Friday, December 30, 2011

On the usefulness of believing

St Augustine's work, in parallel Latin English now at the Logic Museum here.  Scotus quotes this a number of times, so I thought it useful to include. My aim, one day, is to have a hypertext that covers all the 'authorities' (Aristotle, the Church Fathers, the Vulgate of course) linking to all the scholastic texts that quote them or refer to them in any way.

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. 

Thursday, December 29, 2011

Reference fixing by description

Biblioarchy and Anthony have commented on ‘reference fixing’ by description. Anthony objects that in order to fix the referent of 'Shakespeare' as 'the man who wrote the plays and poems traditionally attributed to William Shakespeare of Stratford-upon-Avon", we need to agree on who that was.
If we just leave it floating out there as possibly being one person, and possibly being another person, and possibly being several people, and possibly not being a person at all (maybe aliens wrote the plays), then we haven't fixed it.
Biblioarchy makes a similar point, saying
Some Oxfordians and many Stratfordians believe that more than one hand was at play on many of the texts. Also that they appear to be palimpsests of sorts, revised and rewritten over the years by 'The Author', Shakespeare, whomEver he was, and perhaps, a cadre of University Wits in the Fisher's Folly Days Mid 1580's. This would of course, completely demolish the Stratfordian time-line, setting it back a decade, and disqualify the Stratford man.
Well, the idea of ‘reference fixing’ is not mine. Kripke introduced it in Naming and Necessity, and Gareth Evans discusses it in The Varieties of Reference. Kripke’s point – there is an excellent summary of it in the SEP article on Reference - is that while we can determine the reference of a proper name by some uniquely satisfied description – for example, we can fix the reference of ‘Aristotle’ as ‘the last great philosopher of antiquity’, the semantics of the name cannot be identical with the semantics of the description. For ‘the last great philosopher of antiquity’ might well apply to Plato in a possible world where Aristotle died in infancy.

But these comments do suggest a deeper problem with the whole idea of fixing reference by description, given that primary sources do not give us a single description of a putative historical character, but rather a series of descriptions. What if there wasn’t a single author of the Shakespeare plays? What if one person wrote Hamlet, another person wrote the Tempest? Indeed, I believe Oxfordians have to insist that the authors are different, given a fairly certain dating for the latter play of after 1604, when De Vere died*. What if there wasn’t even a single author of any of the plays? All mathematicians know about Nicholas Bourbaki, who is not a person at all – the name is a pseudonym under which a collective of French mathematicians wrote a series of books about advanced set theory and algebra.

My own subject is Duns Scotus. Who was he? A hundred years ago, we might have fixed the reference of his name by the description ‘the author of De Modis Significandi’. But that would have been wrong, as Grabmann demonstrated in 1922 that this work was by Thomas of Erfurt, a fourteenth century logician belong in to the Parisian ‘modist’ school. The authenticity of the Questions on the Prior Analytics, once attributed to him, is also doubtful. And though his books on the Categories, and on the Sophisticis Elenchis, and of course the monumental Ordinatio are almost certainly authentic, it is clear that we have a series of different descriptions – ‘the author of the Ordinatio’, the author of the Lectura, and so on – rather than a single description.

Scotus' biographical details are even more problematic. We have a handful of details about his life. Records show that someone of that name was ordained at St Andrew's Priory, Northampton on 17th March 1291, from which we infer a probable date of birth of about 1265, given the minimum age of 25 for ordination. So we have the description “person named ‘John Duns Scotus’, ordained in 1265 etc’. We believe he was in Oxford in 1300, based on a single passage in the Ordinatio that I discuss here. His name is on a list of those who opposed King Philip’s attempt to depose Pope Boniface around 1303. We have a few other bits of information. But whether these different descriptions are all satisfied by the same person is little more than conjecture and probable inference. We don’t know for absolutely certain whether there was a single author of his individual works. His Questions on the Perihermenias comes down to us in two separate versions, one of which (Opus I) contains a fragment of what may be another work. It is not certain how much of this was edited or rewritten by his disciple Antonius Andreas. So even a single work has a series of descriptions corresponding to the differing codices or primary sources which have come down to us.


Tuesday, December 27, 2011

Lunatic, Liar or Lord?






Monday, December 26, 2011

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.

