Saturday, June 07, 2008
It goes the other way about
Here is a blog that I don't follow enough. Cambridge logician Peter Smith reflects on some profound issues on the philosophy of logic and language while drinking wine in Tuscany (how much do they pay him?). In this post he makes two points close to my heart.
1) Formal languages don't magically do what ordinary language can't do: they just do ordinary things like use singular terms and quantify in tidier ways.
2) We can't first pick out a class of genuine objects and then locate the genuine singular terms as those that refer to them: it goes the other way about.
Yes. The second point in particular makes a point that divides the philosophers of language from the metaphysicians - a shame Vallicella is in his self-imposed temporary exile. Metaphysically-inclined types will want to look for and investigate 'objects' first. Analytic types will investigate the language by which we talk about objects.
But this still leaves us with the problem of empty names. Signifying follows understanding, as the medievals said: significare sequitur intelligere. And it seems we can understand empty names, so why don't they signify? My understanding of 'Noah' is just the same whether or not 'Noah' refers to an existing person, or not. And 'Noah' seems a 'genuine singular term' in Smith's sense. But there may be no corresponding object.
We could resolve the difficulty by dropping or modifying (1). Perhaps empty names are not those items of ordinary language that we can 'tidy up' using the formal apparatus of constants and quantifiers. But that goes against the spirit of it. Formal language doesn't magically do what ordinary language can't. It is, literally 'formal'. It captures the 'form', literally the figure, that is characteristic of certain propositions and arguments.
There is a difficulty with this that I don't altogether see how to resolve.
1) Formal languages don't magically do what ordinary language can't do: they just do ordinary things like use singular terms and quantify in tidier ways.
2) We can't first pick out a class of genuine objects and then locate the genuine singular terms as those that refer to them: it goes the other way about.
Yes. The second point in particular makes a point that divides the philosophers of language from the metaphysicians - a shame Vallicella is in his self-imposed temporary exile. Metaphysically-inclined types will want to look for and investigate 'objects' first. Analytic types will investigate the language by which we talk about objects.
But this still leaves us with the problem of empty names. Signifying follows understanding, as the medievals said: significare sequitur intelligere. And it seems we can understand empty names, so why don't they signify? My understanding of 'Noah' is just the same whether or not 'Noah' refers to an existing person, or not. And 'Noah' seems a 'genuine singular term' in Smith's sense. But there may be no corresponding object.
We could resolve the difficulty by dropping or modifying (1). Perhaps empty names are not those items of ordinary language that we can 'tidy up' using the formal apparatus of constants and quantifiers. But that goes against the spirit of it. Formal language doesn't magically do what ordinary language can't. It is, literally 'formal'. It captures the 'form', literally the figure, that is characteristic of certain propositions and arguments.
There is a difficulty with this that I don't altogether see how to resolve.
Thursday, June 05, 2008
Hamlet kills Polonius
David Brightly writes: "'Hamlet kills Polonious' is analyzed into the conjunctive sentence 'Hamlet exists &Hamlet kills Polonious.' Something that has been puzzling me is how this doesn't run foul of an infinite regress. Can you explain how interpretation of the second, inner 'Hamlet kills Polonius' differs from that of the first, outer instance, so that this doesn't happen?"
A good point. We could represent that the second proper name by a pronoun. Thus Ockham (the medieval one) says that 'chimaera est non-ens' (the chimera is a non-being) is to be analysed as 'chimaera est aliquid' et 'illud est non-ens' (the chimera is something and it is a non-being'), of which the first is false. Or we could represent it a bound variable thus
E x, x = Hamlet and x kills Polonius.
I don't think either is quite right. My position would be that a proper name, which tells us who the predicate applies to,adds a little bit of information to the word 'someone', which doesn't tell us who the predicate applies to. I.e. 'Someone kills Polonius' asserts the existence of a Polonius-killer. Then we can add a bit of information to the 'someone' by turning it into a proper name, as though the proper name were a sort of adjective. I.e.
Someone (Polonius) kills Hamlet.
Thus there is only one proposition, not two, and we avoid the regress. This raises the difficulty of exactly how a proper name can function as an adjective, logically speaking. More later, possibly.
A good point. We could represent that the second proper name by a pronoun. Thus Ockham (the medieval one) says that 'chimaera est non-ens' (the chimera is a non-being) is to be analysed as 'chimaera est aliquid' et 'illud est non-ens' (the chimera is something and it is a non-being'), of which the first is false. Or we could represent it a bound variable thus
E x, x = Hamlet and x kills Polonius.
I don't think either is quite right. My position would be that a proper name, which tells us who the predicate applies to,adds a little bit of information to the word 'someone', which doesn't tell us who the predicate applies to. I.e. 'Someone kills Polonius' asserts the existence of a Polonius-killer. Then we can add a bit of information to the 'someone' by turning it into a proper name, as though the proper name were a sort of adjective. I.e.
