Just how meaningless is a phrase like "the present President of the United States"?
Bear with me. After taking several passes at reading through the dense analytic philosophy in Bertrand Russell's essay On Denoting that is behind this week's thought experiment, I think it's finally starting to make sense to me. Hopefully I'll be able to convey that to you, but there is definitely a reason that in the 1920s, Frank P. Ramsey referred to On Denoting as "that paradigm of philosophy." In the Stanford Encyclopedia of Philosophy entry Descriptions, Peter Ludlow singled the essay out as "the paradigm of philosophy", and called it a work of "tremendous insight"; "provoking discussion and debate among philosophers of language and linguists for over a century."
Sounds good, right? Okay here's the thought experiment.
--------------------------------------------------
"Your honour, my client's defence is very simple. He accepts that he did indeed write in his newspaper column that "the current manager of the England football team is a liar, an idiot, and a national disgrace." He also accepts going on to say that he "should be shot." But by doing so, he in no way libelled the plaintiff, Mr Glenn Robson-Keganson.
"The reason for this is easy to see. At the time the article was written and published, there was no such person as the England football team manager. Mr Robson-Keganson had tendered his resignation two days earlier, and his offer had been accepted. This news became public knowledge on the day the defendant's article was published.
"The plaintiff claims that the accusations my client made were false. But they were neither true nor false, since they were not about anyone. Indeed, it would be more accurate to say they were meaningless. "Flar-Flar is a racehorse" is true if Flar-Flar is a racehorse, false if she is not, and meaningless if there is no such beast.
"The jury should therefore dismiss the case. It is just nonsense to suggest one can libel someone who does not exist. I rest my case."
Source: "On Denoting" by Bertrand Russell (1905).
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 253.
---------------------------------------------------
In my post Analysing Russell, the Father of Analytical Philosophy, I briefly touched on this puzzle, although I did not wrestle with it in depth. I ended up concluding, perhaps too simply, that:
This over-analysis of grammar known as analytical philosophy is just logic applied to writing. It is important to be clear, but this is a small part of our overarching knowledge. It does not deserve the central role in philosophy departments that it has achieved. It consigns them to the role of fussy nitpicker, rather than the broad-minded lover of wisdom.
I still feel that way about this topic, but who amongst us doesn't feel it's necessary to pick some nits every once in a while? I know I do. And so I feel I should indulge Bertrand Russell on this, especially since he absolutely spent plenty of time on broad-minded pursuits of wisdom too. He wrote this after all:
Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind is also rendered great.
So, let's get studying and see what gets enriched!
(Have I sold you on this enough yet?)
When Baggini discussed this thought experiment, he started by acknowledging the pragmatic real-world response to the legal case by saying, "The jury would probably dismiss [the defence] on the grounds that we know who he meant by 'the current manager of the England football team'." I agree. It is indeed specious to claim the article was not libellous in its intent. By changing one adjective—"current" to something like "previous" or "former" or "the last"—the entire article would still stand, naked with its obvious intent. The moment-to-moment accuracy in the mind of the writer of this one word does not change the meaning or the intent of his entire article. Especially since no one would go to all that trouble to write something about a non-existent person.
So that answers the legal question, but what about the philosophical ones being raised here? Before we dive in to those, keep this plea in mind from the end of Russell's original paper:
Of the many consequences of the view I have been advocating, I will say nothing. I will only beg the reader not to make up his mind against the view—as he might be tempted to do, on account of its excessive complication—until he has attempted to construct a theory of his own on the subject of denotation. This attempt, I believe, will convince him that, whatever the theory may be, it cannot have such a simplicity as one might have expected beforehand.
Okay, we're withholding judgment. So what is "denoting" and what kind of theory do we need to construct about it? Russell wrote:
By a "denoting phrase" I mean a phrase such as any one of the following: a man, some man, any man, every man, the present King of England, the present King of France, [etc.]... We may distinguish three cases: (1) a phrase may be denoting, and yet not denote anything; e.g. "the present King of France." (2) A phrase may denote one definite object; e.g. "the present King of England" denotes a certain man [as it did when this was written in 1905]. (3) A phrase may denote ambiguously; e.g. "a man" denotes not many men, but an ambiguous man.
