Investigations 293

In §293 Wittgenstein considers what it would be if “pain” were a name for a particular kind of inner experience and goes on to show how this picture cannot make sense via his beetle-box example, discussed shortly.
      Suppose that I know what the word “pain” means only from my own case – that is, I know it as a name for a particular sensation that I have. If this is how I know the word, then this must also be how others know the word – that is, Sam knows the meaning of “pain” from his own case, as a name for a particular experience of his, something inward. In order to ascribe “pain” to others, it seems I have to generalize from my own case, something like “When I say I’m in pain I feel this way, so when others say that they are in pain, they feel that way too.” The justification for this generalization is dubious, for I only know one case of application (my own), and cannot infer that others are using it the same way (since I don’t have access to their inner experience). This cannot be the right picture of how I know the word “pain”. We’ll now elaborate.
     Intuitively, it seems that someone can only know what pain is from their own case. Let’s take this intuition seriously and consider the following example. Suppose everyone has a box with something in it called a “beetle”. No one can ever look into anyone else’s box (it is logically impossible), and everyone says he knows what a beetle is only by looking at his own beetle. (We can think of the box as a person’s mind, the beetle as the particular sensation that person has – and the person knows what the beetle is in his own case. In this way, there is analogy to the pain case. There is a sensation of pain [particular beetle] in the “mind” [box], and the public word for the sensation: “pain” [beetle].) In this example, the contents of each person’s box may differ – we can even imagine the contents changing—“beetle” simply designates the box-contents regardless of what is or is not in them.
     In this situation, we cannot say that Sam knows what a beetle is only by looking at his own beetle. Why? Suppose Sam has an orange in his box. You ask Sam “what’s beetle?” He can either say (1) an orange, or (2) whatever is in the box. If (1), we can’t say he knows what a beetle is because for all he knows a pear is in someone else’s box—if “beetle” denotes orange then it shouldn’t denote pear. If (2) then he hasn’t said what a beetle is, for he might as well have said “a beetle is a beetle” or “what is in the box is in the box”. Such an answer is not at all informative, and so not at all meaningful. This echoes §298, where Wittgenstein observes that the fact we’re inclined to say “This is the important thing” – while we focus on our particular inward experience – is sufficient to show how we are inclined to say something which is “not informative”. One cannot know the meaning of “beetle” just from looking at his own beetle.
     Now let’s suppose that these people had a use for the word “beetle”. That is, suppose “beetle” is in fact a meaningful expression. If so, “beetle” couldn’t be a name for a kind of inner experience, for the same reasons stated in the previous paragraph. We cannot name the thing in the box; for suppose someone’s box is empty, “beetle” cannot stand as a name for an orange and as a name for emptiness – we cannot refer to the particular (non)object in any one’s box because it’s contents aren’t part of the language game – whatever it is cannot be shared or expressed, for a private sensation cannot even be given a name that others (or even yourself) can understand. The object in the box is not an object of possible reference, there is no public word for one’s private contents, as we saw in §258. If the word has a use, its use is as something other than a name – it can be publicly understood. If “beetle” has a meaning, it cannot be a name. The idea is that if mental predicates like “pain” are names denoting a kind of object, the object “drops out of consideration as irrelevant” – we can’t actually make sense of our referring to that object. If the word only ever has a public use – is publicly understood – then it cannot ever be used a name for a private object. When I say “I am in pain” I express something we all understand – I do not name a particular inner sensation present to me – this is the sense in which the object “drops out of consideration as irrelevant”.
      §291 buttresses this point. Consider that you might think of a description as a kind of name for an object—“a word-picture of the facts”. On this view, there’s a sense in which the description is idle, it simply depicts a state-of-affairs. But now consider how an engineer might use a description. Drawing a machine, a sort of design, is like a description of what he will build. Recording a measurement is a description that he uses to know where put things or how to put them together. These descriptions have particular uses – they are not “idle”. If we think of words as names for objects, they become idle; if we realize that words have uses (over and above naming objects), we see that words are not mere pictures but rather tools for doing things. The engineer’s description gets its meaning from its use or place in some project – not as a name for his inner imaginings. If we want to grasp the meaning of a word, we must look to its use; if words are merely names for objects (especially for inner qualities), we cannot make sense of how we can use them meaningfully.
      The example in §293 does not show that there is or is not any particular sensation that one stands in relation to. Rather, it demonstrates that the grammar of our language doesn’t allow for this kind of private reference or knowledge of meaning (§304). There is no place in the language for a name for a private sensation, for there is no sense in which we could understand what we are referring to. Insofar as words have uses – and, consequently, meaning – they must be used to talk about something other than private mental contents.

