According to Russell, in language, there are simple symbols and there are complex symbols. Understanding simple symbols requires that we have direct acquaintance with what they mean; they are mere labels of elements of our experience. Complex symbols are composed of simple symbols; we understand them in virtue of our understanding of the simpler symbols out of which they're composed. Therefore, propositions (i.e., declarative sentences) are complex symbols, since we may understand a proposition we've never heard before provided we understand the simpler signs that make it up. For example, even if I've never heard the sentence "Diddy is a bachelor", I can understand it, because of my prior understanding of the constituent words.
Russell believes that philosophy consists mainly in the analysis of propositions. To analyze a proposition is to refine it to make evident what simple symbols make it up. This process is difficult, as symbols that appear simple may actually be complex. Take again the proposition "Diddy is a bachelor". The predicate "is a bachelor" does not name some quality one is directly familiar with. Our understanding of this phrase depends on our understanding of other words and concepts. In this case, it might be analyzed into "is an adult married male". Here we have simpler symbols than "bachelor", but they too would need to be analyzed further. The name "Diddy" might also seem to be simple; but it is not. Since I am not directly acquainted with the person who is the meaning of this expression, for me, the meaning of this phrase is equivalent to something like, "the rapper and producer who used to date Jennifer Lopez and founded Bad Boy records..." (where the ellipsis is to be filled in with the other information I associate with the name "Diddy".) So, just after one stage of analysis, the seemingly simple proposition we started with is refined to: "The rapper and producer who used to date Jennifer Lopez, and founded Bad Boy records, etc., is an adult unmarried male." However, because many of these signs are also not simple, this analysis is not yet complete.
Theoretically, analysis should terminate when all constituent symbols of the analyzed sentence are simple symbols, i.e., those with whose meanings I am directly familiar. According to Russell, through experience and/or reason, we are only directly familiar with sense-data (particular patches in the visual field, bits of sound, or other sensory or emotive input) and properties and relations held by sense-data (e.g., being red, being to the left of, etc.), as well as notions of logical form. So a sign will be simple only if it names one of these. Words such as "this" or "that" used to name sense-data in our immediate experience are simple symbols, as are simple predicates such as "is red".
However, once we reach the level of such simple signs, Russell warns, we should not try to analyze further. One might think that the predicate "is red" could be analyzed using a description such as "has the color produced by light-waves of the greatest visible amplitude" or something along those lines. However, while even simple symbols can be defined by a correct description, as with "is red" above, this does not constitute analysis. Analysis breaks a complex sign into those simple signs which must be understood for the complex sign to be understood. A person needs to know nothing about the theory of light-waves to understand "is red", one must only have had an experience of the perceptual quality it names, so the definition mentioned above does not actually constitute an analysis of this sign. The sign is simple, and what is simple cannot be further analyzed.
I
believe Russell is correct that analyzing a proposition would give us a
better understanding of what we mean by the sentences we utter, as such
a process would reveal what we mean and how we mean it. He is also
right in suggesting that such a process would make a vague
pronouncement more precise. However, it is not at all clear that such
analyses could be carried out in all cases. Consider, e.g., my beliefs
that I would express as "Venus Williams is a star tennis player" and
"Serena Williams is a star tennis player". These seem to be two
different beliefs. Because I am not directly acquainted with Venus
Williams, the name "Venus Williams" must, for me, be complex and
capable of analysis. However, I do not associate much with this name
except something like "a famous African-American female tennis player
who also has a tennis-playing sister." However, this is precisely the same
content I associate with the name "Serena Williams". (I do not follow
tennis enough to know who is older, who has won which titles, etc.)
However, it seems that I am still able to have beliefs about one sister
as opposed to the other simply by using the different names; yet, on
Russell's account, the two beliefs would have precisely the same
analysis. It's true that I could add "and is called by the name
'Venus'" to the analysis of "Venus Williams", but since the two women
are probably often mistaken for one another, Serena is probably also called
by the name "Venus", and I still haven't quite picked out one as
opposed to the other. Perhaps this problem can be dealt with by
appealing to the knowledge of others, or along other lines. However,
unless it can be patched up, there seem to be obstacles to how much
light his theory can shed on language or the mind.
