Russell's Views on Philosophy

2024-2 Frege and Russell Final Exam

#3) What was Russell’s conception of (scientific method in) proper philosophy, and how is it connected With the notion of philosophy as the science of which undermines all metaphysical claims of special kinds of “necessity” (e.g., mathematical (arithmetic, geometrical), physical, causal, biological, psychological, etc.) Rehearse some examples of such kinds of alleged necessities in history. (Hint: Pythagorean theorem, parallel postulate, “more” natural numbers than even natural numbers, fixity of species, earth at rest, natural motions of heavenly bodies are circular, life comes from life; divine right of kings, Hobbes’s view that human nature is inherently self-oriented). In what sense does Russell think (in his 1914 book Our Knowledge of the External World: aka Scientific Method in Philosophy as a field for our knowledge of the external world) that it is the new comprehension principle logic (cpLogic) alone that gives key critical tool that is required for a truly scientific method in philosophy? How in Russell’s view are other kinds of necessity (and their abstract particulars) a prison the fetters the mind? Such passages are in the Problems of Philosophy of 1912. Why then isn’t the new cpLogic said to be the essence of philosophy (i.e., the new scientific method in philosophy) in the 1912 Problems of Philosophy? Hint: what is the status of Ethics in the 1912 work as opposed to the 1914 work? What is the status of the fundamentals of probability theory in these books? Were the probability theory fundamentals synthetic a priori and subsumed into cpLogic?

 

(A) It is widely known that Kant characterized the empiricism-rationalism debate as the problem of getting synthetic a priori knowledge. In Critique of Pure Reason, He wrote:

Metaphysics—a wholly isolated speculative cognition of reason that elevates itself entirely above all instruction from experience, and that through mere experience (not, like mathematics, through the application of concepts to intuition), where reason thus is supposed to be its own pupil… in it reason continuously gets stuck, even when it claims a priori insight (as it pretends) into those laws confirmed by the commonest experience (CPR, B xiv-xv).

On the one hand, knowledge is either synthetic or analytic, yet only the former is informative and thereby extends our knowledge. On the other hand, knowledge is either a priori or a posteriori, yet only the former is necessary and thereby provides certainty. While rationalists (or traditional metaphysicians) held that there is synthetic a priori knowledge, Kant argued that their purported a priori insights are dogmatic because no experience can buttress them. While empiricists avoided such dogmatism by acknowledging the significance of experience, Kant pointed out that they could not escape from skepticism, since for empiricists, all synthetic knowledge is a posteriori.   

Therefore, Kant suggested, like the rationalists, that synthetic a priori knowledge exists, yet, like the empiricists, he held that such knowledge must be underpinned by experience. Kant called the subject of synthetic a priori knowledge transcendental—a priori conditions of possible experience. As noted above, mathematics—geometry and arithmetic—is representative of a synthetic a priori science for Kant. It pertains to the a priori conditions of every possible experience, i.e., space and time. Since space and time belong to the domain of sensibility, intuition is always involved in mathematical knowledge, according to Kant.

The Kantian philosophy of mathematics was, however, challenged by several groundbreaking developments in both mathematics and natural science—Riemannian geometry, Einstein’s theory of relativity, and Frege’s revolutionary philosophy of mathematics. For Kant, logic is a science concerned with the universal and necessary laws of thinking, whose principles never rely on grounds derived from experience (G: 1). Therefore, mathematics and logic are quite distinct sciences: while the former is a synthetic a priori science, the latter is an analytic a priori science.

Frege ferociously attacked the Kantian doctrine by proposing logicism—the view that arithmetic is a branch of logic. For Frege, both mathematics and logic are synthetic a priori sciences. More importantly, he denied the role of experience (in Kantian terms, intuition) in both fields. The informativity of logic (and mathematics) comes from his unique comprehension principle, by which we could comprehend functions. Although Russell and Whitehead disagree with Frege’s views on (the ontology of) functions, they accept the comprehension principle that assures the necessary existence of properties and relations. Like Frege, cpLogic is a unique synthetic a priori science for Russell and Whitehead. It studies “relational structures by studying relations (and properties)” (Landini 2021: 32).

