Russell's Philosophical Development

2024-2 Frege and Russell Final Exam

 

#1) Give a sketch of the ideas of the three main eras of Russell’s work and the main differences in the ontological and philosophical positions he held in each. The eras are: Principles Era (1900-1908), Principia Era (1909-1917), and Neutral Monist Era (1917---). It should be noted that in all the eras, Russell held a specific view about what Philosophy (as a study of necessity), but in Problems (almost) and in Our Knowledge of the External World, Russell speaks of his new Scientific Method in Philosophy which has logic (cpLogic?) as its “essence.”  Explain. Why did Russell regard cpLogic as the “essence” of philosophy and what is its role in destroying the “prisons” that fetter the mind? Give examples of how belief in non-logical necessities create “prisons”. Russell endeavors to rebuff the arguments of the metaphysicians which impose abstract particulars into the sciences (mathematical/logic and otherwise). Give examples. Characteristic of the Principles era is the ontology of propositions (with ‘true’ and ‘false’ as primitives). Explain the difference between Principia’s ϕ ⊃ ψ and the notion x Ɔ y of the Principles era where Ɔ is a relation sign. In the Neutral Monist era, Russell became enamored with Behaviorism. Why? (Hint: what are we acquainted with when we know logic?)  In what sense can Russell’s Neutral Monism be regarded as a 4-dimensional ‘physicalism”, where both mind and matter are both series of physical transitory physical events? Is this compatible with Russell’s so-called “Structural Realist” approach to empirical science? How? Note that in the Principles era, minds are not series of events, but matter is a series of (physical) contingent and transient particular events called “sense data” (events sensed by some or other being) and sensibilia (events that are able to be sensed).

 

(A) It is widely known that Russell’s philosophical development underwent a radical transformation, standing in the way of fully comprehending his body of thoughts. To better understand the landscape of Russell’s philosophy, it is helpful to divide his philosophical development into three main phases: the Principles Era (1900-1908), the Principia Era (1909-1917), and the Neutral Monist Era (1918 onward).

During the first era, Russell published The Principles of Mathematics in 1903 and one of the most influential works in the philosophy of language, “On Denoting,” in 1905 (Irvine 2024). As noted in his works, Russell at this time criticized Frege’s views on mathematics and numbers (as abstract particulars), proposed Russell’s paradox, and developed his theory of descriptions.

The second era includes his most philosophically prolific and controversial works, such as Principia Mathematica (with Alfred North Whitehead, 1910-1914)^[각주:1], The Problems of Philosophy (1912), Theory of Knowledge (1913), and Scientific Method in Philosophy (1914) (Landini 2021: xi). His contributions to the philosophy of logic during this period can be characterized by acquaintance epistemology and the multiple-relation theory of judgment. One notable encounter during this period was with Ludwig Wittgenstein in 1911, who later published the Tractatus, in which Frege and Russell’s philosophies of logic are critically discussed (Irvine 2024). Wittgenstein’s harsh criticism of Russell’s manuscript of Theory of Knowledge left him depressed and ultimately led him to abandon its publication. Russell even confessed that he “could not hope ever again to do fundamental work in philosophy” (Monk 1991).

Finally, after the Principia Era, Russell adopted a form of physicalism called “neutral monism.” Since he abandoned many of his earlier theories, such as acquaintance epistemology and the multiple-relation theory of judgment, the Neutral Monist Era should be treated independently of the other periods. The Analysis of Mind (1921) and An Outline of Philosophy (1927) are representative of this phase. In The Analysis of Mind, Russell rejected his theory of sense-data and acquaintance, and Brentano’s principle of intentionality (Landini 2011: 165). In An Outline of Philosophy, he became enamored with Behaviorism and sought to naturalize the study of mind (Landini 2011: 165).

Before clarifying the characteristics of and differences between each era, it is worth noting that in all the eras, Russell held a specific view about what philosophy is: A study of necessity. In Our knowledge of the External World, he wrote:

The topics we discussed in our first lecture, and the topics we shall discuss later, all reduce themselves, in so far as they are genuinely philosophical, to problems of logic. This is not due to any accident, but to the fact that every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical. (Russell 2009: 26)

But why is every philosophical problem logical? An initial answer to this is that, on the one hand, philosophy is a study of necessity, and, on the other hand, the only necessity is logical necessity (Landini 2011: 162). The latter claim is the overarching thesis of logical atomism, which plays a pivotal role in his method for scientific philosophy. Here, the notion of logic is connected to the philosophical program known as “logicism,” often understood as the doctrine that “mathematics is reducible to logic” (Soames 2014: 361).

Although the philosophies of Frege, Russell, Whitehead, and the early Wittgenstein are commonly characterized as logicism, I will steer clear of the question of the exact nature of logicism and which philosophers deserve this title.^[각주:2] Nevertheless, it is entirely reasonable to regard Russell’s philosophy as a form of logicism and combine this with his doctrine that the only necessity is logical necessity. In a nutshell, Russell held that arithmetic necessity is nothing but logical necessity, and his logicism is justified on the basis of this thesis.