In Russell's terminology, an atomic proposition is a sentence consisting of one or more simple proper names, along with a simple (unanalyzable) predicate or relation word. Simple proper names are those that directly represent elements of our immediate experience, i.e., sense-data (defined in previous question). A simple predicate would be one such as "is red" that cannot be further analyzed. Therefore, if "a" and "b" are used as names of sense-data in my present experience, then "a is red" and "a is left of b" would be atomic propositions.
Atomic propositions are made true or false by reference to atomic facts. For each atomic proposition, there corresponds either a positive or negative atomic fact in the world. For the proposition "a is red", there is either the positive fact that a (the sense-datum) is indeed red, or the negative fact that a is not red. If the fact is positive, then the proposition is true; if the fact is negative, then the proposition is false. There is nothing else to the truth or falsity of atomic propositions.
Molecular propositions consist of one or more atomic (or other) propositions combined together with words such as "and", "or", "if... then..." in such a way that whether or not the whole is true depends entirely on the truth or falsity of the simpler propositions making them up. For example, when the atomic propositions mentioned above are joined with the word "and", the result is "a is red and a is left of b". This molecular proposition is true only if both the constituent atomic propositions are true, and is false if either or both are false. If we were to combine them together instead using the word "or", i.e., "a is red or a is left of b", then again, the truth of the whole would still depend entirely on the truth of the constituents, but in a slightly different way. Here, the whole is true if at least one of the constituent atomic propositions is true, and false only if both are false. Russell believes that molecular propositions are simply made true or false in virtue of their atomic constituents (which in turn are made true or false by atomic facts), and hence, one does not need to suppose that there are distinct molecular facts (complex facts involving metaphysical ands or ors) out there in the world.
General and existence propositions both involve what Russell calls propositional functions. A propositional function is just like an atomic or molecular proposition except containing a variable in the place of a definite name, e.g., "if x is white, then x is round". Because the variable x has not been given a specific value, by itself, this is neither true nor false. A general proposition is one that asserts that a propositional function is true no matter value the variable takes on. For instance, "for all values of x, 'if x is white, then x is round' is true" would be a general proposition. General propositions capture the intuitive notion of all; the example here in effect states that all white things are round.
Existence propositions state that a certain propositional function is true for at least one value of the variable. To take an example, "for at least one value of x, 'x is white and x is round'." This captures the intuitive notion of some; i.e., this example is equivalent to "some white things are round." Because of their relationships to propositional functions and variables, general propositions and existence propositions are highly interrelated. Every general proposition can be understood as the negation of a existence proposition, and vice-versa. For example, claiming "all white things are round" is in effect to deny "some white things are non-round." Similarly, to assert "some white things are round" is in effect to deny "all white things are non-round."
Of course, if a general proposition is true, then quite a number of atomic or molecular propositions of a given form must also be true (e.g., the truth of our previous example entails the truth of "if a is white, then a is round" and "if b is white, then b is round", etc.). However, Russell does not think that general propositions are made true merely by the atomic facts making these moleculars true. Russell also believes in general facts. The supposition that the truth of a general proposition consists in just the truth of the various instances of its propositional function results in an infinite regress, because one need to include in the analysis the additional claim that those are all the instances of that function there are. This would simply be another general proposition to be analyzed in a similar way. So Russell believes that in addition to atomic facts, there also must be general facts; and these make general propositions true. By parallel reasoning, he also believes in existence facts, which make existence propositions true. (For reasons that should be clear from the above, false general propositions are made false by existence facts; and false existence propositions are made false by general facts.)
