for what he calls the method of internal realism, where concepts are intrinsically connected to the objects of reality. As he puts things, “‘Objects’ do not exist independently of conceptual schemes. We cut up the world into objects when we introduce one or another scheme of description. Since the objects and the signs are alike internal to the scheme of description, it is possible to say what matches what.” [p. 52] Putnam, therefore, suggests a transcendental connection which seeks to deny the correspondence theory of truth while upholding the necessity of sense datum being connected to a conceptual scheme. Putnam goes beyond Whewell, precisely by expanding the definition of what is real. The real becomes as well the conceptual.

* This process, under different circumstances and with different objectives, continued with logical empiricism, which declared the principle objective of logic to be the verification and later the confirmation of existing knowledge. Whewell did, however, address a principle weakness of Mill’s inductivism–i.e., its reductionism–while leaving unsettled the question of realism, an epistemological question which awaited the post positivist era to be addressed.

* Bhaskar p. 36 argues that neo-positivism holds that statements about being can be reduced to statements about knowledge, or putting it another way, ontological questions can be transposed into epistemological ones. Bhaskar calls this the epistemic fallacy.

* Popper felt that the initial statement of logical empiricism had complicated matters and that “logical positivism destroys, not only metaphysics, but also natural science. To correct the problem Popper proposed rather than verification, the method of falsification.
* See the contemporary efforts in mathematical logic, chaos theory, far from equilibrium dynamics and rational choice theory.

* Mill’s position on induction and deduction was demonstrated through mathematics. Geometry was considered by him to be based on deductive logic. Mill argued that the conclusions of geometry are based on premises grounded in observation and generalization from these observations. Engels, interestingly, arrived at a similar conclusion.

* This method of dealing with problem of analysis and synthesis reappears in logical empiricism, particularly the work of Carnap and in analytic Marxism, but in the more sophisticated form of the relationship between empirical and theoretical knowledge.

Bhaskar, R.A., 1997 [1975], A Realist Theory of Science, London: Verso
Hörz, Herbert Philosophical Problems in Physical Science (1980). Minneapolis. Marxist Education Press.
Kubitz, O. A. The Development of John Stuart Mill’s System of Logic. (1932).Illinois studies in the social sciences
Mill, John Stuart. (1909) System of Logic. New York. Harper and Brothers
Nagel, Thomas. The View from Nowhere (1986), Oxford University Press
Putnam, Hilary, Reason, Truth and History, (1980), London, Cambridge University Press
V. S. Shvyrev, “Some Problems in the Logico-Methodological Analysis of the Relation Between the Theoretical and Empirical Levels of Scientific Cognition,,Soviet studies in philosophy, Volume 8

About Anthony Monteiro

I am a activist and scholar who is a professor in the Department of African American Studies at Temple University.
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