Investigations 258

In §256, Wittgenstein characterizes a private language as that language which describes my inner experiences and which only I myself can understand. Words of this language cannot be connected with my natural expressions of sensation – if they were, the language could not be private, but is rather public, for anyone might understand my natural expressions and so come to understand my purportedly private language. That is, if a private language is connected with natural expressions, then the expressions of the language are public/observable – its expressions cannot be understood uniquely by me. So if we are to have a private language, it cannot be connected with natural expression – rather, it must work the following way: we have sensations (which are in some sense private) and come to associate names with the sensations and use these names in descriptions (which, presumably, cannot violate the privacy).
In §258, Wittgenstein asks us to consider the following case. I want to keep a diary about the recurrence of a certain sensation or I have. I associate the sign “S” with the sensation, and write this sign in the diary every day on which I have the sensation. This is the only means by which I “express” my experience of the sensation – there are no natural expressions of the sensation, all the outside observer can see is the “S”-writing behavior. I cannot formulate a definition for “S”. Why? Suppose I say, or think, that “`S’ is defined as such-and-such”. If the “such-and-such” is some combination of familiar, public words (in English, let’s say), then my sensation is publicly expressible and cannot be private, contrary to our hypothesis. Or else if the “such-and-such” is some other private sign like “S”, then those signs must also be given some definition, and so on.
Recall that to give an ostensive definition of a thing is to “attach a nametag” to it by gesturing toward the thing and producing an utterance. You might think that “S” could be defined ostensively. Not so. For in what sense can you gesture toward a sensation? It is not as though I could point to the S-sensation in my head (I’d just be pointing at my head!). But you might think that in some sense you can point to your sensation insofar as you “concentrate [your] attention on the sensation [so as to] `point inwardly’”. But this, too, would be a mistake. For we can ask “what is this `ceremony’ of concentrating your attention for?” What does it mean to “concentrate your attention” on this thing rather than that – and what does it actually accomplish? You might think it accomplishes this: by concentrating your attention on the sensation and committing to memory a connection between the sensation and “S”, you bring about the connection between the sensation and “S”.
Committing the connection to memory just means that this process [concentrating the attention] brings it about that I remember the connection correctly in the future. If concentrating your attention makes it the case that you remember the connection correctly in the future, then there must already be some fact of the matter regarding a correct connection between the sensation and “S”. But in the case we are asked to consider, there is no criterion of correctness. I can’t bring it about that I remember the connection correctly in the future unless I have the resources to say that it was correct to apply “S” to the sensation in the first case. There’s a temptation to say that because this is my private sensation and my private language whatever seems correct to me is correct. And so because applying “S” to the sensation seems correct to me, it in fact is. This, however, is not right. To say “whatever seems correct to me is correct” is just to say that “we cannot talk about `correct’”.
A brief elaboration. My “concentration of attention” doesn’t seem like it should change anything about how “S” may be used, nor does it affect the sensation; there is no tangible connection brought about. It cannot be the case that whatever seems right and wrong is in fact what is right and wrong. For if it were, then understanding how to “go on” would just be a matter of conforming to the thought or formula which seems right in your head. But we saw in §154 that understanding how to go on or continue a series is not a matter of having a formula occur in your head and conforming to that. Likewise, what is right or wrong is not so because of some occurrence in your head – like “seeming right”. Suppose I wake up one morning and what seemed right to me yesterday now suddenly seems wrong – has the status of what is right or wrong suddenly changed? Intuitively, we want to say “no”. Because I cannot mentally set my own standard of correctness, then in this situation there can be no “right” or correct use (of “S”).
We can strengthen this point with considerations from §257. If I invent a name for my sensation in my private language, I cannot make myself understood when I use the word. That is, I could never use “S” in a sentence and have someone understand what I mean by it. If I cannot make myself understood to others when I use the sign, then in what sense do I understand “S” when I use it? It seems like I can just stick “S” to whatever sensation I feel like, whenever I feel like—so in what sense could this sign have any meaning to me? Insofar as it a name? Not so, for there is still no criterion of correct usage. A name is used to refer to an object, and I cannot use this name for anything (as no one understands it) – it has no purpose and cannot be used to refer. Should I use “S” to refer to some other thing, no one can tell me I’ve used the sign wrong – if “S” can refer to whatever I like, then there cannot be a fact of the matter as to the correct use of “S”.
In order to give something a name, there must a role existing in the language for that word to occupy. There must be a post at which the word is stationed – a role the world plays. But there is nothing in the grammar of any public language – no station – which fixes the use of the term “S”. So we cannot under the notion of a private language.

Investigations 201

We should first clarify the meaning of “interpretation”. Suppose I’m traveling from Berkeley to Timbuktu. At some point I no longer know the way, but I see a signpost reading, “Timbuktu → ”. The signpost expresses a rule – that is, the signpost is an expression of a rule, namely a rule regarding how to get to Timbuktu. I see that sign and think, “Ah, I ought to proceed East to Timbuktu.” This thought, which represents what I take the signpost to be expressing, constitutes my “interpretation” of the rule expressed by the signpost. If I had seen the sign and thought “I ought to proceed West to Timbuktu”, that thought would also constitute an interpretation of the expressed rule.
The paradox is: no course of action can be determined by a rule because every course of action can be brought into accord with the rule (87). In what way is every action capable of according with a rule? Consider a teacher expressing a rule (regarding a particular series) to his pupil: “Add two each time.” The pupil proceeds: 2,4,…,998,1000 . We would say that he is following or acting in accord with the rule. But then the pupil proceeds: 1004,1008,… . The teacher sees that the pupil must not understand, though the pupil cannot be made to see that he was not “adding two each time”: he maintains he was following the rule expressed. We might think that the pupil understands the order as “Add 2 up to 1000, 4 up 2000…” and so on; that is, his actions are still governed by his interpretation of the rule expressed. He did not follow the rule (that the teacher expressed) – even for the first 500 terms – but his actions for the first 500 terms were in accord with that rule. And his actions after the 500th term were in accordance with his [the pupil’s] interpretation of the rule “add two each time” (81). In §198, Wittgenstein’s interlocuter says, “…whatever I do can, on some interpretation, be made compatible with the rule.” This is like how the pupil failed to see his own misunderstanding the order – on his interpretation of the sign (expression of a rule) “Add two each time”, his actions were compatible with the rule.
If any action, on some interpretation, is in accord with the rule, then no rule can determine a course of action. For then any course of action is acceptable by some interpretation of the rule, so no particular course of action is determined by the rule. Wittgenstein responds to the paradox, “if every course of action can be [compatible] with the rule, then it can also be [incompatible] with it. And so there would be neither accord nor conflict here.” (87) This is to say that there is no fact of the matter as to whether a course of action is compatible with a rule, because there exist interpretations of the rule which conflict with the action and those which do not.
That is, here is an expression of a rule: “Add two each time”. The pupil’s interpretation may be “ f(x)=x+2 ”. But this, too, is a sign to be interpreted. And based on the pupil’s behavior, we can say that the pupil interprets the expression “ f(x)=x+2 ” as “ ∀ x( x<1000 → f(x)=x+2 ) ∧ ∀ x( x ≥ 1000 → f(x)=x+4 ) ”. But now how are we to say the pupil interprets this sign? Prima facie, it looks like we need a rule which tells us how an expression of any given rule is to be interpreted. But this cannot be possible, for it leads to regress. Why? Because a rule saying how an expression of rule is to be interpreted must itself be expressed and interpreted. We would need a rule which says how to interpret that rule, and so on and so forth, never bottoming out.
Wittgenstein asserts that there is a “way of grasping a rule which is not an interpretation” (87). This must be so, lest we end up with the regress problem. Recall §154, where Wittgenstein argues that understanding should not be thought of as a mental process. To say, “Now I understand the series” is not to say “the formula occurs to me” – where the formula occuring is something like the interpretation of the rule expressed by the series. We say “Now I understand” when we can continue the series correctly. So when we say that “the pupil understands the rule,” we are saying that has the ability to apply it correctly. What does it mean to apply a rule correctly? From §201, this way of grasping a rule is “exhibited in what we call `following the rule’ and `going against it’” in each particular case with its particular circumstances (87). This means that the correct application of a rule does not have to do with an occurrence or given interpretation in one’s head. The deviant pupil did not grasp the rule, but not because his interpretation of the rule differs from ours. Rather, his actions did not conform to what we call “following the rule”. His actions deviated from the actions the “add two each time” order is supposed to provoke in this kind of circumstance (given the effects the teacher was trying to produce, what sign was used, etc.).
There is an inclination to say that every action according to a rule is an interpretation (87) – this is why we concocted elaborate formulas in the deviant pupil’s head to account for his misunderstanding. But this isn’t right, for understanding isn’t “in the head”, so to speak. Actions either follow the rule or go against it – this being judged externally, case by case – but actions themselves are not interpretations (though it seems they can be interpreted). Indeed, Wittgenstein says, “one should speak of interpretation only when one expression of a rule is substituted for another.” (87) That is, an interpretation is an expression of a rule; the substitution of one expression for another constitutes an interpretation of the original expression. An interpretation is not to be confused with a rule, nor is it to be confused with a given action.