If Russell's views on analysis are sound, then these distinctions in propositions are genuine. The main metaphysical curiosity to his view consists in the nature of general facts. What are their constituents? What over and above the atomic instances are they? Russell denies that there are metaphysical correlates to and or or; is it any more plausible to suppose that there are metaphysical correlates to all and some? It seems unlikely. The admission of one type of fact without the other seems arbitrary. (Russell himself admits a difficulty here, see p. 104.)
As explained in the previous question, for Russell, a propositional function is derived from a proposition by replacing one or more names with a variable: "x is white", for example. An existence proposition is one that claims that such a propositional function is true for at least one value of the variable: e.g., "for at least one value of x, 'x is white' is true." This is equivalent to saying that there are white things, or white things exist. Claims to the effect that something exists always take this form. For example, "lions exist" is best expressed as "for at least one value of x, 'x is a lion' is true." Claims to the effect that something doesn't exist take the form of denying that a propositional function is true for at least one value of the variable; e.g., "Dragons do not exist," should be analyzed as "it is true for no values of x that 'x is a large winged reptile that breathes fire,' is true," etc.
According to Russell, only this understanding of existence propositions explains how it is that such claims are informative, and potentially false. If existence were instead understood as predicating a certain property of a specific thing, i.e., as taking the form "A exists" one would be faced with the following problem. In order for this claim to be about something, the name "A" must stand for something, or the statement would not be about any particular thing. And if A must already be something for the statement to be meaningful, it seems necessary that A must exist. Other philosophers (e.g., Meinong) were lead by an improper understanding of existence to conclude that there are things that do not exist, but only subsist: a whole realm of nonexistent things (unicorns, golden mountains, Greek gods, free lunches). Russell claims that this view distorts a proper understanding of what is real.
Significant existence statements that seem to be about individual things, Russell would say, are in fact not so: "Romulus does not exist" does not claim something about the person Romulus; after all, if it did, for it to be true, that person would have to exist. Such statements actually contain hidden reference to a propositional function. Russell calls names such as "Romulus" "disguised definite descriptions" (i.e., phrases beginning with "the"). The word "Romulus" means something like "the legendary founder of Rome, brother of Remus, ..." Existence statements involving descriptions are meaningful because the description involves some property or characteristic through which a entity is referred to or picked out; the use of the word "the" presupposes that this property or characteristic is true of exactly one thing. (Therefore, statements involving "the inhabitant of Boston" will be false, as a true use of this statement will require there to be no more than one person who inhabits Boston.) For example, "the inventor of bifocals exists" means something like, "for one and only one value of x, 'x invented bifocals' is true." So "Romulus does not exist", when properly analyzed, means something like "for no single value of x, 'x founded Rome, and Remus was the brother of x, and ...' is true" or suchlike. Here we can see how such statements can be meaningful without presupposing the reality of nonexistent objects.
This approach has many advantages. It rules out including nonexistent objects or unreal things in our metaphysics. Talk about "existence" never amounts to sorting things in the universe into two camps; it instead amounts to sorting properties or descriptions into two camps: those fulfilled by entities in the universe, those unfulfilled. The primary difficulty I see with the approach, however, is that it seems to presuppose a prior understanding of which entities are to be included among "possible values" of the variables for propositional functions. We must have already ruled out merely possible or "fictional" entities like Romulus or Casper the ghost; otherwise, the propositional function "x is a ghost" will be true for some values of the variable. In denying the "reality" of nonexistent objects, Russell really seems to mean this: insofar as an entity does not have be included in the range of our variables, it does not exist. Russell, in believing that, when fully analyzed, only names of sense-data can replace variables, is in effect insisting from the get-go that only sense-data are real. If other particular entities were required for analysis, other entities would be included in the range of the variables. The account of existence by itself provides no independent criterion for determining what entities should be so included, and so it seems that the true question of what "exists" simply reduces to that question.