Got it? We're talking about linguistics here and the correspondence between words and objects in reality. What do our words really refer to and how do we make logical sense of that relationship? Is there always a direct correspondence with some physical or mental object? The folk intuition is to say, "yes, of course our words denote such things," but can such denotation always be explained? Philosophers have had trouble answering this, but Russell offered a new theory for tackling this problem:
My theory, briefly, is as follows. I will take the notion of the variable as fundamental; I use "C(x)" to mean a proposition in which x is a constituent, where x, the variable, is essentially and wholly undetermined. Then we can consider the two notions "C(x) is always true" and "C(x) is sometimes true." Then everything and nothing and something (which are the most primitive of denoting phrases) are to be interpreted as follows:
Hmmm. Maybe it will help to see this in action:
Suppose we now wish to interpret the proposition, "I met a man." If this is true, I met some definite man; but that is not what I affirm. What I affirm is, according to the theory I advocate:
Huh?? If you didn't follow that, you don't want to read what he advocates for "all men are mortal" or how to interpret phrases containing "the." After many logical substitutions, it leads to this:
Thus "the father of Charles II was executed" becomes:
Somewhat incredible?? Yegads. This seems like an awfully difficult way to attempt to reduce denoting phrases to their non-denoting components. So how are we expected to judge all this?
A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them.
Okay, this sounds fun. What are the three puzzles?
(1) If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of Waverley, and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.
Haw, haw, haw. Harumph, harumph. But the law of identity and substitution does not make sense here. "Scott" and "the author of Waverley" do indeed point to the same identical person, but they hardly have the same amount of information in them. They only denote one small part of that person. "Scott" is the name of that person. "The author of Waverley" describes one action that person has performed. Treating such adjectival phrases as indistinct from one another is to completely misunderstand the form and function of language. This first puzzle is no puzzle at all. Next!
(2) By the law of excluded middle, either "A is B" or "A is not B" must be true. Hence either "the present King of France is bald" or "the present King of France is not bald" must be true. Yet if we enumerated the things that are bald, and the things that are not bald, we should not find the present King of France in either list.
Of course you would! The things that are not bald includes all imagined things too. It helps slightly to restate the original question into the form that Russell used to analyse it. In that case, we see that "the present King of France" is not "a bald thing." It's no thing at all, so it's certainly not a bald one either. It's quite weird to say, but "the present King of France is not bald" may technically be considered a true statement. Anyone who has played 20 questions will have experienced this phenomenon. But is it as accurate as it could be? More on that below.
To me, the problem with these first two puzzles (and much of analytic philosophy) is that they are examples of what happens when one attempts to take the rules of logic from mathematics and numbers and tries to apply them directly to the world of words and meaning. Numbers are discrete, objective, singular points. Words are vague, fuzzy, subjective, multipolar concepts. Simple manipulations such as negation, substitution, and addition do not always apply here with the perfect accuracy that logicians want so desperately to have.
From my blog post profiling Bertrand Russell, we saw hints that such clinging to cold and logical mathematics by the adult Russell probably arose because of his emotionally traumatic childhood. I wrote that, "It seems from several quotes that Bertrand came to rely on the bedrock of mathematics as a solid retreat from his chaotic childhood filled with so much promise, change, and death:
In action, in desire, we must submit perpetually to the tyranny of outside forces; but in thought, in aspiration, we are free, free from our fellowmen, free from the petty planet on which our bodies impotently crawl, free even, while we live, from the tyranny of death.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza's God, it won't love us in return.