It is also worth noting that Russell had in mind the cpLogic (impredicative comprehension principle logic) when he was speaking of his new Scientific Method in Philosophy which has logic as its “essence.” As is widely known, logicism defied Kantian philosophy of mathematics, according to which intuition (Anschauung) is always involved in mathematics. In Critique of Pure Reason, Kant famously suggested that geometry and arithmetic are synthetic a priori sciences while formal logic is an analytic a priori science.^[각주:3] Their synthetic features hinge on time and space, which are, according to Kant, a priori conditions of our sensibility. Frege challenged this view by arguing that we can comprehend functions—the heart of his cpLogic. For Frege, the basic form of the comprehension of functions is this:

Therefore, unlike Kant, logic is a synthetic a priori science for Frege. The informativity of logic comes from his comprehension principle.

Russell and Whitehead incorporated Frege’s idea of comprehension into their philosophy, while rejecting another central claim of Frege’s—that functions are unsaturated, primitive, and indefinable entities. Instead, they construed functions as relations having features like:

(∀x)(∀y)(∀z)(xRy ⊃ xRz .⊃. y=z)

Within their ontology of many-one relations, impredicative comprehension are presented as the following axiom schemas:

This assures the necessary existence of properties and relations. As a result, cpLogic became a unique synthetic a priori science for Russell and Whitehead (Landini 2021: 2). Russell often made a contrast between science and metaphysics, and the latter was used in a pejorative sense. Metaphysical propositions, for example, are claimed to be synthetic a priori, though they are not. More generally, every philosophical problem is either a problem that pertains to logical necessity or a pseudo-problem that depends on allegedly “non-logical necessities unique to mathematics, physical science, metaphysics, ethics, and so on” (Landini 2011: 162-163).

Therefore, cpLogic plays a crucial role in destroying the “prisons” that fetter our mind: it debunks the beliefs in non-logical necessities, such as Hegel’s doctrine of historical necessities and Aristotelian doctrine of biological necessities. According to Russell,

Hegel believed that, by means of a priori reasoning, it could be shown that the world must have various important and interesting characteristics, since any world without these characteristics would be impossible and self-contradictory. Thus what he calls “logic” is an investigation of the nature of the universe, in so far as this can be inferred merely from the principle that the universe must be logically self-consistent. I do not myself believe that from this principle alone anything of importance can be inferred as regards the existing universe. (Russell 2009: 30)

So, Hegelian conceptions such as the “cunning of reason” (List der Vernunft) are archetypes of pseudo-necessities that create “prisons” of dogmatism. Aristotelian teleology is another example, imprisoning our minds by imposing the notion of biological necessity and, consequently, problematic essentialism. Russell also held that most philosophical problems arise from confusion rooted in traditional logic. “Traditional logic, since it holds that all propositions have the subject-predicate form, is unable to admit the reality of relations: all relations, it maintains, must be reduced to properties of the apparently related terms” (Russell 2009: 38). Even Frege held the view that numbers are logical objects (abstract particulars). Russell believed that modern mathematics already emancipated itself from such a view. Accordingly, abstract particulars such as numbers, sets, classes, spatial figures are the vestiges in the philosophy of mathematics that must be repudiated and eliminated. For the object of mathematics is not abstract particulars but relational structures. The fundamental aim of scientific methods in philosophy is to get rid of notion of abstract particulars, which were misguidedly introduced by metaphysicians. Mathematics is the study of orders and relations.

Let me now move on to the characteristics of each era. The main characteristic of the Principles era is the ontology of propositions (with ‘true’ and ‘false’ as primitives). It should be noted that Russellian propositions are an esoteric notion, distinct from our modern conception of propositions. To identify this, let us consider the following wff (well-formed formula).

ϕ ⊃ ψ

In our modern notation, ϕ, ψ, and the entire expression, ϕ ⊃ ψ, are formulas, where ⊃ is a logical constant (ϕ ⊃ ψ is logically equivalent to ~ϕ ∨ ψ). This notation is exactly the same as that used in Principia. In the Principles era, however, Russell did not consider ⊃ as such. Rather, x Ɔ y of the Principles presupposes that Ɔ is a relation sign; so it is more like xLy (“x loves y”). Or we can formulate this more vividly as follows:

L (x, y)

Then, in the Principles era, our ordinary material implication sign should be written in the following way:

Ɔ (x, y)

, where both x and y are terms, not formulas. Only the whole expression, x Ɔ y is a formula. Therefore, we cannot read x Ɔ y as “if x, then y.” We can instead read x Ɔ y as “the proposition x implies the proposition y,” where propositions are entities having some strange natures in Russell’s early ontology. Since wffs cannot fill the blanks in [-] Ɔ [-], we must first nominalize formulas to make names. For example, if ϕ is the wff “cat on the mat,” then we can convert it into a name, {ϕ}, meaning “cat’s being on the mat.” The latter expression is now a term, not a formula. Propositions are the reference of such nominalized wffs. The True and the False are primitives in this system; for example, ~x (the negation of x) is defined as x Ɔ f.

