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The Role of Logic in Philosophy:
An Appraisal of Bertrand Russell's Standpoint

by Jahnabi Deka


The history of philosophy through the different stages of its development clearly shows the pivotal role played by logic. 'Logic and philosophy' is not an arbitrary combination of two different words, rather it is the case that logic is what Russell called the 'essence' of philosophy. That is, philosophy in its multifarious faces in the hands of different philosophers is always shaped by some specific logic. This relationship was sought in order to be viewed from the analytic standpoint by the famous British philosopher and mathematician Bertrand Russell, who took up the project of showing that modern logic forms the cornerstone of philosophy. Thus Russell focused on a novel project, not discoverable in any philosopher earlier to him.

Russell was in the forefront of the new criticism of the Hegelian system. The chief target of Russell and G.E. Moore, another pioneer of analytic philosophy, right from the beginning of their philosophic careers, was to attack the monistic heart of the Hegelian idealism. Russell while criticizing Hegel's monism simultaneously developed a philosophical system which is pluralistic in nature. This pluralistic character of his philosophy is the consequence of Russell's relentless endeavour to put philosophy on a sound platform of logic:

'It is in logic that we have a glimpse of the inner structure of thought which itself is expressed in language.[1]

Logic provides the foundation to our thought process and the product of this process is expressed in language. Logic thus imparts consistency to every possible sphere of thinking. Philosophical discourse as well depends for its consistency on logic. Logic concerns itself with reality not like empirical sciences, because logic presents the general structure of the world in its formal language. By contrast, empirical sciences seek to describe the world and also explain it with reference to its physical causes and conditions. Aristotle took logic as an instrument for description of the essential structure of the world and reality. Aristotle's metaphysical theories — for example, that the world consists of substances, their attributes and their relations to the substances etc. — are built upon logic.

Logic came to acquire its glory as a distinct discipline after Aristotle. In his six early works, viz, Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics and Sophistical Refutations, collectively known as the Organon, Aristotle developed a complete system of logic. And this system of logic was so exhaustive, so wide in its scope that logic was thought to be a finished discipline for the next two thousand years or so. Especially his Prior Analytics that dealt with syllogistic reasoning continued to overwhelm philosophical thinking until the turn of the twentieth century. In fact it is the same Aristotelian absolutism with Platonic reservations that is repeated in diverse forms in the hands of the scholastic and medieval philosophers.

Aristotle's syllogism is axiomatic in nature. A syllogism has three 'propositions' (declarative sentences that can be either true or false) one of which 'follows' with logical necessity from the joint consideration of the other two. The one that follows is called the 'conclusion' while the other two are called 'premises'. It is characteristic of a syllogism that the conclusion cannot include anything that is not said in the premises; the latter being of a more general nature than the conclusion. Yet the conclusion is treated as a new derivation. This has the implication that the premises are known before hand; that is, our knowledge of the general is primary to that of the particular.

A syllogism starts with a major premise which is universal in nature (e.g. all philosophers are intellectuals). When pressed, how do we come to know the truth of the major premise, the answer is that it again is the conclusion of a higher order syllogism (e.g. all knowledgeable persons are intellectuals, all philosophers are knowledgeable persons, therefore all philosophers are intellectuals). The process goes on hierarchically upward till we reach the self evident primary premises. These primary premises are not capable of any further syllogistic demonstration. They are known by the direct grasp of the mind (nous).

It is obvious how this syllogistic logic has shaped Aristotelian metaphysics. In his early writings Aristotle distinguished between 'form' and 'matter' and maintained that this distinction is only logical and that one cannot exist independent of the other. But afterwards in his metaphysics, he goes to alter his view to the effect that form can and does exist independent of matter. In his Categories Aristotle regarded concrete individual things and beings ('Socrates' as distinct from 'man') as primary substances. But later in Metaphysics he treats these concrete individuals as combinations of matter and form, and goes to assign primacy to form alone.

