Maverick and Belette on Frege

Back after a software-imposed break. While all this was going on, Maverick philosopher commented on my Frege post, gently supportive but questioning whether cognitive value or informational content can be had by such subsentential items as 'morning star' and 'evening star.' I think it can be had. We both agree the proposition "grass is green" has informational content. This content differs from the content of "grass is yellow". How? How does changing the word 'green' to the word 'yellow' change the informational content of the whole proposition? Surely because the informational value of the word 'green' is different from the informational value of the word 'yellow'. Thus the informational value of a term is precisely its contribution to the informational value of the whole sentence. Frege says somewhere that the same sense corresponds to the same word, and that is why language is useful. We could use a single sign for the whole proposition, as with a train signal (red = the track is closed, green = the track is clear), but he says that would not be very helpful, as we would have to devise a new sign for every different thought we wanted to express. So we split the thought up into parts, with a different sign corresponding to each part of the thought.  If we understand 'informational value' in this way - as the contribution to the informational value of a whole proposition, my argument is sound.

Cmmenting on the post back here, Belette wondered whether my argument was valid at all. I argued as follows.

(1) The sentence “the morning star is the evening star” has informational content.
(2) The sentence “the morning star is the morning star” does not have informational content.
(3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.

Belette says that ‘the morning star’ really means ‘Venus, at certain positions in its orbit’. I’ll alter this (because I’m not sure the morning/evening distinction is anything to do with the orbit of Venus, as opposed to the rotation of the earth on its axis) to ‘Venus as it is in the morning’. Perhaps I am not understanding him, but I think he means that this expression is something that has a referent in the morning, but at no other time. As the earth rotates and Venus appears to rise in the sky and disappear in the glow of the rising sun, the reference of the expression fails, and becomes non-existent. And as the sun ‘sets’, the referent of ‘Venus as it is in the evening’ comes into existence. Thus the referent of ‘Venus as it is in the morning’ only exists in the morning, and the referent of ‘Venus as it is in the evening’ only exists in the evening. Venus, of course, exists all the time.

But if that is true, the argument above is no longer sound. The sentence “the morning star is the evening star” actually means “Venus as it is in the morning is Venus as it is in the evening”. But this is always false, for if the term on the left has a referent, it must be morning, in which case the term on the right has no referent, and the identity statement is false. Conversely, in the evening, the left term has no referent, and the right term does. Or neither term has a referent, in which case there can be no identity either (identity being a relation between existing things). Hence the second premiss is false, on the assumption that a sentence which is false in virtue of its meaning contains no information.

I question whether ‘the morning star’ does mean that. Surely it is a description picking out a certain object by means of its visibility in the morning. It is not part of its meaning that the object must cease to exist once morning has passed. It may cease to exist, of course, just as the light in the fridge ceases to exist when we shut the door. But continuation or cessation of existence is not part of its meaning. (Perhaps it is different for ‘the prime minister of England’, but that is a different case, I think).

Explaining 'the morning star'

Belete suggests here that the ‘Morning star’ example in the SEP article on intensional logic is not very well explained.
I’m not seeing that, but let me explain the it in my own terms, here. Assume you do not know much about astronomy, but you know how to identify the “morning star”, namely as the heavenly body that is visible in the East in the morning, and you also know how to identify the “evening star”, namely the heavenly body that is visible in West in the evening. Then you may assume these are different objects, and so, if I tell that the morning star is in fact the same object as the evening star, I have given you some useful information. I could go on to tell you that it is not a star at all, but a planet, in fact the planet Venus, which rises and sets with the sun because it is much closer to the sun than we are. But that is not relevant here. The point is that the sentence “the morning star is the evening star” is informative, it tells you something you could not have worked out from the meaning of the terms alone. By contrast “the morning star is the morning star” gives you no information at all. Given that you know what the morning star is, it is simply an expression of the principle of identity, A = A for all A, which presumably you knew, or would have assumed, already. Thus ‘the morning star’ and ‘the evening star’ have different informational content.

Summarising:

(1) The sentence “the morning star is the evening star” has informational content.
(2) The sentence “the morning star is the morning star” does not have informational content.
(3) Therefore, the term “the morning star” does not have the same informational content as “the evening star”.