Russell believed that philosophy is the study of necessity, which is fundamentally implemented by cpLogic, since the only necessity is logical necessity. Non-logical necessities (e.g., mathematical (arithmetic, geometrical), physical, causal, biological, psychological, etc.) are ultimately revealed as either logical necessities or disguised dogmatism.

Therefore, cpLogic is a pillar of Russell’s scientific method in philosophy; it is called scientific, since scientists have already incorporated cpLogic into their empirical observations. According to Russell, philosophical knowledge is not different from scientific knowledge because both combine a knowledge of cpLogic with empirical scientific methods (Landini 2021: 23). However, philosophy still has its specialized area—to distinguish logical necessities from non-logical pseudo-necessities. In a nutshell, “the essential characteristic of philosophy, which makes it a study distinct from science, is criticism” (Russell 2001: 87).

Therefore, the essence of Russell’s method for scientific philosophy is twofold: in its positive sense, scientific philosophy is an attempt to construct the ontology of logic—which he believes it to be only right ontology—and reconstruct science based on it by showing that the only necessity is logical necessity. Along the way, genuine philosophical problems are identified and solved. The method for scientific philosophy, in its negative sense, aims to debunk the claims regarding metaphysical necessities and dissolve pseudo-problems in philosophy. Russell thought that many of his predecessors had committed errors by regarding non-logical necessities as genuine ones. He used the term ‘metaphysics’ in a pejorative sense in this regard. For instance, in The Problems of Philosophy, Russell wrote:

Most of the great ambitious attempts of metaphysicians have proceeded by the attempt to prove that such and such apparent features of the actual world were self-contradictory, and therefore could not be real. The whole tendency of modern thought, however, is more and more in the direction of showing that the supposed contradictions were illusory, and that very little can be proved a priori from considerations of what must be (Russell 2001: 84-85; my emphasis).

Like Kant’s critical philosophy, Russell construes the task of philosophy as debunking claims about other kinds of necessity (and their abstract particulars) that fetter our minds. Russell called these “prisons.” The way to escape from these prisons is to recognize that the supposed contradictions are illusory.

Let me consider several examples. First, Russell held that Cantor shows that the impossibility of infinite collections, posited by Kant and his contemporaries, was a mistake. “They are not in fact self-contradictory, but only contradictory of certain rather obstinate mental prejudices” (Russell 2001: 85).

Second, as is widely known, the Euclidean parallel postulate was long considered a necessary axiom, constituting the only possible geometry. However, Riemannian geometry demonstrated that Euclidean geometry is not the only possible geometry and that the parallel postulate is not necessary for constructing geometric systems.

Some of Euclid’s axioms, which appear to common sense to be necessary, and were formerly supposed to be necessary by philosophers, are now known to derive their appearance of necessity from our mere familiarity with actual space, and not from any a priori logical foundation. By imagining worlds in which these axioms are false, the mathematicians have used logic to loosen the prejudices of common sense, and to show the possibility of spaces differing—some more, some less—from that in which we live (Russell 2001: 85).

Third, Einstein’s theory of relativity and quantum theory were not only counterintuitive but also considered inconceivable until the revolution in mathematics (Landini 2021: 25). Likewise, Darwin’s theory of evolution and natural selection debunks Aristotelian biological necessities and teleological essentialism (Landini 2021: 25). Similarly, modern physics and astronomy reveal pseudo-necessities, such as the supposed necessity of circular uniform motion for celestial bodies and the necessity of absolute rest as the natural state of matter (Landini 2021: 26).