From this background, we see perhaps why Russell attempted the whole project of co-founding analytical philosophy with his student Ludwig Wittgenstein. But in my post on Wittgenstein, I noted:
After the completion of his first book, Tractatus Logico-Philosophicus in 1918, Wittgenstein believed he had solved all the problems of philosophy and he abandoned his studies. However, in 1929 he returned to Cambridge and began the meditations that ultimately led him to renounce or revise much of his earlier work, rejecting the analytical fantasy that a philosophical language could be derived mathematically from first principles, in favor of a more descriptive linguistic philosophy. This change of mind culminated in his second magnum opus, the Philosophical Investigations, which was published posthumously. In it, Wittgenstein asks the reader to think of language as a multiplicity of language-games within which parts of language develop and function. He argues philosophical problems are bewitchments that arise from philosophers' misguided attempts to consider the meaning of words independently of their context, usage, and grammar, what he called "language gone on holiday.” According to Wittgenstein, philosophical problems arise when language is forced from its proper home into a metaphysical environment, where all the familiar and necessary landmarks and contextual clues are removed. He describes this metaphysical environment as like being on frictionless ice: where the conditions are apparently perfect for a philosophically and logically perfect language - the language of the Tractatus - where all philosophical problems can be solved without the muddying effects of everyday contexts; but where, precisely because of the lack of friction, language can in fact do no work at all. Wittgenstein argues that philosophers must leave the frictionless ice and return to the "rough ground" of ordinary language in use.
What a perfect criticism of these puzzles on denotation so far. But let's get back to Russell's original paper and see the third and final puzzle, which actually raises an interesting question. Next!
(3) Consider the proposition "A differs from B." If this is true, there is a difference between A and B, which fact may be expressed in the form "the difference between A and B subsists." But if it is false that A differs from B, then there is no difference between A and B, which fact may be expressed in the form "the difference between A and B does not subsist." But how can a non-entity be the subject of a proposition? ... Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connection to Meinong, that to admit being also sometimes leads to contradictions. Thus if A and B do not differ, to suppose either that there is, or that there is not, such an object as "the difference between A and B" seems equally impossible. The relation of the meaning to the denotation involves certain rather curious difficulties, which seem in themselves sufficient to prove that the theory which leads to such difficulties must be wrong.
I have to jump back here to a passage about Meinong to make sense of this. Russell wrote that:
The evidence for [my] theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meinong. This theory regards any grammatically correct denoting phrase as standing for an object. Thus "the present King of France," "the round square," etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round; etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred.
Okay, we are finally at the heart of this denoting problem. Basically, when philosophers invent an impossible strong of words such as "the present King of France" or "the round square", we seem to be able to understand these phrases and even perform logical analyses using them, but they actually refer to nothing. In case you missed it, Russell summarised this above when he said, "But how can a non-entity be the subject of a proposition?"
His own answer was to go through the incredible manipulations and substitutions shown above in order to remove all denoting phrases from the logical analysis of language. Thus, "I met a man" became "'I met x, and x is human' is not always false"; and "the father of Charles II was executed" became "It is not always false of x that x begat Charles II and that x was executed and that 'if y begat Charles II, y is identical with x' is always true of y." In Russell's words, this "gives a reduction of all propositions in which denoting phrases occur into forms in which no such phrases occur."
Besides being incredibly abstruse and unhelpful, I don't think Russell actually achieved his goal since language is nothing but referrals and denotations. It is literally impossible to remove denoting phrases from language. This is why Wittgenstein later abandoned the project of "a philosophically and logically perfect language." But then where does that leave us with regard to puzzle number (3) and how a non-entity can be the subject of a proposition?
I'm not well enough versed in the language and history of formal logic to know the answer to this, but to me it seems like the kind of problem that was solved in mathematics by the invention of the concept of zero. Just like "the present King of France" or "the round square", the number zero doesn't actually refer to anything. It is just a symbol that represents nothing, which we sometimes find useful in mathematical calculations. In the same way that zero is neither positive nor negative, non-denoting phrases may be neither true nor false. And this would help answer the calculation problem that Baggini raised in his analysis of this thought experiment. He said:
The problem is that, in logic, the negation of a false statement is true. So, for example, if "the sun orbits the Earth" is false, then clearly "the sun does not orbit the Earth" is true. That means, however, that if "the King of France is bald" is false, then "the King of France is not bald" must be true. But it can't be true that the King of France is not bald, because there is no such monarch. And so it seems that such statements as "the King of France is bald" when there is no king and "the current manager of the England football team is a liar" when there is no such manager are neither true nor false. If a statement is neither true nor false, doesn't that make it meaningless? You might think so, but surely the meaning of the statement "the current manager of the England football team is a liar" is perfectly clear. And a meaningless statement, the meaning of which is clear, would seem to be a contradiction in terms.