Someone (Polonius) kills Hamlet.
Thus there is only one proposition, not two, and we avoid the regress. This raises the difficulty of exactly how a proper name can function as an adjective, logically speaking. More later, possibly.
Friday, May 30, 2008
Fictional objects
There is more stuff on existence going on at Bill Vallicella's place. This time, 'fictional objects', which I cannot bring myself to take seriously.
The gist of it is, characters such as Bilbo, creatures such as hobbits and imaginary places such as Hobbiton are objects in some sense. And if they are, and given that the fiction is all the information we have about them, these objects must be in some sense incomplete. We are not told what Bilbo's mother was called. So she is incomplete, not having a name. Indeed, we are not told whether Bilbo had a mother at all. So, he is incomplete. And so on.
Now this really is language on holiday. Suppose I write:
In 1998 a planet the size of Jupiter was miraculously created in the orbit between the Earth and Venus.
Does writing this miraculously create a fictional object the size of Jupiter? And does it get created just now, in May 2008, or 10 years ago in 1998, when it was claimed to have been created? Or should we be more prosaic and say that no object was created at all? For it says above that such a planet was created, and, as far as we know, no such planet ever was.
And if we do believe some object has just been created, is it really incomplete in the sense that Vallicella et alia suggest? Isn't it just the reverse? I can go on to make any false statement I like about this planet: it is a gas giant, not a gas giant, has frozen helium at its core, a black hole, whatever. Since any statement 'about' this planet has to be false, it does not matter what I say. All are equally incorrect. For information about x to be truly incomplete, there has to be at least the possibility that there are further true statements that could be made about x, i.e. statements that say that x is so, and where x is in fact so. No such possibility exists in this case. For example I can say
In 1998 a planet the size of Jupiter was miraculously created in the orbit between the Earth and Venus. It was made entirely of iron.
Which simply adds more falsity to what is already there. There is a great temptation to talk like this, and many serious and respectable people do. Perhaps it is enlightening, from the standpoint of human psychology, that they do. But perhaps it ought to be resisted.
The gist of it is, characters such as Bilbo, creatures such as hobbits and imaginary places such as Hobbiton are objects in some sense. And if they are, and given that the fiction is all the information we have about them, these objects must be in some sense incomplete. We are not told what Bilbo's mother was called. So she is incomplete, not having a name. Indeed, we are not told whether Bilbo had a mother at all. So, he is incomplete. And so on.
Now this really is language on holiday. Suppose I write:
In 1998 a planet the size of Jupiter was miraculously created in the orbit between the Earth and Venus.
Does writing this miraculously create a fictional object the size of Jupiter? And does it get created just now, in May 2008, or 10 years ago in 1998, when it was claimed to have been created? Or should we be more prosaic and say that no object was created at all? For it says above that such a planet was created, and, as far as we know, no such planet ever was.
And if we do believe some object has just been created, is it really incomplete in the sense that Vallicella et alia suggest? Isn't it just the reverse? I can go on to make any false statement I like about this planet: it is a gas giant, not a gas giant, has frozen helium at its core, a black hole, whatever. Since any statement 'about' this planet has to be false, it does not matter what I say. All are equally incorrect. For information about x to be truly incomplete, there has to be at least the possibility that there are further true statements that could be made about x, i.e. statements that say that x is so, and where x is in fact so. No such possibility exists in this case. For example I can say
In 1998 a planet the size of Jupiter was miraculously created in the orbit between the Earth and Venus. It was made entirely of iron.
Which simply adds more falsity to what is already there. There is a great temptation to talk like this, and many serious and respectable people do. Perhaps it is enlightening, from the standpoint of human psychology, that they do. But perhaps it ought to be resisted.
Wednesday, May 28, 2008
Summa 94-103, Logic Museum
Questions 94-103 now available. There are some interesting observations on sexual reproduction in question 98. How would humans have reproduced in Paradise, without original sin, and in a state of innocence? Gregory of Nyssa said that the human race would have multiplied by some other means than the usual one. St Thomas objects that the usual method is natural to man by reason of his being an animal. And the 'corporeal members' must have had a natural use before sin. Thus the order of nature requires that there should be 'concurrence' of male and female for purposes of generation.
However, in the state of innocence there would have been no 'excessive concupiscence' (immoderata concupiscentia), when the lower members were entirely subject to reason. For which reason Augustine says (De Civ. Dei xiv, 26): "We must be far from supposing that offspring could not be begotten without concupiscence. All the bodily members would have been equally moved by the will, without ardent or wanton incentive, with calmness of soul and body."
However, in the state of innocence there would have been no 'excessive concupiscence' (immoderata concupiscentia), when the lower members were entirely subject to reason. For which reason Augustine says (De Civ. Dei xiv, 26): "We must be far from supposing that offspring could not be begotten without concupiscence. All the bodily members would have been equally moved by the will, without ardent or wanton incentive, with calmness of soul and body."