Investigations 154

In §154, Wittgenstein claims that understanding should not be thought of as a mental process.
      We asked to consider when we are justified in saying that a pupil understands some system, or to consider when we ourselves are justified in saying, “Ah, now I understand the system”. That is, what is it that goes on in these situations when one is credited with understanding. Consider four pupils each examining the same series of numbers: 1, 5, 11, 19 …. We say that a pupil understands the series if he can correctly produce the next term of the series; for if a pupil did not understand the series, then he would not be able to correctly continue the series. So we say one understands when they can “go on” continuing the series correctly. The question, then, is what does this understanding consist in?
Suppose each pupil can correctly carry on the series, establishing that the fifth term is 29. What is going on in the pupil’s head when he realizes he can correctly continue the series? It seems there are many processes that could have been at work. For instance, it might “occur” to the first pupil that the first four terms can be united under the formula: a_n = n^2 + n - 1 . The formula did not, in contrast, occur to the second pupil. Instead the second pupil notices a progressive series of differences: 4, 6, 8 …, and infers that the next difference is 10 so the fifth term should be 29. For the third pupil, it could be the case that this series is simply as familiar to him as the ordinary series of natural numbers, and from this familiarity can “go on”. The fourth pupil might have some immediate intuition that the fifth term is 29. Regardless of what particular process occurred in each pupil’s head, we will still credit each pupil with having understood, for they can continue to correctly carry on the series. The moral is that there is not one unique “occurrence” in one’s head that constitutes understanding. Understanding cannot consist merely in having the appropriate formula occur to you; for the pupil who notices the differences and yet doesn’t having a formula occur to him is still credited with understanding. Because of this we cannot say that “Now I understand the series” means the same thing as “the formula occurs to me”. To emphasize this point, consider a pupil to whom the appropriate formula does in fact occur. It could still be the case that they misapply the formula, and fail to correctly carry on the series with 29. Consequently we will say that this pupil does not understand the series, even when the correct formula occurs to him. So understanding must be something besides merely having the appropriate formula occur to you.
     If when I say “Now I understand” I have not said “the formula occurs” to me, what then does it mean to say “Now I understand”? You might think that understanding is a (presumably mental) process which somehow occurs behind or along with the occurrence or utterance of the formula. How are we to think of mental processes? Wittgenstein suggests that a pain’s increasing or decreasing, or the listening to a tune or sentence are mental processes. The pain experience or the auditory experience are mental processes insofar as they are particular occurrences “in one’s head”, so to speak. These processes may be interrupted; for instance, I may be in pain and then fall asleep. When I fall asleep, we do not continue to attribute the mental process of being in pain to me. Or if Barry Stroud falls asleep at the opera, his mental process of listening to the tune has been interrupted; we no longer attribute the listening of a tune to him. In a similar way, the occurrence in your head of the appropriate formula is a kind of mental process. You may be representing the appropriate formula, fall asleep, and so cease to be in a state of representing the formula (or of having it occur to you).
      Understanding does not seem to be a mental process in the same sense as the listening to a tune. Sam, grandmaster of chess, we attribute understanding of chess to. When Sam falls asleep, we do not say that his understanding is interrupted. When Sam is asleep we still say he understands chess. Sam doesn’t understand chess merely when the appropriate chess move occurs to him during a game (as when a particular formula may occur to you during a math problem). Sam’s being in a state of sleep does not strip him of his ability to play chess. In this way, Sam’s understanding cannot be identified with the occurrence of some mental process that happens alongside his action.
      So when a pupil thinks “Now I can go on” and utters the correct formula, what can we point to which actually justifies the pupil’s thinking “Now I can go on”? We’ve seen that we cannot point to some unique occurrence in his head, for there were many various occurrences which accompanied each pupil’s ability to go on (e.g. representing the appropriate formula or seeing the sequence of differences). Nor can we point to some mental process, for mental processes can be interrupted in ways that the understanding seemingly cannot. We cannot point to something inside the pupil’s head and say that that’s what the understanding consists in; consequently, we should look at the circumstances of the situation outside of just what is in one’s head. This leads Wittgenstein to suggest that if there is something which justifies the pupil’s thinking “Now I can go on”, it is the particular circumstances which underly the utterance of the formula (or the noticing of the series of differences). There is something about the pupil and the external situation he’s in which determines whether we are justified in saying that he understood. It is not enough for the the formula to occur to the pupil, but the formula must occur to the pupil in the right circumstances, where the pupil reacts in the right way to the given external stimulus (e.g. the series). If the external stimulus had been different but the pupil reacted the same way we would not credit him with understanding. To see that someone has understood, we must look at more than what goes on in their heads, but also what the external stimulus was and what the external reaction on the part of the pupil is. In this way, we see understanding as more of an external process – an ability or a “can-do” – than any particular mental process.

Investigations 32

This post explains §32 of Philosophical Investigations, further explicating the main thrust: that Augustine’s description of how one learns a language presupposes that one already has some kind of language.
      Before examining §32, we should explain ostensive explanation. To give an ostensive explanation or definition of a thing is to “attach a nametag” to it by gesturing toward the thing and producing an utterance (which presumably is the name). For instance, suppose my tutor attempts to provide me with an ostensive explanation or definition of the number two. He points to two black bolts and utters, “this number is called `two’” (18). He does not merely utter “two”, lest he be misconstrued as (a) naming this particular group of bolts “Two”, (b) naming this kind of arrangement of objects “Two”, (c) naming the black color of the bolts “Two”, and so on. By qualifying his explanation with “this number” we specify the role of the word “two” in the language, namely as a counting-word, so that it is not confused with (a), (b), or (c) (18).
             For his ostensive explanation to be successful, however, I must already understand what the word “number” means, or else I will not understand that he meant to define “two” as a counting-word and may miscontrue him in any of the aforementioned ways and I will not come to use the word correctly. If I don’t know the meaning of “number”, then this must be given an ostensive explanation as well; such an explanation will consist, presumably, in other words. And those words would have to be explained via other words, and so on, ad infinitum. The moral is that in order for ostensive explanations to be successful, we must be equipped with some words which we can use to understand the words we are being taught – our minds must already be prepared in a certain way. If we have to resources to understand the role the word plays in language, then we can come to correctly use, and so understand, the word.
      Suppose I am visiting a foreign country. In §32, Wittgenstein observes that I will learn the language of the inhabitants by the ostensive explanations they give me. But we saw that ostensive explanations are given through words, which must be defined in a similar way. He further observes that I will have to guess how to interpret their explanations. If an inhabitant says – in his language – “This number is called two”, but I do not know how the word “number” is used, then I must make a guess as to the meaning of number, if I am to interpret his explanation of “two”. In some cases I may guess correctly and in other cases not. If I guess incorrectly, the inhabitants will take it that I do not understand the meaning “two”.
      The main thrust of §32 is that Augustine describes the manner in which learn our first language as if we were learning a foreign language. That is, in his explanation of the learning of language, he presupposes that we already have a certain “language of thought” or that we can “talk to ourselves” – prior to the learning of any public language (19). Imagine we all in fact have such a language of thought. Then learning our public language (e.g. English) involves something like the following: we learn what English nametags correspond to the words of the language of my thought. This is like the learning of foreign language, where we identify the word of the foreign language with the word we already have command of the use of in our non-foreign language. To have a language of thought is to have a place “prepared” (19) for the learning of language.
      Reconsider my going to a foreign country and recall that I must guess in order to interpret the inhabitants’ ostensive explanations. In order for me to interpret the ostensive explanation of “two”, I must make a guess that “number” (or the inhabitant’s word for it) signifies that “two” is to be a counting-word. In order for me to make this kind of guess, I must already have my own concept of number. This means I must speak some kind of language already; otherwise, I would have no word or sign I could use to represent the concept of number to myself. For me to already be a speaker of a language is for me to have a place prepared for the learning of other words in the foreign language – I am already familiar with the various roles and uses of words. If I did not already have my own language and word for the number concept, I would not be able to guess the interpret the inhabitants’ explanation of “two” as indicating a counting-word. So in order to learn a foreign language through ostensive explanation, I must already have a place in my mind prepared; I must already have some kind of language of thought. And so I am merely connecting the inhabitant’s word with my own way of thinking of things – I am applying a new nametag to an old concept.
   Augustine, in describing the learning of language as a matter of learning what nametags go to what objects, presupposes that we already have some kind of language of thought. In this way, he describes learning language as the same kind of process that goes on when you learn the language of a foreign country via the ostensive explanations of its inhabitants.