If we take the mathematical properties of zero, however, and apply the same type of logical properties to these non-denoting phrases, then we can get something that is not contradictory and is still clear. We know that 6 is a positive number and -6 is a negative number. If we multiply either number by zero, we get zero, which is neither positive nor negative. In the same way, "is bald" is a positive / true assertion and "is not bald" is a negative / false assertion. If we modify / multiply either of these assertions with something like "the present King of France", we get statements that have zero value. They are neither true nor false.
Indeed, in his essay, "On Referring", P. F. Strawson criticised Russell's "characterization of statements where the object does not exist, such as "the present King of France", as being false. Such statements, Strawson held, are neither true nor false but, rather, absurd. Strawson believed that, contrary to Russell, use does determine the meaning of a sentence. To give the meaning of an expression is to "give general directions for its use." Because of this, Strawson argued that, were someone to say the King of France was wise, we would not say their statement is true or false, but, rather, decide they must be under a misapprehension since, normally, the question would not arise as there is no King of France."
Thus, in the same way that mathematical equations with the number zero in them are meaningful and understood and may result in answers that are neither true nor false, non-denoting phrases that are "absurd" are also meaningful and understood, even if they result in phrases that are neither true nor false.
It seems shocking to any schoolchild now that it took thousands of years to invent the number zero, but perhaps we see why it took so long because of how the same difficulty can be seen to be playing out in the linguistic logic of analytical philosophy. Since zero doesn't refer to anything real or imagined, it's a really hard concept to invent. The word "absurd" already has other connotations that involve disbelief and falsehood, and a quick read of Strawson's essay would seem to indicate to me that he didn't make the connection between the emptiness of zero and the emptiness of absurd phrases, so if I got to rename this concept, I might call it something new like xero. As in, the article in this thought experiment is neither true nor false, it is technically xero.
And with that conjecture about how to help solve the puzzle of denotation, I'll end this long post. If anyone out there is enough of an expert in analytical philosophy to help me judge whether this is a new idea or not, I would love to receive feedback on it. If not, then this will have just been another one of those difficult exercises wrestling with the logic and understanding of the world that has somehow enlarged my appreciation for it. Thanks for taking that journey with me.
Sounds good, right? Okay here's the thought experiment.
--------------------------------------------------
"Your honour, my client's defence is very simple. He accepts that he did indeed write in his newspaper column that "the current manager of the England football team is a liar, an idiot, and a national disgrace." He also accepts going on to say that he "should be shot." But by doing so, he in no way libelled the plaintiff, Mr Glenn Robson-Keganson.
"The reason for this is easy to see. At the time the article was written and published, there was no such person as the England football team manager. Mr Robson-Keganson had tendered his resignation two days earlier, and his offer had been accepted. This news became public knowledge on the day the defendant's article was published.
"The plaintiff claims that the accusations my client made were false. But they were neither true nor false, since they were not about anyone. Indeed, it would be more accurate to say they were meaningless. "Flar-Flar is a racehorse" is true if Flar-Flar is a racehorse, false if she is not, and meaningless if there is no such beast.
"The jury should therefore dismiss the case. It is just nonsense to suggest one can libel someone who does not exist. I rest my case."
Source: "On Denoting" by Bertrand Russell (1905).
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 253.
---------------------------------------------------
In my post Analysing Russell, the Father of Analytical Philosophy, I briefly touched on this puzzle, although I did not wrestle with it in depth. I ended up concluding, perhaps too simply, that:
This over-analysis of grammar known as analytical philosophy is just logic applied to writing. It is important to be clear, but this is a small part of our overarching knowledge. It does not deserve the central role in philosophy departments that it has achieved. It consigns them to the role of fussy nitpicker, rather than the broad-minded lover of wisdom.
I still feel that way about this topic, but who amongst us doesn't feel it's necessary to pick some nits every once in a while? I know I do. And so I feel I should indulge Bertrand Russell on this, especially since he absolutely spent plenty of time on broad-minded pursuits of wisdom too. He wrote this after all:
Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind is also rendered great.
So, let's get studying and see what gets enriched!
(Have I sold you on this enough yet?)