What’s wrong with that? We might want to make a few extra assumptions to make it logically watertight. For example, to add the assumption that if all the component parts of two sentences have the same informational content, then the sentences themselves have the same informational content (the compositionality principle). But I don’t see what’s desperately wrong with it as it stands.

Did Shakespeare write Shakespeare?

I just found this again, a nice summary of the method by which we can establish that Shakespeare really did write Shakespeare, and which illustrates some of the ideas I developed in my last post.

The method is to construct a number of ‘description clusters’, and then demonstrate that these clusters can only be satisfied by a single historical individual. A description cluster is a number of sub-descriptions of which it is beyond question that they are satisfied by a single individual. Thus we have the ‘William Shakespeare the author’ cluster, consisting of the subdescriptions “Shakespeare the author of Titus Andronicus”, “Shakespeare the author of Henry VI Part 2”, “Shakespeare the author of Romeo and Juliet”, etc. We know (or are at least very certain) these sub-descriptions apply to the same person, because those plays were published with the name ‘William Shakespeare’ in his own lifetime.

Then we have the description cluster William Shakespeare the actor, consisting of the subdescriptions ‘Shakespeare who played in the King’s Men, 19 May 1603’, ‘Shakespeare who appeared on Sir George Home’s list of "Players"’ etc. We are very certain they are uniquely satisfied because it is unlikely the same company would have had two actors of exactly the same name.

Similarly we have description clusters for ‘William Shakespeare the Globe-sharer’, consisting of descriptions found in legal titles to shares in the globe theatre. Finally we have a cluster for ‘William Shakespeare of Stratford’. Each of these clusters is satisfied by a single person. To prove that they are all satisfied by a single person, rather than four separate people, we look for little overlaps, where it seems highly like that two or more sub-descriptions in different clusters are satisfied by a single person. For example, a sub-description in the ‘William Shakespeare of Stratford’ cluster contains the information ‘is legally entitled to be called “gentleman”’. So does a subdescription in the ‘William Shakespeare the Globe-sharer’ cluster. Similarly, a subdescription in ‘William Shakespeare of Stratford’ matches a subdescription in the ‘William Shakespeare the author’ cluster.

The available evidence, at least if the website linked to is correct, is that because of a significant number of overlapping subdescriptions, the four big clusters are satisfied by a single person.  There is actually a fifth cluster (or perhaps it's a subcluster of the 'Will Shakespeare of Stratford' cluster) of descriptions attached to Shakespeare's monument in Stratford church.  These refer to Shakespeare (i.e. the subject of the monument) as a great writer within a few years of his death. 

Belief reports versus evidence reports

Biblioarchy has commented here on what Oxfordians believe. He says " Bacon was not De Vere, and no Oxfordians believe this. Take my word for it, I know them." I do take his word for it, and it is a further objection to Eric Schwitzgebel's view that such belief ascriptions have an indeterminate truth value.

Nor do I see any difference between "The Oxfordian theory is that Edward de Vere was Shakespeare", which Eric agrees does have a determinate truth value, and "Oxfordians believe that Edward de Vere was Shakespeare" which, as I understand Eric, does not have a determinate truth value.

Biblioarchy's comment also reminds me of other verbs that create intensional contexts, such as 'is emphatic that', 'holds that', 'insists that', 'has received evidence that', 'has good reason to claim that' and so on. It is entirely implausible that the substitution problem connected with these verbs is different in any way from the problem of belief ascriptions.

On Lois Lane and rationality

Lois Lane has the following two beliefs

(1) that Clark Kent cannot fly, and that Superman can fly.

Yet Clark Kent and Superman are identical. Substituting ‘Superman’ for ‘Clark Kent’ in the first belief gives us the beliefs

(2) that Superman cannot fly, and that Superman can fly.

Clearly it is irrational to hold the beliefs characterised by (2). Does this mean that Lois has irrational or illogical beliefs in believing (1)? Or is the inference from (1) to (2) invalid? Contra: the beliefs characterised in (1) are clearly not irrational. For we base our beliefs on evidence. The evidence given to us in the Superman stories suggests that Clark Kent and Superman are identical. The reader is always shown evidence that Clark Kent is Superman, by means of scenes showing him changing from his office suit and glasses to his Superman costume, without glasses. The same stories show us that Lois Lane does not have the benefit of this evidence. She is looking the other way, or is looking for shoes or handbags while Clark is changing his costume. Therefore

(3) The reader of the stories has evidence that Clark Kent is Superman

(4) Lois Lane does not have evidence that Clark Kent is Superman

Therefore, I argue, it is not irrational for Lois to have the beliefs expressed by (1). It is not irrational to believe that of which one has no evidence to the contrary – even though other people, such as the reader, have evidence to the contrary. Therefore the inference from (1) to (2) is invalid.