Friday, December 23, 2011


Sorry not to have responded to comments.  I've been in the North (Liverpool in fact, then Manchester, then Sheffield).  I'll catch up at some point.  If I don't, I wish all my readers and commenters a very happy Christmas.


Tuesday, December 20, 2011

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.

Monday, December 19, 2011

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.
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.

Sunday, December 18, 2011

On the true nature of reality

I have finished the first draft of a translation of Chapter 51 of Ockham's Summa. To put this in context, it is part of chapters 40-62 which cover Aristotle's ten categories or 'praedicamenta' or 'genera'. In this part of the book, Ockham argues that the categories are not ten kinds of thing that exist in reality, outside the mind, but rather they are kinds of term - ten terms that signify the same thing in different ways. He writes (my translation)
For it should not be thought that the ten genera are things outside the soul, or that they signify ten things, each of which is signified by only one of the genera, but rather the teaching of the Peripatetics shows that the ten genera are ten terms signifying the same things in different ways. For just as the eight parts of speech can be distinct, and yet signify the same thing, e.g. 'white', 'whitening', 'to whiten', 'go white', so the identity of the things which they convey can be consistent with the distinctness of the categories.
Is that right? It is consistent with Ockham's strategy throughout this part of the book. Instead of saying 'Socrates has wisdom' we should say 'Socrates is wise'. We should not suppose that the abstract term 'wisdom' is some king of thing outside the soul, which bears some odd relation to Socrates such as 'instantiation' or 'inherence'.

Someone will object (perhaps they are from Phoenix) doesn't this miss something out? Is 'wise' just another way of referring to or 'suppositing for' Socrates? Surely not. Socrates himself - per se ipsum - is not the referent of 'wise'. There must be something in reality which, in addition to Socrates, makes 'Socrates is wise' true. There must be some difference between the fact that 'Socrates' refers to Socrates, and the fact that 'wise' refers to Socrates. And that difference would be wisdom itself. Whereas it is part of the meaning of 'Socrates' that it signifies him, it is not part of the meaning of 'wise'. There must be something more to reality than the referent of subject and predicate.

I reply: there may well be something more, but as I have argued before, this 'missing part' of reality cannot be conveyed by noun phrase. I won't repeat these arguments in detail, but briefly, Socrates and wisdom gives us two separate things, but not Socrates being wise. And Socrates being wise is not enough, since we want to know whether his being wise is a fact, is the case etc. There is always something missing from a noun phrase that makes it incapable of expressing reality. To express reality we need a verb. But realists always insist on talking about reality using noun phrases. What do they have against verbs?  Why this discrimination? If verbs were a part of society, they would be a disadvantaged minority, socially excluded, if realists had their way.

And note also that it is not the nature of the verb to express action. For 'action' is an abstract noun phrase. For there to be action, the action must take place, or happen.  In any case, there are verbs that do not signify actions at all, such as 'to rest', 'to remain', 'to endure' and so on. As Arnauld says in his Logic, Part II chapter 2, "On the verb", 'Peter lives' is a proposition and 'Peter living' is not. If you add 'is' to 'Peter living' to get 'Peter is living', you get a proposition, and this is because the participle 'living' does not signify affirmation, whereas the verb 'is' does. "From this it appears that the affirmation that does or does not exist in a word is what makes it a verb or not".

Is there something in reality that corresponds to the noun-verb structure that is essential to all language? If so, we could not talk about it, at least, not using nouns. We could express reality, but not signify it.

Friday, December 16, 2011

Ockham's Fregean moment

I am working on chapter 67 of Ockham's master work, where I find something that reminds me of Frege.  Ockham is talking about 'material supposition'.  This is a mode of supposition where a word stands for itself.  It's rather like when a word is enclosed in quotation marks (which the medievals didn't have), except the whole point of quotation marks is that we create a new word to stand for the unquoted word, and so the word precisely doesn't stand for itself.

Ockham claims that there are situations when a word signifies something that it does not materially supposit for. His example is the sentence "animal is predicated of man", in Latin: animal praedicatur de homine.  Note the word 'homine', which is the ablative case of the word 'homo'.  This is important, for Ockham's sentence is true because 'a man is an animal' is true, which in Latin is homo est animal.  Note the nominative case of 'homo'.  So when we say "animal is predicated of man", we mean that animal is predicated of homo, not homine.  But we can only say that using the word homine, at least in Latin.  (Or perhaps the same is really true in English, except the ablative of the word 'man' is the same as the nominative?)  Thus the quoted homine signifies itself, i.e. homine, but supposits for its nominative homo. (Hope that makes sense).