When Baggini discussed this thought experiment, he started by acknowledging the pragmatic real-world response to the legal case by saying, "The jury would probably dismiss [the defence] on the grounds that we know who he meant by 'the current manager of the England football team'." I agree. It is indeed specious to claim the article was not libellous in its intent. By changing one adjective—"current" to something like "previous" or "former" or "the last"—the entire article would still stand, naked with its obvious intent. The moment-to-moment accuracy in the mind of the writer of this one word does not change the meaning or the intent of his entire article. Especially since no one would go to all that trouble to write something about a non-existent person.
So that answers the legal question, but what about the philosophical ones being raised here? Before we dive in to those, keep this plea in mind from the end of Russell's original paper:
Of the many consequences of the view I have been advocating, I will say nothing. I will only beg the reader not to make up his mind against the view—as he might be tempted to do, on account of its excessive complication—until he has attempted to construct a theory of his own on the subject of denotation. This attempt, I believe, will convince him that, whatever the theory may be, it cannot have such a simplicity as one might have expected beforehand.
Okay, we're withholding judgment. So what is "denoting" and what kind of theory do we need to construct about it? Russell wrote:
By a "denoting phrase" I mean a phrase such as any one of the following: a man, some man, any man, every man, the present King of England, the present King of France, [etc.]... We may distinguish three cases: (1) a phrase may be denoting, and yet not denote anything; e.g. "the present King of France." (2) A phrase may denote one definite object; e.g. "the present King of England" denotes a certain man [as it did when this was written in 1905]. (3) A phrase may denote ambiguously; e.g. "a man" denotes not many men, but an ambiguous man.
Got it? We're talking about linguistics here and the correspondence between words and objects in reality. What do our words really refer to and how do we make logical sense of that relationship? Is there always a direct correspondence with some physical or mental object? The folk intuition is to say, "yes, of course our words denote such things," but can such denotation always be explained? Philosophers have had trouble answering this, but Russell offered a new theory for tackling this problem:
My theory, briefly, is as follows. I will take the notion of the variable as fundamental; I use "C(x)" to mean a proposition in which x is a constituent, where x, the variable, is essentially and wholly undetermined. Then we can consider the two notions "C(x) is always true" and "C(x) is sometimes true." Then everything and nothing and something (which are the most primitive of denoting phrases) are to be interpreted as follows:
- C(everything) means "C(x) is always true"
- C(nothing) means " 'C(x) is false' is always true"
- C(something) means "It is false that 'C(x) is false' is always true
Hmmm. Maybe it will help to see this in action:
Suppose we now wish to interpret the proposition, "I met a man." If this is true, I met some definite man; but that is not what I affirm. What I affirm is, according to the theory I advocate:
- " 'I met x, and x is human' is not always false"
Huh?? If you didn't follow that, you don't want to read what he advocates for "all men are mortal" or how to interpret phrases containing "the." After many logical substitutions, it leads to this:
Thus "the father of Charles II was executed" becomes:
- "It is not always false of x that x begat Charles II and that x was executed and that 'if y begat Charles II, y is identical with x' is always true of y."
Somewhat incredible?? Yegads. This seems like an awfully difficult way to attempt to reduce denoting phrases to their non-denoting components. So how are we expected to judge all this?
A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them.
Okay, this sounds fun. What are the three puzzles?
(1) If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of Waverley, and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.
Haw, haw, haw. Harumph, harumph. But the law of identity and substitution does not make sense here. "Scott" and "the author of Waverley" do indeed point to the same identical person, but they hardly have the same amount of information in them. They only denote one small part of that person. "Scott" is the name of that person. "The author of Waverley" describes one action that person has performed. Treating such adjectival phrases as indistinct from one another is to completely misunderstand the form and function of language. This first puzzle is no puzzle at all. Next!
(2) By the law of excluded middle, either "A is B" or "A is not B" must be true. Hence either "the present King of France is bald" or "the present King of France is not bald" must be true. Yet if we enumerated the things that are bald, and the things that are not bald, we should not find the present King of France in either list.