Note, and this is actually is my main point against Eric’s position here, that it is invalid for exactly the same reason that the following inference is invalid.

(5) Lois Lane has evidence that Superman can fly, therefore she has evidence that Clark Kent can fly.

The puzzle about substitution and belief statements is the same as the puzzle about substitution and evidence statements. Even though Clark Kent is identical with Superman, the evidence that Clark Kent is Superman is different from the evidence that Clark Kent is identical with himself.

On learning the law of identity

Anthony asks whether we could learn in 2012 that Shakespeare is identical with Shakespeare, given that we learned in 2012 that the Oxfordian theory is correct. I reply, this makes it difficult to distinguish between principles like the law of identity, and flaky theories like the Oxfordian theory. Consider the following two statements.

(1) It follows from the law of identity that Shakespeare is identical with Shakespeare
(2) It follows from the Oxfordian theory that Shakespeare is identical with Edward de Vere

It would clearly be false to say – even if it did turn out that the Oxfordian theory was correct - that it follows from the law of identity that Shakespeare is identical with Edward de Vere, i.e. that it follows from a logical principle that some fringe theory is correct. Otherwise we could prove all sorts of strange theories from logical principles, which of course we can’t.

Frege's Puzzle and In-Between Cases of Believing

There was a post this weekend at Eric Schwitzgebel's The Splintered Mind about Frege's puzzle, which continues to preoccupy philosophers of mind, and is "is a heck of a mess in philosophy of language" according to Eric.

Frege's puzzle is this. Lois Lane believes, it seems, that Superman is strong. And Clark Kent is, of course, Superman. So it seems to follow that Lois Lane believes that Clark Kent is strong. But Lois would deny that Clark Kent is strong, and it seems wrong to say that she believes it. So what's going on?

Eric suggests the problem is that "Almost all the participants in this literature seem to take for granted something that I reject: that sentences ascribing beliefs must be determinately true or false, at least once those sentences are disambiguated or contextualized in the right way".

I have discussed this problem before, notably here, in the context of impersonal verbs taking that-clauses.  The problem is that whatever applies to belief-ascriptions, must apply also to impersonal ascriptions such as "there is evidence that p", "it was discovered that p in yyyy", "according to the theory of X, it is the case that p", for these sentences, as will become clear, also suffer from the substitution problem. Thus, if Eric is right, sentences like "there is little evidence that Edward de Vere was the author of Macbeth" are not determinately true or false, which seems counterintuitive.

Let me explain. I often warn people against unquestioning acceptance of Wikipedia, but what it says here today seems unquestionably right.

"The Oxfordian theory of Shakespearean authorship proposes that Edward de Vere, 17th Earl of Oxford (1550–1604), wrote the plays and poems traditionally attributed to William Shakespeare of Stratford-upon-Avon.

That is surely true. That is what the Oxfordian theory is. Whether the theory is right or not is irrelevant. The question is whether this characterisation of the theory is correct. It is, and it uses, without mentioning, the proper names 'Edward de Vere' and 'Shakespeare'.  But there are circumstances in which its truth would not survive substitution. Let's suppose we discover that Francis Bacon were identical with Shakespeare, as Cantor famously believed, spending much of his personal fortune trying to prove it.  If so, we should be able to substitute 'Francis Bacon' for 'William Shakespeare' in a sentence telling us what the Oxfordian theory is.  But it is not true that, according to the Oxfordian theory, Edward de Vere was Francis Bacon.  Nor would be true to say that plays and poems such as 'Macbeth' were traditionally attributed to Francis Bacon, even if Shakespeare were Bacon.  Nor would it be true to say that we discovered that Shakespeare was Shakespeare in 2012, even if it were true that we discovered that Shakespeare was Bacon in 2012.