The Liar Paradox and the Measurement Problem

Just a quick observation.  I think that a telling analogy can be drawn between the measurement problem in quantum mechanics (QM) and the liar paradox.  This aside is just meant to draw out those intuitions.

The liar paradox amounts to more or less the following statement.   ‘This sentence is false.’  You know the drill.  If the sentence is true, then it must be false (for it asserts its own falsity).  And if the sentence is false, then it must be true (for the negation of its falsity is its truth).  In light of this (and to avoid infinitely ‘looping’ through the truth-values of the sentence), we say that we cannot ascribe any truth-value to the sentence at all, dub it a paradox, and call it a day.

Another account of the measurement problem can be found here.  Nevertheless, here’s the gist.  The dynamic equations of motion (DEM) (the third axiom of QM) are thought to certainly determine the states and motions of all particles (all states and motions are calculable [via the Schroedinger equation]).  By DEM, if we measure the color of a hard electron, the measurement outcome should be in a superposition of being both black and white.  But this isn’t actually what happens (and is where the fifth axiom of QM comes in).  The measurement outcome is always either definitely black or definitely white (with each result have a probability of exactly .5).  (Somehow measurement ‘disrupts’ the outcome, collapsing the superpositional state into just one of its terms.)

Say our goal is to identify what ‘the liar paradox’ would look like in a physical, rather than linguistic, system.  Superposition seems like a good candidate.  When the hard electron is going through the color box, it is in a superposition of being both black and white.  But we only really understand what superposition means in a negative sense.  An electron in a superposition of being black and white is not black, nor is it white, and it is not definitely both black and white, but nor can it be neither — and what that means, we don’t really know (so we introduce the term, ‘superposition’).  In one sense, it seems that, prior to the measurement outcome, a color-property simply cannot even be predicated of the electron.  With regard to its color, literally nothing can be said.  (Until it emerges from the device, but this isn’t as relevant.)

And this starts to look like a liar paradox.  We refuse to ascribe a truth-value to ‘this sentence is false,’ in the same way we refuse to ascribe a color-property to the hard electron going through the color box.

DEM says that the result of a measurement is superposition, but the collapse postulate predicts a probalistic outcome of .5 for black.  (And how could you ever even see a superposition?)  Suppose the outcome is black.  When you measure a second hard electron, the outcome will necessarily be white.  And when you measure a third, the outcome will be black.1  This sounds like saying: suppose ‘this sentence is false’ is true.  Evaluate the truth-value of the sentence again; it must be false.  And on the next evaluation, it must be true.

The difference between the two is that, empirically, measurements must have outcomes, while the liar paradox doesn’t demand a truth-value in the same way — we can reserve our judgment.

  1. We’re fudging a bit here, but bear with me. 

A Note on Empty Sets and Quantifiers

We talk about many things that do not exist. Dragons, unicorns, perhaps the modern maritime megalopolis of Atlantis, and so on. More practically, we may posit and discuss theoretical scientific entities — entities whose existence we have no evidence for apart from their theoretical or explanatory virtue. For instance, we can talk of the inclement weather as a result of Zeus’s wrath. A set of non-existent entities is empty. Consider the set of all dragons and count its elements. 0. Same for unicorns and modern maritime megalopoleis. That is, they are all equivalent to the null set.

Still, we want to be able to make nontrivial assertions about non-existent entities. We should be able to say things about them, for instance, “Kronos was a titan.”  Suppose someone said “No Kronos was a titan”.  On a certain level this seems contradictory.  But on the following logical construal, we can make sense of it.

Take the proposition, (1) “all dragons are green”. Because the set of dragons is just the null set, this proposition is trivially true. For we express it as, \forall x (Dx \rightarrow Gx). Which is to say: for all x, if x is a dragon, then x is green. Because no x is a dragon, the antecedent of the conditional, “if x is a dragon”, is always false. Therefore, the whole conditional is always true; so “all dragons are green” is true.

Now take the proposition (2) “no dragon is green”. (1) and (2), prima facie, are contradictory. But (2) turns out to be true, also. We express (2) as, \neg \exists x (Dx \wedge Gx). Or: it is not the case that there exists an x which is both a dragon and green. Because there does not exist a dragon, (2) will always be true.

But the logical representation isn’t exactly faithful to the assertive content of the linguistic utterances (1) and (2).  Existence, or lackthereof, is not explicitly asserted in (1) or (2).  This becomes apparent when we translate the logical sentences back into natural language.  “\neg \exists x (Dx \wedge Gx)” translates back into, “there does not exist an object such that it is both a dragon and green.”  And “\forall x (Dx \rightarrow Gx)” translates back into, “for all objects, if that object is a dragon then it is also green.”   These seem a little bit different than their counterparts in (1) and (2).

A different approach.  Prima facie it seems that “no dragon” and “all dragons” denote the same object, namely the null set.  And the predicates are the same.  So we are supposed to admit that the sentences are saying the same thing.  But it seems contrary to intuition to say that these sentences “say the same thing” for lack of a better word.  They denote the same thing insofar as their subjects and predicates denote the same things.