Of course you would! The things that are not bald includes all imagined things too. It helps slightly to restate the original question into the form that Russell used to analyse it. In that case, we see that "the present King of France" is not "a bald thing." It's no thing at all, so it's certainly not a bald one either. It's quite weird to say, but "the present King of France is not bald" may technically be considered a true statement. Anyone who has played 20 questions will have experienced this phenomenon. But is it as accurate as it could be? More on that below.
To me, the problem with these first two puzzles (and much of analytic philosophy) is that they are examples of what happens when one attempts to take the rules of logic from mathematics and numbers and tries to apply them directly to the world of words and meaning. Numbers are discrete, objective, singular points. Words are vague, fuzzy, subjective, multipolar concepts. Simple manipulations such as negation, substitution, and addition do not always apply here with the perfect accuracy that logicians want so desperately to have.
From my blog post profiling Bertrand Russell, we saw hints that such clinging to cold and logical mathematics by the adult Russell probably arose because of his emotionally traumatic childhood. I wrote that, "It seems from several quotes that Bertrand came to rely on the bedrock of mathematics as a solid retreat from his chaotic childhood filled with so much promise, change, and death:
In action, in desire, we must submit perpetually to the tyranny of outside forces; but in thought, in aspiration, we are free, free from our fellowmen, free from the petty planet on which our bodies impotently crawl, free even, while we live, from the tyranny of death.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza's God, it won't love us in return.
From this background, we see perhaps why Russell attempted the whole project of co-founding analytical philosophy with his student Ludwig Wittgenstein. But in my post on Wittgenstein, I noted:
After the completion of his first book, Tractatus Logico-Philosophicus in 1918, Wittgenstein believed he had solved all the problems of philosophy and he abandoned his studies. However, in 1929 he returned to Cambridge and began the meditations that ultimately led him to renounce or revise much of his earlier work, rejecting the analytical fantasy that a philosophical language could be derived mathematically from first principles, in favor of a more descriptive linguistic philosophy. This change of mind culminated in his second magnum opus, the Philosophical Investigations, which was published posthumously. In it, Wittgenstein asks the reader to think of language as a multiplicity of language-games within which parts of language develop and function. He argues philosophical problems are bewitchments that arise from philosophers' misguided attempts to consider the meaning of words independently of their context, usage, and grammar, what he called "language gone on holiday.” According to Wittgenstein, philosophical problems arise when language is forced from its proper home into a metaphysical environment, where all the familiar and necessary landmarks and contextual clues are removed. He describes this metaphysical environment as like being on frictionless ice: where the conditions are apparently perfect for a philosophically and logically perfect language - the language of the Tractatus - where all philosophical problems can be solved without the muddying effects of everyday contexts; but where, precisely because of the lack of friction, language can in fact do no work at all. Wittgenstein argues that philosophers must leave the frictionless ice and return to the "rough ground" of ordinary language in use.
What a perfect criticism of these puzzles on denotation so far. But let's get back to Russell's original paper and see the third and final puzzle, which actually raises an interesting question. Next!
(3) Consider the proposition "A differs from B." If this is true, there is a difference between A and B, which fact may be expressed in the form "the difference between A and B subsists." But if it is false that A differs from B, then there is no difference between A and B, which fact may be expressed in the form "the difference between A and B does not subsist." But how can a non-entity be the subject of a proposition? ... Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connection to Meinong, that to admit being also sometimes leads to contradictions. Thus if A and B do not differ, to suppose either that there is, or that there is not, such an object as "the difference between A and B" seems equally impossible. The relation of the meaning to the denotation involves certain rather curious difficulties, which seem in themselves sufficient to prove that the theory which leads to such difficulties must be wrong.
I have to jump back here to a passage about Meinong to make sense of this. Russell wrote that:
The evidence for [my] theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meinong. This theory regards any grammatically correct denoting phrase as standing for an object. Thus "the present King of France," "the round square," etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round; etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred.
Okay, we are finally at the heart of this denoting problem. Basically, when philosophers invent an impossible strong of words such as "the present King of France" or "the round square", we seem to be able to understand these phrases and even perform logical analyses using them, but they actually refer to nothing. In case you missed it, Russell summarised this above when he said, "But how can a non-entity be the subject of a proposition?"