In this respect, scientific methods in philosophy undermine all metaphysical claims of special kinds of “necessity” by using cpLogic—the only science that deals with synthetic a priori truths. In Our knowledge of the External World, Russell said:

Modern logic, as I hope is now evident, has the effect of enlarging our abstract imagination, and providing an infinite number of possible hypotheses to be applied in the analysis of any complex fact. In this respect it is the exact opposite of the logic practised by the classical tradition. In that logic, hypotheses which seem prima facie possible are professedly proved impossible, and it is decreed in advance that reality must have a certain special character. In modern logic, on the contrary, while the prima facie hypotheses as a rule remain admissible, others, which only logic would have suggested, are added to our stock, and are very often found to be indispensable if a right analysis of the facts is to be obtained. The old logic put thought in fetters, while the new logic gives it wings. (Russell 2009: 48)

One might ask, then, why the new cpLogic is not said to be the essence of philosophy (i.e., the new scientific method in philosophy) in the 1912 Problems of Philosophy. This is because Russell at this time considered the possibility that not every synthetic a priori knowledge is that of logic (Landini 2021: 26). One possible candidate for this is probability theory, including the inductive principle. However, since Russell simultaneously held that the fundamentals of probability belong to logic, this did not make him reluctant to assert that cpLogic is the essence of philosophy (Landini 2021: 27).

Instead, he seriously considered ethical knowledge as a candidate for being a non-logical genuine necessity. In the Problems of Philosophy, he wrote:

A priori knowledge is not all of the logical kind we have been hitherto considering. Perhaps the most important example of non-logical a priori knowledge is knowledge as to ethical value. I am not speaking of judgements as to what is useful or as to what is virtuous, for such judgements do require empirical premisses; I am speaking of judgements as to the intrinsic desirability of things. If something is useful, it must be useful because it secures some end; the end must, if we have gone far enough, be valuable on its own account, and not merely because it is useful for some further end. Thus all judgements as to what is useful depend upon judgements as to what has value on its own account…In the present connexion, it is only important to realize that knowledge as to what is intrinsically of value is a priori in the same sense in which logic is a priori, namely in the sense that the truth of such knowledge can be neither proved nor disproved by experience. (Russell 2001: 42-43)

This passage clearly implies that Russell did not firmly hold his fundamental doctrine—that the only necessity is logical necessity—in 1912. However, he later rejected the thesis that there are a priori principles in ethics and decided to exclude ethics from philosophy in 1914 (Landini 2021: 28).

 

References

Irvine, Andrew David (2024). “Bertrand Russell,” The Stanford Encyclopedia of Philosophy (Winter 2024 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/win2024/entries/russell/>.

Kant, Immanuel (1998). Critique of Pure Reason. Translated by Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.

Kant, Immanuel (1998). Groundwork of the Metaphysics of Morals. Translated and edited by Mary Gregor. Cambridge: Cambridge University Press.

Landini, Gregory (1998). Russell’s Hidden Substitutional Theory, Oxford: Oxford University Press.

Landini, Gregory (2007). Wittgenstein’s Apprenticeship with Russell, Cambridge: Cambridge University Press.

Landini, Gregory (2011). Russell. New York: Routledge.

Landini, Gregory (2021). Repairing Bertrand Russell’s 1913 Theory of Knowledge. London and Basingstoke: Palgrave-Macmillan.

Monk, Ray (1991). Ludwig Wittgenstein: The Duty of Genius. New York: Vintage.

Russell, Bertrand (1959). “The Relation of Sense-Data to Physics.” In: Mysticism and Logic and Other Essays. London: George Allen & Unwin LTD.

Russell, Bertrand (2001). The Problems of Philosophy. Oxford: Oxford University Press.

Russell, Bertrand (2009). Our Knowledge of the External World As a field for scientific method in philosophy. London and New York: Routledge.

Soames, Scott (2014). The Analytic Tradition in Philosophy. Vol. 1 The Founding Giants. Princeton and Oxford: Princeton University Press.

Wittgenstein, Ludwig (1921). Tractatus Logico-Philosophicus. Translated by Pears and McGuinness. New York: Routledge.