Here’s the thought we are addressing. The set of all dragons is empty. So, prima facie, “no dragon” and “all dragons” refer to the same set (the empty set). So when we predicate “is green” to both “no dragon” or “all dragons” we are referring to the same thing, and consequently the predicate must be true of both.

But “no dragon” and “all dragons” do not denote the same set. “Dragons” denotes the (empty) set of dragons. But quantifiers do not operate on the set they are attached to (e.g. “no” [or “all”] does not qualify the subject “dragons”). Instead, quantifiers modify the denotation of the predicate; in this case, “is green”. “No” means that “is green” is not true of anything in the salient set (this case, dragons). “All” means that “is green” is true of everything in the set. So (1) says, “the predicate, ‘is green’, is true of every individual in the set of dragons”. And (2) says, “the predicate, ‘is green’, is true of no individual in the set of dragons. So the conjunction of (1) and (2) says “the predicate, ‘is green’, true of both all the elements and none of the elements in the set of dragons”. And this is more than just apparently contradictory, it is actually contradictory, for nothing, regardless of its existential status, can be both p \wedge \neg p.

“All” and “No” do not modify the set of dragons. If they did, then there is no contradiction between (1) and (2) because the same predicate, “is green”, is applying to all the same elements. But “all” and “no” modify predicates, not sets. Consequently, in the conjunction of (1) and (2) “is green” and “is not green” are applied to all the same elements, and therein lies the contradiction.

Is the Present King of France Bald?

What is the truth-value of the following statement?

(1) “The present king of France is bald.”

The State of Play

In this post I will explain why this kind of sentence does have a truth-value.  This is a preliminary response in that I have not read any literature specific to this question.  Rather, a while ago the question was posed to me, and it hasn’t been until now that I have taken the time to give it any real consideration.

Trivially, the sentence, “the present king of France is bald” cannot be true.  This is because, as we are all well aware in the 21st century, France has no king.  Consequently the sentence cannot be true, for it is true if and only if there is a present king of France who is in fact bald.  And so we are left with two options.  Either the sentence is false or the sentence lacks any truth-value whatsoever.

It is potentially illuminating to consider another, slightly different sentence, for comparison.  Assume that that there does not exist an escalator in South College.

(2) “John is on the escalator in South College.”

Now ask yourself, is (2) true, false, or neither?  Like (1), (2), trivially, cannot be true, for (2) is true if and only if John is in fact on the escalator in South College, which is impossible as the escalator in South College does not exist.  So again we are left with two options.  Either (2) is false or else it lacks a truth-value whatsoever.

If your intuitions are anything like mine, you will suspect that (1) lacks a truth-value (and so is not false), while (2) is, in fact, a false statement.  We will see if this is so.


On Subjects and Predicates

Before we begin, it is useful to analyze and characterize the relevant subjects and predicates, how they work, and how they relate to each other.

In (1), there is a subject, “the present king of France”, and a predicate, “is bald”.  And in (2), there is a subject, “John”, and a predicate, “is on the escalator in South College”.  Typically a subject is some kind of individual (or object).  A predicate should be thought of as a set, not an object.  The predicate, “is bald”, denotes the set of all objects that are bald.  So when we say that “the present king of France is bald”, we are asserting that the object denoted by the determinative-phrase, “the present king of France”, is an element of the set of all bald things.  Predicates, like “is on the escalator in South College”, may consist in determinative-phrases, such as, “the escalator in South College”.  This does not change their status as predicates, for a legitimate set is still defined for which any object may be tested or assessed for membership.

A Closer Look at John and the King of France

As another preliminary matter, we should make explicit the truth-conditions for both (1) and (2).

(1T) “The present king of France is bald” is true iff the present king of France is bald.

(2T) “John is on the escalator in South College” is true iff John is on the escalator in South College.

The present king of France cannot be bald, for there does not exist a referent for “the present king of France”.  And John cannot be on the escalator in South College, for that escalator does not exist.  Does it follow from this that (1) is false?  Certainly not immediately.  For if (1) is false, then its negation must be true.  The negation of (1), and its corresponding truth-condition, is:

(-1T) “It is not the case that the present king of France is bald” is true iff the present king of France is not bald.

[For the sake of continuity, we include the negation and corresponding truth-condition of (2), as well:]

(-2T) “It is not the case that John is on the escalator in South College” is true iff John is not on the escalator in South College.

Now we ask, is (-1) true?  Assuming that (1) is false, it is logically necessary that (-1) is true.  But here we run into the same quagmire as (1).  It cannot be the case that the present king of France is not bald, because there is no present king of France to which the predicate can be applied.  So (-1) is either false or lacks a truth-value.  But if (-1) is false, then (1) must we true — and (1) we know to be false.  (-1) and (1) cannot both be false, for this flouts the law of noncontradiction.  And neither one can be true.  This strongly suggests that both (-1) and (1) lack truth-values.

And again for continuity, is (-2) true?  Because there exists no escalator in South College, the set defined by “is on the escalator in South College” will necessarily have no actual elements.  So John cannot be a member of that set.  Consequently, it is true that John is not a member of that set.  So (-2) has a truth-value, namely True.  Therefore it is logically necessary that (2) is false.  Though this is consistent with our initial intuitions, it suggests a nontrivial difference between sentences of kind (1) and sentences of kind (2).  We may consider these differences later.


Consideration of Logical Form

But let’s take a closer look at the logical form of (1).

(1L) There exists an x such that x is the present king of France and x is bald.  Or \exists{x}(Fx \wedge Bx).

And its negation:

(-1L) It is not the case that there exists an x such that x is the present king of France and x is bald. Or, \neg \exists{x}(Fx \wedge Bx).

Now we ask, is (-1L) true?  Well it is true that there does not exist an object that is both bald and the present king of France.  And this seems to be exactly what (-1L) says.  So intuitively, (-1L) is true.  But then it is logically necessary that (1L) be false.

And now we’re in a real pickle.  On our first level of analysis we found that a sentence like (1) must lack truth-value.  But on our logical level of analysis, we find that sentences like (1) must have a truth-value (namely, False).  We cannot have it both ways.  And since the disjunction of both analyses exhausts the realm of possibilities, one of the two must be right.

Note we could also express (1) with a universal:

For all x, if x is the present king of France, then x is bald.  Or, \forall{x}(Fx \rightarrow Bx)

And on this rendition, (1) is actually vacuously true!  No x is the present king of France, therefore it all x is -Fx which means that the antecedent of the material conditional is always false and so the entire conditional is always true.

We will have something to say about this.


Picking up the Pieces

There must be a difference between (1) and (1L).  This difference is in what I will refer to as “the assertive content” of the statements (1) and (1L).  Here is the literal translation of 1L:  

(3) Something is the present king of France and bald.