That seems trivial.  But it seems remarkably close to Frege's famous puzzle about the concept horse.  Frege held that simple propositions like 'Red Rum is a horse' are composed of Object and Concept.  The object is signified by the object word "Red Rum" and is thus Red Rum himself.  The concept is signified by the predicate " - is a horse".  Let's call that the concept Horse.  But now the puzzle.  The sentence "the concept Horse is a concept" is also a simple sentence, where the term "the concept Horse" occurs in subject position.  So it signifies an Object, according to Frege.  And so is not a Concept.   Thus, the concept Horse is not a concept.  Frege admits this is odd.
It must indeed be recognised that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept, whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano.
This seems remarkably similar to Ockham's puzzle about homine, although it would take some work to tease out the underlying basis of it, if any.

Thursday, December 15, 2011


A long title to go with the other one today. Michael Sullivan’s perceptive and entertaining ramble on Ockham and Scotus is well worth looking at.

Does a Common Term Suppositing with a Present Tense Verb Supposit Only for Presently Existing Things?

Sorry for the strange title but it is a literal translation of one of the questions (Latin: Utrum terminus communus supponens verbo de praesenti supponat tantum pro praesentibus) in Scotus’ Questions on the Perihermenias, and I am struck by the increasing resemblance between the discussion going on here, and the discussions on the same subject going on in the late 13th century in Oxford and Paris. In my last post, I discussed the slightly paradoxical syllogism
(1) No y is identical with Caesar
(2) Some x was identical with Caesar
(3) Some x is not identical with any y
to which David Brightly objected that
For (1) to be true it's clear that the range of the quantified expression 'no y' cannot be all men who ever were. Rather the present tense 'is' modifies the quantifier 'no man' restricting the ys in (1) to the presently existing men. Similarly in (2) the past tensed 'was' modifies the quantifier 'some x', restricting the xs to the men who ever were, ie, no restriction at all.
Well that’s true, and that’s one solution proposed by some of the scholastics, who thought that the present tense of the main verb of the sentence restricts (Latin: restringit) a common term like ‘man’ to suppositing (i.e. ranging over) presently existing men (praesentibus).

What’s wrong with that solution is the present tense that we have to use when we say what things are in the domain or range of quantification. David says that using a verb in the past tense allows the quantifier it to range over all the man that ever were. The problem is the implied present tense of the ‘ranging’. How is it that the quantifier ‘ranges’ – present tense – over past men, men who longer exist? Surely it can’t. Nor can the domain now ‘contain’ all such men. It used to contain them, but now it doesn’t. So the second premiss (2) cannot be true. There cannot be any x that was identical with Caesar, because however wide the domain or range of quantification, the domain exists in the present. It has to exist in the present because we say that it is the range of our quantification, and to say that we must use the present tense.

Anthony is closer when he says that the real problem is presentism, but there are problems with presentism also, which I will talk about later.

Wednesday, December 14, 2011


David Brightly has rightly questioned whether my argument is valid:
Caesar was a man
Caesar is not (any longer) a man
Some man is not a man
It's not, unless our domain of quantification consists only of men.  But I can easily restate the argument
No y is identical with Caesar
Some x was identical with Caesar
Some x is not identical with any y
I don't see any way round that.  Of course, some x was identical with some y (for y = Caesar, where the verb "=" has past tense).  And perhaps we could read the existential quantifer as tensed - there was an x such that x is not identical with any y.  But there's no way we could make any sense of it in standard predicate logic.  Moreover, the standard way of understanding quantification as a kind of relation between variables or open sentences or predicates on the one side, and objects on the other, makes no sense either.  For example, logicians say that the predicate "- was an emperor" is satisfied.  Is satisfied?  Or was satisfied?

Monday, December 12, 2011

Quantifying over

In an earlier post I asked whether some men are not men. Intuitively all men are men, and so ‘some men are not men’ is false. Yet if the term ‘man’, occurring in the subject position of a sentence, means something like ‘someone who is, was or will be a man’, and given that Caesar was once a man, but is no longer a man, i.e. not now a man, it seems to follow that some men (e.g. Caesar) are not men, i.e. were men but aren’t now. Thus, counterintuitively, some men are not men. From this we derived the even more puzzling ‘some present events are not present events’. Caesar’s crossing the Rubicon was once a present event. And if ‘present event’ means ‘event which is, or was once, or will be present’, and since Caesar’s crossing the Rubicon is not present, it apparently follows that at least one present event (crossing the Rubicon) is not a present event.