Bertrand Russell along with Whitehead and others came forward with a new 'logic' to unearth the loopholes involved in Aristotelian logic. Russell examined the influence of Aristotelian logic upon many philosophers and brought to light the fact that these philosophers shaped their philosophy in accordance with the Aristotelian model of logic. In his celebrated essay 'Logic as the Essence of Philosophy', Russell claimed that Aristotelian logic is a 'trivial nonsense', a scholastic collection of technical terms and rules of syllogistic inference. Western metaphysics is a direct result of the Aristotelian conception of subject-predicate logic in which we have to posit a subject term as fundamental. Hegel, as Russell points out, although he started with a critical attitude toward Aristotle's logic, could not help being influenced by Aristotle, with the result that he came to believe that if every proposition ascribes a predicate to a subject, then there can be only one subject, namely the Absolute. This point is directly based on the Aristotelian belief in the universality of the subject-predicate form.

Again, the Hegelian confusion between the 'is' of predication and the 'is' of identity became an object of criticism for Russell. Hegel's example of the sentences 'Socrates is mortal' and 'Socrates is the philosopher who drank the hemlock' depicts this confusion. Hegel asserted that in the second sentence, 'Socrates is a philosopher who drank the hemlock', the copula 'is' expresses a relation of identity between the subject and the predicate. So he argued that it should be the same relation with regard to the first sentence also, i.e. 'Socrates is mortal'. The copula 'is' is supposed to express the relation of identity in both the cases. But this cannot be the case as 'Socrates' is particular and 'mortal' is universal. To say 'particular is the universal' is self-contradictory. Yet in spite of this obvious contradiction, Hegel did not suspect the legitimacy of his logic, but proceeded to synthesize particular and universal in the individual and tried to justify his position by his theory of the 'concrete universal', according to which subject and predicate exhibit 'identity-in-difference', or 'unity-in-plurality'.

In Spinoza also we find that substance is the reality and its innumerable attributes make up the infinite nature of reality. His theory reflects the assumption that reality is expressible only in a language having subject-predicate form.

Again traditional logic does not make any distinction between the two propositions, 'Socrates is mortal' and 'All men are mortal'. Both these statements were regarded as 'A' propositions. But modern logic points out that there is a gulf of difference between the two. The former is a singular proposition while the latter is a general proposition. The logical grammar of the two is completely different from each other. Aristotle and his followers failed to take notice of the difference and took both the propositions to be of the same class. Frege and Peano long after Aristotle pointed out the distinction between the two.

Aristotelian logic is deficient in many other points. One such important deficiency is that it does not recognize the reality of relations. The subject-predicate form being the only form of propositions, all other propositions including relational ones are to be converted to that form. But Russell points out that it is not possible to convert all relational propositions to subject-predicate form. In 'A is older than B', this proposition cannot be interpreted as A's possessing the quality of being older than B; rather does it express a relation between two individuals A and B. This recognition of the reality of relations has the further import of recognizing the reality of a multiplicity of subjects instead of one. Aristotelian logic with its denial of the reality of relations ends with only one subject — the Absolute.

The Leibnizian thesis that the reality is a plurality of monads, which could be derived from the logic of multiplicity of independent terms, is built upon the basis of the logic of terms and propositions. In his paper 'Logic and Philosophy,' L.C. Mulatti gives a lucid presentation of the influence of logic on Leibniz's philosophy. He writes:

'Did not the structure of Leibniz's metaphysics, for example, spring from his logical doctrine? Particularly, his conception of the monad as a substance, which contains all its states within itself and whose history consists merely in a gradual unfoldment of these states, is derived, it is claimed, from his logical theory that all propositions have one and the same logical form which consists in assigning a predicate to a subject — a theory which he shared with all traditional logicians, including Aristotle.'[2]

At this point it may be observed that Leibniz's metaphysics is the result of two opposite logics. Leibniz had a programme of replacing Aristotelian logic, which he thought to be grossly mistaken, with a new logic of his own. However, his profound regard for Aristotle deterred him from executing his plan. Still unsatisfied, Leibniz introduced pluralism into his metaphysics. Reality is not one, but a multiplicity of monads. But among these monads he had to deny any relation as it would go against the Aristotelian teaching. The monads were therefore left to themselves as self-contained, 'windowless'.

