The use of propositions and propositional functions by Russell in Logical Atomism

Question

I recently had a chance to go through a book by Bertrand Russell : - "The philosophy of logical atomism" . I guess Russell abandoned some of this philosophy later on his life but nevertheless I had trouble understanding some things he is saying in this book and would like to know what could be the possible interpretation of what he is saying.

In philosophy of logical atomism , Russell wishes to get to the logical atoms which comprise the world. According to Russell , what exists in the world are entities known as facts and particulars. Facts are those things which determine the truth value of a proposition.And thus a proposition and its falsehood both are symbols for the fact. A thing is symbolised by a name . Whereas a fact is symbolised by a proposition p and its negation not-p. For ex: - the fact symbolised by "It is raining" is those state of things in the world which determine whether it is raining or not.

I think Russell wishes to break down the world into its logical building blocks. Hence he says that what is real are entities such as primary sense data - a patch of blue or a sound. And facts which give the relations between these primary entities which he calls particulars. For ex :- the fact which is symbolised by a proposition such as "This patch of blue is to the right of the that patch of red".

But as we know there are complex entities in the world such as chairs , tables, human beings and so on. According to Russell, the word "chair" is a symbol , but an incomplete symbol or a description. According to him when analysed properly it will lead to propositions about the primary sense data which make up the chair.

He even denies the existence of entities such as numbers, classes , saying that all these are logical fictions. He says that complex entities such as human beings , numbers , classes , can all be analysed away using propositional functions .

So my query is what is the ontological status of these propositions and propositional functions ? Do they exist according to Russell and if so how ?

He is calling everyday objects a logical fiction and analysing them using propositions and propositional functions , hence I thought whether those propositional functions themselves are fictions or not ?

Thanks.

Answer 1

One potentially controversial answer might be to say that Russell adopts a position that problematizes the notion of ontology. Russell is sometimes read as a Structural Realist (e.g. William Clement, 1953), in that while he takes the world to be made up of parts, they are realized in the world as a whole and accessed through the structural similarity between thought and fact given by Logic. Logic is what splits the world up into manageable and malleable chunks of data, rather than things coming as pre-packaged individuals.

Part of what lets him do this is that he's working on the foundations of his earlier work in mathematical logic given in his Principia Mathematica (Wiki article). There, Russell attempted to consolidate earlier work by Gottlob Frege to yield definitions for mathematical classes from an axiomatization of a restricted, higher-order logic framework. Class/set discourse is very expressively useful in both analytic philosophy and mathematical model building, and showing that these "fictions" can be reduced to fairly simple assumptions of logical relations or Types of symbols in our language means that logical work has a much broader scope of application. (The literature on this general project is enormous, but the SEP article on "Conceptions of Analysis" might be helpful as an intro!)

Russell in PoLA thinks that as long as languages (any suitably grammatically integral languages, not just those adopted by professional mathematicians) have a properly typed logical grammar where we distinguish elements of interest as "particulars", we can use the most useful bits of set theory and mathematical/philosophical analysis without requiring that we have abstract mathematical "objects" to refer to. Moreover, once we do have this, we'll be able to find that we generally need far fewer particulars than we first thought to account for all of the facts we want to account for, because what counts as an individual hinges on logical theory rather than surface syntactic form. Lecture 7 looks at some of this in more detail, but the following quote seems particularly apt:

The theory of types is really a theory of symbols, not of things. In a proper logical language it would be perfectly obvious. The trouble that there is arises from our inveterate habit of trying to name what cannot be named. If we had a proper logical language, we should not be tempted to do that. Strictly speaking, only particulars can be named. In that sense in which there are particulars, you cannot say either truly or falsely that there is anything else. The word "there is" is a word having "systematic ambiguity", i.e. having a strictly infinite number of different meanings which it is important to distinguish.

Propositional functions seem to be understood in terms of formal relationships between the different parts of a properly logical symbolic language. The problem we might have now is as to what, strictly speaking, we ought to say about the foundations of proper logical structure and the idea of a logical particle, and you're right to point out that without some sort of model theory, Propositional functions seem completely mysterious. There doesn't seem to be any particular consensus on what Russell had in mind in terms of what they really are (see the SEP article on this issue).

But reading Russell as a Structural Realist may give some clues as to how someone trying to renew his philosophical project might be able to think about the nature of propositions and propositional functions. Russell's Principia stipulates what logical statements there are and how they relate through his axiom systems. A Structural Realist might say that when we engage with the world, what we are engaging with is its axiomatically systemic nature, which we take to be "the same as" our logical language. We build and work with axiomatic theories of the propositional structure of the world by relying on Principia's specifications of logical structures. And as such, ontology is strictly subordinate to logical specification.