David Brightly, taking the approach of a contemporary logician, helpfully suggests that “we just stipulate in advance which men we propose to quantify over and this bounds what 'some man' may refer to. It could be men alive, dead or alive, living in Midsomer, ever been married, whatever is appropriate, as long as we make it explicit and make appropriate adjustments elsewhere.”

I object that it is a problem either way. If the English word ‘man’ in fact only means presently existing man, it immediately follows that we can’t quantify over men in the 13th century, for there are none to quantify over. Nor were there any. ‘Some man lived in the 13th century’ is false, unless there is a 700 year old man still alive. The question is what the word ‘man’ ranges over. If only presently existing entities, then there were no men alive 10 years except for those alive now, thus very few men who were alive 90 years ago. Census records are all false. There were not 7 million people living in London in the 1920s. More like a few thousand (namely all present Londoners who are old enough to have lived here 90 years ago).

If by contrast we accept that there were 7 million Londoners in the 1920s, we have to accept that most of these, namely the ones who have died, are no longer Londoners. Thus, some Londoners are not Londoners. You can’t escape the problem by specifying ‘domains of quantification’.

Sunday, December 11, 2011

On believing the same thing

I asked: If Tom believes that snow is white, and Carol believes that snow is white, are they believing the same thing or not?  And Anthony asked rhetorically, if I am eating a hamburger, and you are eating a hamburger, are we both eating the same thing or not? If I am nervous, and you are nervous, are we both experiencing the same emotion? If I have 5 apples, and you have 5 apples, do we both have the same number of apples? I'm reading a copy of "The Great Gatsby". You're reading a different copy of "The Great Gatsby". Are we both reading the same thing?

If we are both eating a hamburger, then in one sense we are eating the same thing, namely hamburger.  Perhaps we could say the sameness in question is a 'formal' identity.  In another sense we are not, given that there are probably two hamburgers in question, hence there is no sameness in the sense of 'numerical' identity.  Clearly there is no numerical identity between what Tom and Carol believe, even though they both believe that snow is white.  But if the identity is formal, where is the matter which has the form?  The form of  hamburger is embedded an organic carbon compound (meat).  The form of "The Great Gatsby" is embedded in another compound (tree pulp, paper).  What is the material that embeds the form of the proposition 'snow is white'?

Friday, December 09, 2011

On an existential problem suggested by Anthony

I am beginning to appreciate more the comments provided by Anthony (if only he would think before commenting, and not endlessly comment and delete - bear in mind that any comment whether deleted or not comes through my email box).

I suggested earlier that some things used to exist, but no longer exist.  Given my acceptance of Brentano's equivalence - that "some A is B" is equivalent to "Some A that is B exists", Anthony has spotted that this entails that some things are no longer things, and are thus not things (although, to be sure, they were things).  And indeed some men (e.g. Caesar) who were a man, are no longer a man.  Ergo, some men are not men.

This has the distinct whiff of paradox, which I will investigate later.

Ockham and Bradley's regress








Tuesday, December 06, 2011

Does everyone believe something?

Anthony asks whether ‘that it will rain next week’ is something. The quotes are scare quotes, but I could rephrase his question using real quotes. Does the noun phrase “that it will rain next week” name anything? And if so, what kind of thing is it? Is it located in space? Indeed, is it located in time? If I say that grass is green today, and you say the same thing tomorrow, is what you say tomorrow numerically identical with what I say today? Is the object of saying, stating, thinking, believing etc. a timeless eternal object, located nowhere in space itself? Is that Platonic idea consistent with nominalism?

I'm not sure a logician needs to worry about questions like these. A logician is worried about whether an arguments like

Everything said by Tom is true
That snow is white is said by Tom
That snow is white is true

Tom believes that snow is white
Tom believes something

are valid.  And surely they are.  If Tom believes that snow is white, then the simplest answer to the question of what 'that snow is white' refers to is simply that it is what Tom believes. Why bring space and time into it?