And this is a far cry from (1), “the present king of France is bald”.  Why?  Statement (3) consists in a subject, “something”, and is ascribed a predicate that is the conjunction of two sets, namely the set of present kings of France and the set of all bald things.  But (1) consists in a subject, “the present king of France”, and a single predicate, “is bald”.  Consequently, these two statements differ in assertive content.  (3) asserts the existence of an object which is an element of both the aforementioned sets.  (1) does not explicitly assert the existence of a present king of France, rather what is explicitly asserted is just that the present king of France is an element of the set of all bald things.  The existence of the present king of France is presupposed (and, consequently, not asserted).

What does it mean to presuppose the subject?  Existence is not a predicate.  Predicates stand for the properties of subjects, and no subject has the property of existence.  A subject either exists or it does not, but its existential status is not a property of the subject qua the definition of the subject.  For instance, we can define God as omniscient, omnipotent, and omnibenevolent.  But we cannot include in our specification that God, in addition to having the properties of the three O’s, also exists.  Defining God to have the property of existence does not make it such that God exists.  This is because, in ascribing properties (or predicates) to a subject, we must presuppose the existence of that subject.  In order to ascribe the three O’s to God, I must presuppose the existence of God.  So the ascription of predicates to entities of dubious existence amounts to something like a conditional statement: If so-and-so were to exist, then it would have such-and-such properties. And this especially highlights the fact existence is not a predicate, for consider: If so-and-so were to exist, then it would have the property of existence.  And this is a tautology.

Because no such object exists, contrary to (3)’s explicit assertion, we intuitively found it false.  Because the existence of the present king of France is not explicitly asserted in (1), there was no explicit phrase which could entail the falsity of (1) (for [1] seems to presuppose a present king of France prior to [1]’s assertion).  (1) and (3) differ in assertive content, this difference accounts for our differing intuitions.  But this raises a new question.  Are we to interpret (1) in the manner of (3)?  That is, if Donald Trump, in conversation with you, said “the present king of France is bald”, should you think you had been told something false or should you think that Trump has said something that is simply neither true nor false?

This question acknowledges our conclusion that the truth-value, or lackthereof, of statements like (1) is determined by the particular level of analysis we bring to bear.  But it raises a pragmatic point, on what level of analysis do we interpret the utterances of others in our day-to-day conversations?


The Pragmatic Point

This section marks a departure from our original question.  It seems we are headed toward some contemporary debates in pragmatics and the theory of meaning.  It is not my intention to wade through any of these arguments.  Instead, I will sketch out why I think that, if someone were to assert (1) in conversation, they would assert something false, rather than something sans-truth-value.  The following is primarily influenced by John Perry’s theory of meaning.  (A theory which I think has many virtues.  Though my own views are unsettled.)

Interpreting meaning in conversation is significantly distinct from assessing the meaning (that is truth-conditions [or truth-value, depending on who you ask]) of a statement in isolation.  This distinction stems from the interaction of two fields, viz. semantics and pragmatics.  Semantics aims to understand the truth-functional structure of language — that is, how each lexical item (or word) in a sentence directly contributes to the meaning of a sentence by way of truth-functional application.  Pragmatics, on the other hand, seeks to understand language (and meaning) insofar as a language is a way of doing things with words.  Conversation is an activity, not a rigid exercise in isolated truth-functional application.  In conversation we try to do things like change each others’ beliefs, get somebody to do something (like pass you the salt), or share information.  And when we share information, we do so with the understanding that our interlocutor has a unique set of pre-existing beliefs, modes of presentation, and ways of thinking about the world (that is, the relations between his or her concepts).  In light of this, meaning in pragmatics will be more dynamic than meaning in semantics.

In conversation (the domain of pragmatics), we do not interpret only the explicit, assertive content of another person’s utterance.  We are sensitive to myriad background and contextual factors in determining speaker-meaning.  For example, you exit the airport in the Basque country.  A man approaches you and utters the sound “/ninaizdjon/”.  He means something by his sounds, but before we can assess the meaning or truth-conditions we need some more information.  Suppose I think that the man is speaking English.  In that case, I take him to have said “Nina is John”.  This is a puzzling statement — it is not often that a person two names, let alone both a feminine and a masculine name.  Perhaps we were wrong to think that the man was speaking English.  Suppose we had some understanding of the Basque language.  When the man says, “/ninaizdjon/”, and I interpret him as speaking Basque, then I will take the man to have said, “Ni naiz John” (which, in English, is “I am John”).  Conversation doesn’t enjoy the luxuries of print; in print we can easily determine the language and parse sounds (for they are, more or less, already parsed for us on the page), but in conversation we are subjected to a constant stream of phonemes and so must bring some background, interpretive theory to make sense of an otherwise disorienting stream of sound.

This demonstrates our sensitivity to background conditions and contextual factors.  When we place the “is speaking English”-background condition on the man’s utterance, we end up with a sentence that is true if and only if “Nina” and “John” co-refer.  But when we place the “is speaking Basque”-background condition on the man’s utterance, we end up with a sentence that is true if an only if the man is named ‘John’.  Nothing in the isolated sound “/ninaizdjon/” can help us determine which of the two aforementioned background conditions is salient/relevant/appropriate/what-have-you.  We cannot determine the meaning without making this choice; context may affect meaning just as much as isolated semantics.  Here is another example.  Suppose that some time ago, Quine said “Cicero wrote beautiful prose”.  The utterance, “Quine said that Tully wrote beautiful prose”, will true if and only if, as a background condition, Quine believes that “Cicero” and “Tully” co-refer to the same object.  For if he did not have this belief, then we would be misattributing a Tully-belief to Quine when Quine has only Cicero-beliefs.  If we were attuned only to the explicit content of an utterance, we would miss out on or be mistaken about the actual meaning of another person’s utterance.  We would incorrectly assess the truth of the utterance “Quine said that Tully wrote beautiful prose”.

An utterance like (1) presupposes the existence of the subject which takes on a predicate. But in ordinary conversation, that presupposition places a background truth-condition on the utterance. The background truth-conditions of an utterance directly contribute to the judgment of the truth-value of that utterance.  So (1) is subject to the following truth conditions.

The explicit (1T): “The present king of France is bald” is true iff the present king of France is bald.

The background: AND iff there exists a present king of France (or, alternatively, there exists an individual uniquely denoted by the determinative-phrase “the present king of France”).

   AND iff (1) is a sentence in English

(1) is true iff both the explicit and the background are true.  Because the existential-background truth-condition is not satisfied, (1) is not satisfied, and so (1) must be false.

To reiterate, one last time, the findings of this post: In an isolated context a sentence like (1) will not have a truth-value.  But language is used in varying contexts, and in its use, there must be some additional background truth-conditions which are not explicitly contained in the assertive content of the sentence.  An example of such a background condition will be the existence of the presupposed subject, the present king of France.  I hope that my response to our initial question doesn’t come across as a sort of “Well, it does and it doesn’t”.  I am more inclined toward pragmatic accounts of meaning rather than semantic; so to be unequivocal: if Trump says, “the present king of France is bald”, he would be asserting something false.