Now, we shall turn to Russell's endeavour to nurture his philosophy basing it on a sound logical platform. To justify Russell's attempt, we must take up his theory of definite descriptions, his philosophy of logical atomism and theory of types.

Russell's theory of descriptions was most clearly expressed in his 1905 essay 'On Denoting', published in Mind. Russell's theory is about the logical form of expressions involving denoting phrases, which he divides into three groups:

1. Denoting phrases which do not denote anything, for example 'the present King of France'.

2. Phrases which denote one definite object, for example 'the present King of England' (Edward VII at the time Russell was writing). We need not know which object the phrase refers to for it to be unambiguous, for example 'the tallest spy' is a unique individual but his or her actual identity is unknown).

3. Phrases which denote ambiguously, for example, 'a man'.

Definite descriptions involve Russell's second group of denoting phrases, and indefinite descriptions involve Russell's third group. Propositions containing descriptions typically appear to be of the standard subject-predicate form. Russell proposed his theory of descriptions in order to solve several problems in the philosophy of language. The two major problems are of (a) co-referring expressions and (b) non-referring expressions.

The problem of co-referring expressions originated primarily with Gottlob Frege as the problem of informative identities. For example, if the morning star and the evening star are the same planet in the sky (indeed they are), how is it that someone can think that the morning star rises in the morning but the evening star does not? That is, someone might find it surprising that the two names refer to the same thing (i.e. the identity is informative). This is apparently problematic because although the two expressions seem to denote the same thing, one cannot substitute one for the other, which one ought to be able to do with identical or synonymous expressions.

The problem of non-referring expressions is that certain expressions that are meaningful do not seem to refer to anything. For example, by 'any man is good ' we have not identified a particular individual, namely any man, that has the property of being good (similar considerations go for 'some man', 'every man', 'a man', and so on). Likewise, by 'the present King of France is bald' we have not identified some individual, namely the present King of France, who has the property of being bald (France is no longer a monarchy, so there is currently no King of France).

Thus, what Russell wants to avoid is admitting mysterious non-existent entities into his ontology. Furthermore, the law of excluded middle requires that one of the following propositions, for example, must be true: either 'the present King of France is bald' or 'it is not the case that the present King of France is bald'. Normally, propositions of the subject-predicate form are said to be true if and only if the subject is in the extension of the predicate. But, there is currently no King of France. So, since the subject does not exist, it is not in the extension of either predicate (it is not on the list of bald people or non-bald people). Thus, it appears that this is a case in which the law of excluded middle is violated, which is also an indication that something has gone wrong.

Russell offers the analysis: 'there is one and only one x such that x is the present King of France and x is bald.' According to this analysis, both statements about the present King of France can be false, without violating the law of excluded middle.

Russell did not consider metaphysical assumptions as a prerequisite to his logical doctrine. His first suggestion of logical atomism was:

'I shall try to set forth... a certain kind of logical doctrine and on the basis of this a certain kind of metaphysics.'[3]

He generalizes this approach to metaphysics in his famous article Logical Atomism in 1924 as follows:

'Logic is what is fundamental in philosophy... schools should be characterized rather by their logic than by their metaphysic.[4]

Metaphysically, logical atomism is the view that the world consists in a plurality of independent and discrete entities, which by coming together form facts. According to Russell, a fact is a kind of complex, and depends for its existence on the simpler entities making it up. The simplest sort of complex, an atomic fact, was thought to consist either of a single individual exhibiting a simple quality, or of multiple individuals standing in a simple relation.