His own answer was to go through the incredible manipulations and substitutions shown above in order to remove all denoting phrases from the logical analysis of language. Thus, "I met a man" became "'I met x, and x is human' is not always false"; and "the father of Charles II was executed" became "It is not always false of x that x begat Charles II and that x was executed and that 'if y begat Charles II, y is identical with x' is always true of y." In Russell's words, this "gives a reduction of all propositions in which denoting phrases occur into forms in which no such phrases occur."
Besides being incredibly abstruse and unhelpful, I don't think Russell actually achieved his goal since language is nothing but referrals and denotations. It is literally impossible to remove denoting phrases from language. This is why Wittgenstein later abandoned the project of "a philosophically and logically perfect language." But then where does that leave us with regard to puzzle number (3) and how a non-entity can be the subject of a proposition?
I'm not well enough versed in the language and history of formal logic to know the answer to this, but to me it seems like the kind of problem that was solved in mathematics by the invention of the concept of zero. Just like "the present King of France" or "the round square", the number zero doesn't actually refer to anything. It is just a symbol that represents nothing, which we sometimes find useful in mathematical calculations. In the same way that zero is neither positive nor negative, non-denoting phrases may be neither true nor false. And this would help answer the calculation problem that Baggini raised in his analysis of this thought experiment. He said:
The problem is that, in logic, the negation of a false statement is true. So, for example, if "the sun orbits the Earth" is false, then clearly "the sun does not orbit the Earth" is true. That means, however, that if "the King of France is bald" is false, then "the King of France is not bald" must be true. But it can't be true that the King of France is not bald, because there is no such monarch. And so it seems that such statements as "the King of France is bald" when there is no king and "the current manager of the England football team is a liar" when there is no such manager are neither true nor false. If a statement is neither true nor false, doesn't that make it meaningless? You might think so, but surely the meaning of the statement "the current manager of the England football team is a liar" is perfectly clear. And a meaningless statement, the meaning of which is clear, would seem to be a contradiction in terms.
If we take the mathematical properties of zero, however, and apply the same type of logical properties to these non-denoting phrases, then we can get something that is not contradictory and is still clear. We know that 6 is a positive number and -6 is a negative number. If we multiply either number by zero, we get zero, which is neither positive nor negative. In the same way, "is bald" is a positive / true assertion and "is not bald" is a negative / false assertion. If we modify / multiply either of these assertions with something like "the present King of France", we get statements that have zero value. They are neither true nor false.
Indeed, in his essay, "On Referring", P. F. Strawson criticised Russell's "characterization of statements where the object does not exist, such as "the present King of France", as being false. Such statements, Strawson held, are neither true nor false but, rather, absurd. Strawson believed that, contrary to Russell, use does determine the meaning of a sentence. To give the meaning of an expression is to "give general directions for its use." Because of this, Strawson argued that, were someone to say the King of France was wise, we would not say their statement is true or false, but, rather, decide they must be under a misapprehension since, normally, the question would not arise as there is no King of France."
Thus, in the same way that mathematical equations with the number zero in them are meaningful and understood and may result in answers that are neither true nor false, non-denoting phrases that are "absurd" are also meaningful and understood, even if they result in phrases that are neither true nor false.
It seems shocking to any schoolchild now that it took thousands of years to invent the number zero, but perhaps we see why it took so long because of how the same difficulty can be seen to be playing out in the linguistic logic of analytical philosophy. Since zero doesn't refer to anything real or imagined, it's a really hard concept to invent. The word "absurd" already has other connotations that involve disbelief and falsehood, and a quick read of Strawson's essay would seem to indicate to me that he didn't make the connection between the emptiness of zero and the emptiness of absurd phrases, so if I got to rename this concept, I might call it something new like xero. As in, the article in this thought experiment is neither true nor false, it is technically xero.
And with that conjecture about how to help solve the puzzle of denotation, I'll end this long post. If anyone out there is enough of an expert in analytical philosophy to help me judge whether this is a new idea or not, I would love to receive feedback on it. If not, then this will have just been another one of those difficult exercises wrestling with the logic and understanding of the world that has somehow enlarged my appreciation for it. Thanks for taking that journey with me.