As a sort of post-script, I would like to note that when I began writing this, I intended to argue that sentences like (1) have no truth-values.  When I almost finished, I changed my mind and came to the here-written conclusions.

I should also note that there are conversational contexts where one could say, “the present king of France is bald” without necessitating the existential-background truth-condition.  If I am in a conversation with Trump, and we have both already acknowledged the fact that there is no present king of France, then later in our conversation, when Trump says “the present king of France is bald”, I will know that he does not mean to assert or imply the existence of the present king of France.  (This is because I know that he knows there the present king doesn’t exist, and so will not mean to say as much.)  In light of this, one possible interpretation of Trump might be, “if there were a king of France in the present day, he would be bald”.  (Perhaps Trump is making a point about the dangers of contemporary aristocratic French diet, or perhaps he means to say that the genetic line of French kings is prone to premature baldness.)


Davidson, Indirect Discourse, and “That”

In this post I will explain Davidson’s analysis of sentences containing indirect discourse and how we ought to treat their logical form.  This will pay close attention to the role of samesaying with an utterance.  The analysis here will reveal how sentences containing indirect discourse are a type of performative utterance.  Bringing these observations to bear, we will explain how and when we can substitute co-referring terms in that-clauses on Davidson’s account.  Finally, we will assess the adequacy of Davidson’s analysis by considering the similarity between samesaying and sense and reference, in order to show that Davidson’s prima facie anti-intensionalist stance is, in fact, intensional; and discuss how Davidson might reply.

The problem with sentences containing indirect discourse is that surface grammar does not adequately account for their meaning.  In “Scott said that Venus is an inferior planet”, we can substitute “is an inferior planet” for “is identical with Venus or Mercury” and not affect the truth of the sentence (for the former is co-extensive with the latter) (204).  But intuitively, this seems illegitimate because it no longer seems to represent what it is that Scott said, and so the meaning of the whole sentence has changed (204).  An adequate theory of meaning for utterances with that-clauses will specify how the meaning of the utterance depends upon the meanings of its finite component elements and syntactic structure (205) (so that we can construct a finite set of truth-conditions).  And the theory must also explain when the substitution of co-referring terms in a that-clause is permissible.

For Davidson, a sentence containing indirect discourse involves (1) an utterance referring to a speaker S in a context, (2) an utterance conveying the content of a that-clause, (3) an utterance of S with the same content of (2).  I say, “Galileo said that the earth moves”.  S is Galileo in context, and “the earth moves” conveys the content of an utterance of Galileo’s.  What Davidson wants to bring out here is that there is some judgment of synonymy between (2) and (3).

Such synonymy is what Davidson calls samesaying.  Samesaying is when you use words of the same “import here and now” as someone else used them “then and there” (210).  So in indirect discourse, when I say “Galileo said that the earth moves”, I am trying to represent Galileo and I as samesayers by attributing an expression to him (“the earth moves”) that is the same in purport to what he said – that is, synonymous, or has precisely the same content.  This is the key to appropriate substitution of co-referring terms, discussed later.

In light of our new notion of samesaying, how should we think about the logical form of utterances containing indirect discourse?  Suppose Galileo uttered, “eppur si muove”, and I say that “the earth moves”.  Then Galileo and I are samesayers, for our words are of the same import relative to our respective contexts – but this is not to say that it has been asserted that we are samesayers, just that it is so.  Because we are samesayers, there must exist an utterance asserting that Galileo and I are samesayers.  The logical form of such an utterance is: ∃x(Galileo’s utterance x and my utterance y make us samesayers) (210).  So I can attribute any utterance x to Galileo, provided that an utterance of mine y, corresponds to x (is the same in import as x) (210).  So consider (210):

(1) The earth moves.

(2) ∃x(Galileo’s utterance x and my last utterance make us samesayers).  Note that ‘y’ has been substituted for my last utterance, namely “the earth moves”.

If we abbreviate the second line, we get:

(1) The earth moves.

(3) Galileo said that.

How does it get abbreviated this way?  “That” is a demonstrative singular term which refers to an utterance, viz. the utterance of Galileo’s such that it samesays with my last utterance, (1).

So how does this inform the logical form of an utterance containing indirect discourse?  Such utterances consist in (a) an expression referring to a speaker (e.g. “Galileo”), (b) the two-place predicate “said”, and (c) a demonstrative “that”, referring to an utterance of the referent of (a) which samesays with the content of the that-clause (e.g. “the earth moves).  So it should be analyzed and recognized as two semantically distinct sentences, viz. “Galileo said that” and “the earth moves” (212).  From the logical form and the semantic distinctness of clauses of utterance with indirect discourse, it follows that these kinds of utterances are performatives.

A performative is an expression which introduces an utterance in a particular kind of way..  For example, “this is a joke: knock-knock…”.  The “this is a joke” functions to introduce the following utterance, “knock-knock…”, as (importantly) something other than just an assertion, viz. that it is a joke (and perhaps not to be taken seriously) (211).  Intuitively, “Galileo said that” and “the earth moves” looks like an introducing clause and an introduced clause (211).  “Galileo said that” is the performative part of the utterance (211); it’s point is to announce a further utterance in a particular way.  In this case, it introduces my further utterance as one that conveys the content of another’s utterance (Galileo’s), and must function as such.  This is to say that I announce my utterance of “the earth moves” as an action which samesays with an utterance of Galileo’s.  Notice that performative utterances have truth-values.  Suppose I said, “Galileo said that Obama is Kenyan”; this must be false, as clearly Galileo said no such thing.  Likewise, if I said, “this is a joke: Trump won the Republican Primary”, then I said something false, for Trump’s victory is a fact and not a joke (or at least not a funny joke).  So in both cases the entire performative utterance is false.