The methodological and metaphysical elements of logical atomism come together in postulating the theoretical, if not the practical, realizability of a fully analyzed language, in which all truths could in principle be expressed in a perspicuous manner. Such a 'logically ideal language', as Russell at times called it, would, besides logical constants, consist only of words representing the constituents of atomic facts.

In such a language, the simplest sort of complete sentence would be what Russell called an 'atomic proposition', containing a single predicate or verb representing a quality or relation along with the appropriate number of proper names, each representing an individual. The truth or falsity of an atomic proposition would depend entirely on a corresponding atomic fact. The other sentences of such a language would be derived either by combining atomic propositions using truth-functional connectives, yielding molecular propositions, or by replacing constituents of a simpler proposition by variables, and prefixing a universal or existential quantifier, resulting in general and existential propositions.

In 'On the Relations of Universals and Particulars' (1911), Russell used logical arguments to resolve the ancient problems of universals. Ordinary language certainly permits the attribution of a common predicate to more than one subject: 'a is P' and 'b is P' may both be true. If only particular things exist, then a and b would be distinct, featureless beings whose likeness with respect to P could only be understood as a shared — and hence universal — property. If only universal things exist, then P would exist in two places at once, which would fail to account for the distinctness of a and b. Thus, Russell argued, both universals and bare particulars exist; only a robust realism can explain both the sameness and the diversity that we observe in ordinary experience.

More generally, Russell's lectures on Our Knowledge of the External World (1914) and Logical Atomism (1918) offered a comprehensive view of reality and our knowledge of it. As an empiricist, Russell assumed that all human knowledge must begin with sensory experience. Sense-data provide the primitive content of our experience, and for Russell, these sense-data are not merely mental events, but rather the physical effects caused in us by external objects. Although each occurs immediately within the private space of an individual perceiver, he argued, classes of similar sense-data in various perceivers constitute a public space from which even unperceived (though in principle perceivable) sensibilia may be said to occur. Thus, the contents of sensory experience are both public and objective.

From this beginning, according to Russell, all else follows by logical analysis. Simple observations involving sense-data, such as 'This patch is now green,' are the atomic facts upon which all human knowledge is grounded. What we ordinarily call physical objects are definite descriptions constructed logically out of just such epistemic atoms. As Russell claimed in the fifth chapter of The Problems of Philosophy (1912),

'Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.'[5]

Careful application of this principle, together with the techniques of logical analysis, accounts for everything we can know either by acquaintance or by description.

Modern logic is thus in Russell's philosophy has got the status of a tool in philosophical analysis. By following the Russellian tool of analysis we can conclude that what can be known by acquaintance is certain, whereas what can be known by description is inferred and problematic. Russell's motto by following which we may be able to reach the certainty is a version of Occam's razor:

'Whenever possible, substitute constructions out of known entities for inferences to unknown entities.'

Russell's logical atomism, in spite of facing severe attacks from different quarters, is capable of making a demarcation between the pluralistic system of thought and monistic systems. Russell's attempt to provide a logical foundation to philosophy contrary to the traditional philosophers thus proved to have long-lasting influence. Russell's philosophical realism has been no less influential. As a result, modern logic has become scientific and imparts this scientific spirit both to philosophy and to other branches of the sciences.

Footnotes

1. Pradhan, R. C., Recent Developments in Analytic Philosophy, P. 35

2. Krishna, Daya , Modern Logic : Its Relevance to Philosophy, P. 53-54

3. Urmson, J. O. Philosophical Analysis, P. 6

4. Russell, Bertrand, Logical Atomism, Logic and Knowledge, P. 323

5. Russell, Bertrand, Problems of Philosophy, p. 54

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-------- My Philosophical Development (Routledge, London & New York, 1959)

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© Jahnabi Deka 2008

E-mail: jahnabideka@gmail.com

Dept of Philosophy
B. Borooah College
Gauhati University
Guwahati City
Assam, India