Monday, December 05, 2011

Wikipedia and the Enlightment





Sunday, December 04, 2011

Ockham on the continuum

Newly translated, for the first time on the Internet etc., here is chapter 45 of part I of Ockham's Summa Logicae.  Here, Ockham's applies his nominalism to the age-old question of the continuum.  Is a point something separate and indivisible from the line of which it is a point?  Is number something different from the things which are numbered?

Ockham says no. Aristotle’s intention, according to Ockham, was to deny that there is anything indivisible 'in this world below' (in istis inferioribus).  Continuous quantity is nothing other than a single thing having one part at a distance from another part, and discrete quantity (number) is nothing other than the numbered things themselves. The difference between continuous and discrete quantity is simply that the parts of continuous quantity mutally protude onto one another [ad se protensae mutuo], whereas the parts of discrete quantity (i.e. two men) can be as near or as far as you like, with no 'medium' between them.
... in the case of discrete quantity it does not matter whether or not the items which constitute the discrete quantity are distinct in place and situation or not, or whether there is a medium between them. Hence, for two men to be 'two', it does not matter whether there is a medium between those two men or not. For they are two when there is no medium between them, just as when they are distant from each other by a hundred leagues, nor does the predication 'two' of those men vary because of anything to do with nearness or distance. On the contrary, if they were in the same place at the same time they would be two, just as if they were not in the same place.
 The translation is new, and has not been through any of the review stages required in the Logic Museum, so all suggestions welcome.

Saturday, December 03, 2011

Bad performance

Sometimes just the performance can make music horrible, even though the performers are skilled, and the rendition has no obvious flaws.  Here's Guarachi Guaro by the Salvadorean band Proyecto Acústico. Compare it with the arrangement it was taken from by Cal Tjader and his quintet from 1953.  Much better, but why?

Here also is the original by Dizzy Gillespie, arranged by Gerald Wilson. Only 276 views, though superior to the others. Love the wind up gramophone.  I have one of these in the attic, I may take it out for a 'spin' some day.

The insoluble problem of future tense statements

Vallicella finally addresses the problem of Excluded Middle and Future-Tensed Sentences.  A prediction in 1996 that the FTSE would reach 10,000 by 2011 would have been wrong at the time the prediction was made.  As he points out (using the US Dow index as his example), subsequent events merely made it evident that the content of the prediction was false, rather than bring it about that the prediction had a truth-value.  Not even God can restore virginity*.

This suggests that the Law of Excluded Middle applies to future tense statements, but this causes him puzzlement, expressed in the following 'aporetic triad'.

1. Law of Excluded applies unrestrictedly to all declarative sentences, whatever their tense.
2. Presentism: Only what exists at present exists.
3. Truth-Maker Principle: Every contingent truth has a truth-maker.

They can't all be true, according to him, because the conjunction of any two implies the negation of the third. So here is a genuine insoluble problem. Each has a strong claim to our acceptance, but all of them cannot be true together.

Is that right? First, I don't see why the three statements are logically inconsistent.  Why can't the truthmaker for a future tense statement exist now, in the present? However, presumably Maverick buys the argument I gave here.  If the truthmaker exists now, and given that we cannot change the immediate present or the past, we cannot change the truthmaker’s existence. So we cannot change the future, for the truthmaker that exists now makes the future true, but we can change the future, ergo etc.  So we can assume the additional premise

4. The truthmaker for any contingently true proposition exists only at the time for which the proposition is true.

By the expression 'time for which' a proposition is true, I am attempting to translating the medieval Latin pro tempore, meaning, roughly, any time at which any present tense statement corresponding to a non present tense statement is true. For example, if I truly say 'it will rain next week', when today is 3 December 2011, the time for which my statement is true = any day next week, i.e. the week commencing Monday 5 December.  The corresponding present tense statements are 'it is raining today', uttered on Monday, or on Tuesday, Wednesday etc.

But statements 1-4 above cannot all be true.  If only things in the present exist, future truthmakers do not exist. It may be that they will exist, but they don't now.  So the statement 'it will rain next week' has no truthmaker (although, if it does rain, it may be that it will have one).  And yet law of excluded middle surely applies to any statement whatever.  If it does rain next week, and I say that it will rain next week, then surely we can say next week that 'Edward was right'.

Which of the four statements above is incorrect?  (Rhetorical question, for those who read my blog regularly).

*Pace Peter Damian.