Now that we have explained samesaying, the logical form of an utterance containing indirect discourse, and why utterances of indirect discourse are performatives, we now have the resources to explain legitimate substitution of co-referring terms in a that-clause.  Consider the utterance “Quine said that Cicero wrote beautiful prose”.  This expression (a) refers to a speaker (Quine), (b) has a two-place ‘said’ relation, and (c) ‘that’ refers to an utterance of Quine’s.  We divide the sentence into “Quine said that” and “Cicero wrote beautiful prose”.  “Cicero” and “Tully” are co-referring terms; would substituting “Cicero” for “Tully” be a legitimate substitution?  So consider “Quine said that” and “Tully wrote beautiful prose”.  “Quine said that” announces the following utterance, “Tully wrote beautiful prose” in such a way that the entire performative utterance is true iff “Tully wrote beautiful prose” samesays with an utterance of Quine’s.  So we need to look at the conditions under which “Cicero wrote beautiful prose” (which we assume is what Quine actually said) and “Tully wrote beautiful prose” samesay.  They samesay iff the “Tully” in our substitution is used with the same import as “Cicero” in Quine’s utterance.  But to know if they have the same import, we will have to know something about Quine.  Namely, we will have to know whether Quine believes that “Cicero” and “Tully” co-refer to the Roman orator or not, when he made his utterance.  Suppose he did believe that “Cicero” and “Tully” co-refer.  Then, for him, “Tully” will have all the import of “Cicero”, and consequently “Tully wrote beautiful prose” and “Cicero wrote beautiful prose” will samesay and our substitution will be legitimate.  But suppose he did not believe that “Cicero” and “Tully” co-referred.  Rather, the only “Tully” he knows is a delinquent undergraduate.  So for Quine, “Cicero” and “Tully” cannot have the same import when he uses them.  Consequently, our substitution of “Tully” for “Quine” is illegitimate, for if you asked Quine if he had said that “Tully wrote beautiful prose” he would deny it (for no delinquent undergraduate writes beautiful prose). This is how Davidson would characterize the substitution of co-referring terms in a that-clause.  If the substitution preserves the import (of Quine’s utterance) – samesays – then the substitution is successful.  But if the substitution does not samesay, then the substitution is not successful (for if the substitution does not samesay with the speaker’s utterance, then it falsely attributes an expression to the speaker).

But Davidson’s account is not immune to criticism.  His notion of samesaying is particularly suspect.  If we take samesaying to be “using words the same in import ‘here and now’ as his ‘then and there’”, then this just sounds like a matter of using some combination of words with the same sense and reference as words spoken by the attributed speaker.  It is not as though import could be the semantic value of an expression, for that’s just a truth-value.  Nor could import mean the corresponding extension, for then we would not have said anything about the problem of substitution of co-referring terms.  So it seems most natural to think of import as sense or mode of presentation.  But if this is so, then this creates a problem for Davidson.  Sense is a Fregean notion, and is the “thought” grasped in virtue of hearing the utterance.  “Tully” and “Cicero” are two different ways of thinking about the same individual, and consequently one could believe that “Cicero wrote beautiful prose and Tully did not”.  That is, the words may be of different import.  But if import just is sense, then Davidson’s account cannot be successful.  This is because Davidson is committed to Tarski’s truth criterion: the meaning of the utterance depends upon the meanings of its finite component elements and syntactic structure.  “Cicero” and “Tully” denote the same individual, so they must mean the same thing.  But if they mean the same thing, then I could not believe that “Cicero wrote beautiful prose and Tully did not”.  But if I could believe that “Cicero wrote beautiful prose and Tully did not”, then I must have different ways of thinking about “Tully” and “Cicero” – that is, the expressions must differ in their senses.  Consequently, what determines the legitimacy of samesaying between expressions is the manner in which each expression is thought of.  And this violates Tarski’s truth criterion because manner of thought is not truth-functional notion, so Davidson’s account cannot be successful.  

In light of this, Davidson might respond by offering a more robust characterization of “import”.  Take “import” to be the truth-conditions of an utterance and reconsider “eppur si muove” and “the earth moves”.  Each is true iff the earth moves; intuitively they have the same import.  Now consider “Cicero wrote beautiful prose” and “Tully wrote beautiful prose”.  The former is true iff Cicero wrote beautiful prose; the latter is true iff Tully wrote beautiful prose.  So substitution of “Tully” for “Cicero” is illegitimate.  In this way, Davidson preserves his account without invoking sense, and so conforms to Tarski’s truth criterion.  Samesaying relies on identity between the concrete – truth-conditions – not some abstract, like mode of presentation.

But this is not an effective reply.  For if we intend to samesay with an utterance of Quine’s, then we will need to know what Quine took the truth-conditions of his utterance to be.  But we cannot always know what the speaker to whom we’re attributing an utterance takes the truth-conditions of his utterance to be.  So we cannot always know when it is legitimate to substitute co-referring terms because we do not know if we will preserve identity of truth-conditions of the attributee’s utterance.  So we cannot determine whether our performative utterance is true or false.  For me to truly assert that “Quine said that Tully wrote beautiful prose”, I must know that Quine believed that “Tully” and “Cicero” co-refer for our utterances to samesay.  While it will often be the case that we know what the truth-conditions of the speaker’s (to whom utterance is attributed) utterance are, this is not always so (as suggested by Tully the delinquent undergraduate).  

It seems that we want a way to attribute utterances to speakers when we do not have sufficiently reliable knowledge of the contents of their beliefs.  One way of accomplishing this might be to revise samesaying such that when there is not reliable knowledge of the content of the speaker to whom the utterance is attributed’s beliefs, then samesaying will instead be: when my utterance conveys the same content to the hearer as the attributed-speaker’s utterance conveyed to himself.  On this view, it is legitimate for me to substitute “Tully” for “Cicero”, even if Quine did not believe that they co-referred, because to the hearer, the utterance just means the same thing as “Cicero wrote beautiful prose”.  And now the hearer knows something true about Quine, namely that he thought that Cicero wrote beautiful prose.  He is just ignorant of the fact that Quine does not believe that “Tully” and “Cicero” co-refer.

But I think that this move starts to veer off-track.  The notion of samesaying begins to looks more broad, less clear, and more context dependent.


Works Cited

Martinich, Aloysius, and David Sosa. The Philosophy of Language. New York: Oxford UP, 2013. Print.

The Fregean Conjecture

“Semantic composition is functional application” – the Conjecture.

In an extensional theory of linguistic meaning, there are only three kinds of things: individuals, functions, and truth-values.  The meaning of a sentence is determined by the individual meanings of each of its words as well as its syntactic structure.  A simple example:

Jack drinks

There is “Jack”, an individual, and there is “drinks”, a function.  Drinks is a function which takes a single argument (in this case, “Jack”), and maps it to a truth-value.  The meaning, then, is a truth-condition: “Jack drinks” is true iff Jack drinks = T.  Suppose Jack does in fact drink.  Then we plug in “Jack” into the function “(x) drinks”, and the output will be the truth-value, T.  Suppose instead that Jack’s been sober almost two months.  The function “(x) drinks” will map “Jack” onto the truth-value, F.  (Probably.)  More formally:

[Jack](Let F be that function f  such that For All x in domain, f(x) = T  if and only if x drinks, otherwise f(x)=F.) = T

As sentences grow in complexity, it can be difficult to keep track the syntactic structure – that is, exactly which component of the sentence is an argument for whatever other function in the sentence.  It can be useful to see an example of a sentence broken up into its constituents.

The cowboy on the cliff rides hard into the west.

([The [cowboy]] [[on] [the [cliff]]) ([[rides] [hard]] [[into] [the [west.]]])

Note that the only individuals in this sentence are “cowboy”, “cliff”, and “west”.  This means that rest of the words are functions.

(Will update.)