As I noted earlier, Russell became enamored with Behaviorism during the Neutral Monist era. To understand the shift in his viewpoint, it is important to note that, during this period, Russell was influenced by Eddington’s explanation of the theory of relativity. In the Principles era, minds are not series of events, whereas matter consists of a series of (physical) contingent and transient particular events called “sense-data” and “sensibilia.” On the one hand, sense-data are parts of a whole that may be singled out by attention, such as particular patches of color or specific sounds (Russell 1959: 147). Sensibilia, on the other hand, are defined as “objects which have the same metaphysical and physical status as sense-data, without necessarily being data to any mind” (Russell 1959: 148). From these two basic notions, the “matter” of physics is defined as series of sense-data, as follows:

Now physics has found it empirically possible to collect sense-data into series, each series being regarded as belonging to one “thing,” and behaving, with regard to the laws of physics, in a way in which series not belonging to one thing would in general not behave. If it is to be unambiguous whether two appearances belong to the same thing or not, there must be only one way of grouping appearances so that the resulting things obey the laws of physics. It would be very difficult to prove that this is the case, but for our present purposes we may let this point pass, and assume that there is only one way. We must include in our definition of a “thing” those of its aspects, if any, which are not observed. Thus we may lay down the following definition: Things are those series of aspects which obey the laws of physics. That such series exist is an empirical fact, which constitutes the verifiability of physics (Russell 2009: 88).

However, Russell’s view retained the components of traditional epistemology and the philosophy of mind, i.e., “the existence of the subject and treated acquaintance as a relation between subject and object” (Russell 2001: 95). The traditional distinctions between mind and matter, and subject and object, were maintained. Eddington’s book, published in 1920, argued that traditional materialism is no longer tenable within the framework of modern physics. According to Eddington, the traditional notion of matter has been replaced by a series of events in space-time within the theory of relativity (Landini 2011: 283). Eddington’s interpretation led Russell to regard events in space-time as the fundamental constituents of the world, and as a corollary, subjects (or perceivers) must be incorporated into series of events.

Now I regard the subject also as a logical construction. The consequence is that one must give up the distinction between sensations and sense-data; on this question I now agree with William James and the school of American realists. The changes which as a result need to be made in my theory of knowledge are to be found in my Analysis of Mind. (Russell 2001: 95-96)

William James offered a form of neutral monism, according to which the self is a non-entity. He held that consciousness is a process, not a fixed entity. As a result, Russell’s neutral monism encompassed James’s neutral monist view on minds within a four-dimensionalism—namely, that matter is not a continuant persisting through time but is constituted by a series of transient events (Landini 2011: 179, 282). Space-time events are the fundamental neutral stuff, bridging the gap between mind and matter (Landini 2011: 335).  

Therefore, Russell was attracted to a behaviorist approach to psychology. According to behaviorism, terms like consciousness and introspection must be eliminated and replaced with stimulus and response, which are governed by psychological laws. Russell thought that some series of events (if they pertain to matter) realize the laws of physics, while other series of events (if they pertain to the mind) realize the laws of psychology.

One might raise a doubt as to whether Russell’s Four-Dimensional Physicalism is compatible with his so-called “Structural Realist” approach to empirical science. Structural Realism, roughly speaking, is the view that only the structure of the world can be known to us through empirical science. Such a structure is expressed by mathematical logic; but the intrinsic properties of the objects constituting the world cannot be known (Landini 2011: 331). Russell’s response to this concern is to retreat from rigorous structural realism. He acknowledged that, in addition to the mathematical structure type, it can also be known that there is an isomorphism between the structure of a stage in a mind and that of the event causing it (Landini 2011: 333).

1. Principia Mathematica consists of three volumes, published in 1910, 1912, and 1913, respectively. Whitehead also attempted to complete a fourth volume in 1914, but it remained unfinished (Landini 2021: xi). [본문으로]
2. It is especially tricky to give a proper interpretation of the meaning of the doctrine that “mathematics is reducible to logic.” Frege, for instance, tried to show that arithmetic is logic. But he never thought geometry is reducible to logic in the same way. For Russell, the logicism claim is that every “pure” mathematics is logic, where the meaning of ‘pure’ remains unclear among scholars (Landini 1998: 13). For Wittgenstein, mathematics is a logical method, since “the logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics” (TLP 6.2, 6.22). But it is again unclear whether Wittgenstein think that mathematics is reducible to logic. [본문으로]
3. I circumscribe Kant’s claim that logic is an analytic a priori science to the domain of formal logic since Kant also offered his unique transcendental logic in his book. It is beyond the scope of this paper to discuss whether transcendental logic can be considered genuine logic. [본문으로]