Yet sentences like "Oxfordians believe that Edward de Vere wrote the plays and poems traditionally attributed to William Shakespeare" are unquestionably true, i.e. determinately true (or false).  By equal reasoning, since the problem seems identical, this suggests that sentences ascribing beliefs must be determinately true or false.

On discovering what we already knew

A priori textual analysis continues to amuse. David Brightly has objected that indiscernibility of identicals (Leibniz II) applies only to names, not to descriptions like 'the murderer' or 'Shakespeare', when used in the sense of 'the man who wrote the plays'. Nishadani has objected that 'Shakespeare' is not the name of a single person.

I will discuss these objections later. Meanwhile, another puzzle. If Leibniz II is correct, we can substitute any two proper names so long as they are names for the same person, salva veritate. Thus, if Shakespeare and Edward de Vere (another contender for the identity) were the same person, it follows that

• We have always known that Shakespeare was De Vere, since we have always known that Shakespeare was Shakespeare, a logical truth.
• We could never discover that Shakespeare was De Vere, since you cannot discover what you already know.

And so on.

Textual analysis using pure logic

I have been having an amusing conversation with 'Nishadani' on his Wikipedia talk page. Nishadani is one of those tireless defenders of orthodoxy on Wikipedia, fighting the battle against (in his case) all sorts of interesting theories that 'the man from Stratford' did not write the plays published in his name. There is more about the whole issue on Wikipedia here, although the article misses the interesting fact that the great mathematician Georg Cantor (the transfinite man) spent much time and money trying to prove that Bacon was the author of the Shakespeare plays. He writes (to Dedekind, 28 July 1899)

The big question was whether, besides the alephs, there are also other powers of
sets; for two years now I have been in possession of a proof that there are no
others; so that, for example, the arithmetic linear continuum (the totality of
all real numbers) has a determinate aleph as its cardinal number.
The Bacon-Shakespeare question, on the other hand, is for me completely
finished; it cost me a great deal of time and money; to pursue it further I
should have to make much greater sacrifices, travel to England, study the
archives there, etc. With warm greetings to you and your sister [etc.]

It's interesting because Cantor made one of the greatest contributions to mathematicians and logic in the whole history of the subject (e.g Godel's proof and much else ultimately depends on the insights of Cantor's elegant diagonal argument), and yet here he is spending 'much time and money' on something generally regarded as, well, a bit cranky.

But enough of that. The aim of this post to is show 'Nishadani' and his like that we can prove the falsity of Baconian, Oxfordian Marlovian theories etc. etc., without any tedious recourse to textual analysis, biography or any other such un-philosophical considerations. We can prove it by pure logic. Let ‘Shakespeare’ denote whoever it was that wrote the plays attributed to the man of that name.

1. Shakespeare and Bacon were one and the same person.
2. There is no doubt as to whether Shakespeare wrote The Tempest
3. There is some doubt as to whether Bacon wrote The Tempest
4. If a=b and Fa then Fb (Indiscernibility of identicals)

Since the four propositions are aporetic, i.e. jointly yield a contradiction, one of the premisses must be false. The first is a mere assumption. Clearly the second is true: obviously the man who wrote the 'Shakespeare' plays called himself 'Shakespeare', just as 'Nishadani' calls himself 'Nishadani'. That is pure logic. The third is true - there wouldn't be so much arguing and gnashing of teeth on Wikipedia if there were no doubt at all. And the fourth (from Leibniz) is beyond all doubt. If Shakespeare and De Vere (or Marlow or whoever) were one and the same person, and De Vere was accused of pederasty, then so was Shakespeare. If De Vere died in 1604 (or whenever) then so did Shakespeare, assuming the identity.

But all four imply a contradiction. By substitution of 'Bacon' for 'Shakespeare' in proposition (2), and by indiscernibility of identicals (4), we have

(*) There is no doubt as to whether Bacon wrote The Tempest

But this proposition contradicts (3) above. It cannot be true that there is some doubt that Bacon wrote the Tempest (even a tiny bit of doubt) and that there is no doubt. Contradiction. Therefore the weakest of the four propositions above must be rejected, namely that Bacon and Shakespeare were the same person.

So forget the historical and textual crap. By purely logical and philosophical methods we can clarify all manner of difficult questions like this.