Actually, structures are "out there" as realized in the empirically observed world too (in as much as the idea of an "out there" makes sense in Russell's metaphysics; it would be probably more technically accurate but much less charitable to say the structure is "just there"), but in order to further evaluate some structure as an object, we would need to logically situate it inside another axiomatic theory to give us its objects and functions. (This can in principle be done, since Type theory is hierarchical, but the behaviour of higher types or a type/category of "fictions" isn't very well specified by Russell's theory) The question of "what we say" about propositional functions and individual bare particulars beyond what prior specified logical axioms can tell us would be thus easily answered: "nothing at all". (The structuralist strategy and some consequences of it for maths received much more attention after Paul Benacerraf's arguments in "What Numbers could not be" (1965))

If this is what we're committed to, we can still get propositions and propositional functions out of it at the end, because that's how logic seems to work, but their identities are in some sense parasitic on how the world is "organized" into facts. Had the world been radically different, with more complicated types than we currently think there are, the identities of propositions and propositional functions might also have been different. That may be a step too far for anyone looking for logical structure to serve as a stable foundation.

(all quote marks are scare quotes, and not necessarily Russell's own terminology.)

Answer 2

Your question is very good. There is no consensus among Russell scholars what Russell could consistently mean by "proposition" and "propositional function." I will just address what Russell says about them in the 1918 logical atomism lectures. Russell says:

A propositional function is simple an expression containing an undetermined constituent, or several undetermined constituents, and becomes a proposition as soon as the undetermined constituents are determined...A propositional function is nothing, but, like most of the things one wants to talk about in logic, it does not lose its importance through that fact. (The Philosophy of Logical Atomism, Lecture V, pages 192-193)

What does that really mean? Let's confine ourselves to written symbols for the moment. Then a flat-footed reading would be: it means that the propositional function is a string of symbols, at least one of which is a variable, which we judge to be true or false. On that reading, propositional functions are not entities, but are used to make judgments about the world. Propositional functions are not part of the stuff in the world, but are used by us in judging how the world is.

Propositions likewise "are nothing" (The Philosophy of Logical Atomism, Lecture IV, page 56). They are merely used to make judgments about how the world is, whether in written symbols, spoken words, or in thought. So propositions, like propositional functions, are not really entities: however they are is parasitic on the nature of judgment.

What are judgments, though? Russell says they are a kind of fact (a kind involving two verbs), one that exists in virtue of our mental act of judgment:

Suppose you take any actual occurrence of a belief...I am talking of the actual occurrence of a belief in a particular person's mind at a particular moment, and discussing what sort of fact it is. If I say "What day of the week is this?" and you say "Tuesday," there occurs in your mind at that moment the belief that this is Tuesday. (The Philosophy of Logical Atomism, Lecture IV, page 49)

So whatever exists in the world are not propositions nor propositional functions, but there are judgment-facts (or belief-facts).

But, you might object, isn't that enough to force that there are propositions after all? Isn't the thing we believe a proposition (or a propositional function)? That would be a very astute objection because Russell spends a few pages denying that very point! Russell argues that you cannot understand judgment-facts in a way that is analogous to perception (ibid., pages 56-61). In perception one might say that a subject s perceives a sense-datum d, that is, s-Perceives-d. But Russell denies that we can similarly understand belief as s believing the proposition p, that is, s-Believes-p. This would be a confusion about the logical form of judgment-facts (or belief-facts).

As for his positive account of the accurate logical form of judgment-facts (the one that is supposed to avoid the psuedo-analysis into s-Believes-p), Russell is more tentative, as he confesses:

I hope you will forgive the fact that so much of what I say to-day is tentative and consists of pointing out difficulties. The subject is not very easy and it has not been much dealt with or discussed. (ibid., page 61)

And so we are left with questions, some of which Russell raised in 1918, about the nature of judgment that philosophers continue to discuss today.

Answer 3

one thing that might help you is: http://plato.stanford.edu/entries/logical-atomism/

from that article, we read: "In the proposition Socrates is human, the person Socrates (the man himself) occurs as term, but humanity occurs as concept. In the proposition Callisto orbits Jupiter, Callisto (the moon itself) and Jupiter (the planet) occur as term, and the relation of orbiting occurs as concept."

So pretty clearly propositions exist and relatively untendentiously so, on Russell's LA theory.