According to Russell, all significant propositions must be analyzed to a stage in which every constituent names something we are directly acquainted with (see first question). Consequently, any sentence that makes a claim about ordinary physical objects (tables, chairs, desks), or about people, must be analyzed this way. Because Russell also believes that we are only directly acquainted with sense-data, their properties and relations, he concludes that all significant propositions about ordinary objects must be analyzed in terms of sense-data. Russell claims that an object such as a desk would be best understood as a collection of certain actual or possible objects of perception: colors, textures, sounds, odors, etc. In effect, the desk is a series of classes of those sense-data through which its presence could be known. On this theory, any proposition involving the phrase "the desk" must be analyzed as a proposition about a certain series of classes of sense-data. In the case of people, they can be understood as collections of sense-data as well; specifically, as the series of classes of their experiences.
Complicating Russell's position further is his contention that classes (i.e., sets) and series, are not genuine objects, but are themselves logical constructions or mere figures of speech. If we were to assume that classes really are genuine things, we run into logical paradoxes. Instead, Russell thinks that any proposition about a class must be analyzed as a statement about the entities making up the class and those properties they have in common. For example, the sentence "the class of humans is a subset of the class of mortal beings" is best analyzed as "every human being is mortal". Because talk about physical objects and people is to be analyzed in terms of series and classes, and because these are themselves to be analyzed away, in effect, all talk about people and ordinary objects can be analyzed away in virtue of the sense-data making them up and their properties and relations to one another. For example, the statement "the desk in front of me is brown"; becomes something like, "all those visual sense-data continuous both spatially and temporally with the sense-datum in the center of my visual field that can be seen in periods of bright illumination are brown". In this analysis, actual reference to "the desk" has disappeared. Because all propositions about ordinary objects and people reduce to statements about various sense-data in a similar fashion, Russell calls such "objects" as desks "logical fictions"; they are not genuine entities, but simply complicated figures of speech used to make complicated assertions about sense-data easier to state.
Russell contrasts his position with the traditional view that ordinary physical objects are substances: i.e., individual things lying behind what we perceive, that endure through time. On this view, there is a substance, the desk itself, and all the various perceptions of the desk had by various people at various times share a certain relation with this substance, which cannot itself be perceived. Similarly, a person is thought of as mental substance--a mind or soul--something which is not itself any of its experiences, but is that which has experiences. While officially, Russell is agnostic about whether such "substances" might exist, he points out that, if they did, we would have no direct awareness of them. He also points out that if we make a judgment such as "this desk is the same as the one I saw yesterday", if that is analyzed as meaning "the perceptions I'm having now were caused by the same underlying substance as those that caused my previous perceptions", without having perceptions directly of the substance, our judgments would be mere hypotheses incapable of verification. However, if we understand desks as "logical constructions", simply ways of talking about sense-data, it is a matter of linguistic convention as to what relationship two sense-data must have to each other to count as parts of "the same desk". Here, we can simply appeal to that which is common in our experience between the various perceptions of the desk, and the "sameness" of the desk is more easily verified.
Russell claims that his position is in keeping with the scientific principle of Occam's razor: the principle that in choosing between rival theories, all other things being equal, one ought to favor the simpler theory. In his case, because his theory only really requires commitment to one kind of entity: sense-data, organized in different ways, rather than a pluralistic metaphysics consisting of mental objects, material objects, and so on, he considers his theory to be a simpler one.
It is on this last point that I think Russell's position is the weakest. While his theory is simpler in some ways, it is not simpler in all ways. He is forced into claiming that even the particles of atomic physics: atoms, electrons, and so on, are "logical fictions": complicated ways of talking about perceptions one can have using scientific instruments. This actually would make the fundamental laws of physics much more complicated than most practicing physicists take them to be. Consider the following proposition of physics: "electrons and positrons are oppositely charged". If Russell is correct, then this would have to be analyzed as an extremely complicated statement about the sense-data obtainable in laboratories. This reversal of simplicity actually seems to contravene Occam's razor, not accord with it. Perhaps allowing these sorts of entities to be more than "logical fictions" would actually make for a simpler worldview overall.