Wednesday, May 21, 2008
The Theologian's Fallacy
So many blogs have started discussing Alan Rhoda’s ‘Theologian’s Fallacy’ that it’s time for me to get in on the act. In this case, merely as an index. Alan’s original post is here
with a follow up here. There are also:
Siris, plus follow-up [22 May] here.
Mormon metaphysics
Maverick philosopher
Triablogue
Declarations of the Dismissed
[added 22 May] WenatcheeTheHatchet
with a follow up here. There are also:
Siris, plus follow-up [22 May] here.
Mormon metaphysics
Maverick philosopher
Triablogue
Declarations of the Dismissed
[added 22 May] WenatcheeTheHatchet
Saturday, May 17, 2008
Existence and assertion
Bill Vallicella's otherwise excellent discussion of 'thin' theories of existence in a series of posts at the Maverick Philosopher website has so far ignored the difference between theories where the existence of a singular referent is presupposed, and theories where it is asserted.
Consider 'Socrates is wise'. This affirms wisdom of Socrates. Does it also affirm existence of him? Does it then consist of two propositions, one of which affirms existence, the other of which affirms wisdom? Or does it consist of just one, that affirms wisdom without affirming existence? The latter view, sometimes called the 'Strawsonian' or 'presupposition' view, involves the following problem.
If Socrates does not exist, the negation of 'Socrates is wise', i.e. 'It is not the case that Socrates is wise' must be true. But if 'Socrates is wise' does not assert the existence of Socrates, neither does its negation (for a negation can deny no more than the corresponding affirmation affirmed). In which case the negation expresses exactly the same thing as if Socrates had existed, and wisdom was being denied of him, i.e. expresses exactly what 'Socrates is non-wise' expresses. But then it affirms non-wisdom of something, and so requires the existence of Socrates. But that cannot be, if Socrates does not exist.
But there is no such problem with the view that existence, as well as wisdom, is asserted. Then the negation of 'Socrates is wise' is the negation of a conjunction, and so is equivalent to the disjunction 'There is no such person as Socrates, or wisdom does not apply to Socrates'. There are different facts corresponding to Socrates' not existing, and Socrates existing but not having wisdom, and so the falsity of 'Socrates is wise' does not imply that a non-wise Socrates exists.
[edit] For an early defence of assertionism, see my translation of chapters 12 and 14 of the Ockham's Summa Logicae II here. For a later one that should be familiar to almost everyone, see Russell's Theory of Descriptions.
Consider 'Socrates is wise'. This affirms wisdom of Socrates. Does it also affirm existence of him? Does it then consist of two propositions, one of which affirms existence, the other of which affirms wisdom? Or does it consist of just one, that affirms wisdom without affirming existence? The latter view, sometimes called the 'Strawsonian' or 'presupposition' view, involves the following problem.
If Socrates does not exist, the negation of 'Socrates is wise', i.e. 'It is not the case that Socrates is wise' must be true. But if 'Socrates is wise' does not assert the existence of Socrates, neither does its negation (for a negation can deny no more than the corresponding affirmation affirmed). In which case the negation expresses exactly the same thing as if Socrates had existed, and wisdom was being denied of him, i.e. expresses exactly what 'Socrates is non-wise' expresses. But then it affirms non-wisdom of something, and so requires the existence of Socrates. But that cannot be, if Socrates does not exist.
But there is no such problem with the view that existence, as well as wisdom, is asserted. Then the negation of 'Socrates is wise' is the negation of a conjunction, and so is equivalent to the disjunction 'There is no such person as Socrates, or wisdom does not apply to Socrates'. There are different facts corresponding to Socrates' not existing, and Socrates existing but not having wisdom, and so the falsity of 'Socrates is wise' does not imply that a non-wise Socrates exists.
[edit] For an early defence of assertionism, see my translation of chapters 12 and 14 of the Ockham's Summa Logicae II here. For a later one that should be familiar to almost everyone, see Russell's Theory of Descriptions.
Sunday, April 13, 2008
Caesar in the Logic Museum
Caesar is not really logic at all. But the Logic Museum does have parallel texts, and there is now a parallel Latin English version of the Gallic wars in there.
Saturday, March 01, 2008
Is Caesar dead?
Yes, Caesar is dead. And to prove it, a number of additions to the Logic Museum. Simon Faversham, in a question from his book of questions on the Sophistical Refutations. And Radulphus Brito, two questions from the Old Logic.
Saturday, February 16, 2008
Additions to the Logic Museum
Two new things in the Logic Museum. One a well known piece by Boethius of Dacia, but a new translation and in parallel with the Latin. The other by Siger of Brabant, previously untranslated and also with the Latin (of course: The Logic Museum never publishes a translation without the original).
The pieces concern the familiar question of whether universal propositions are true when nothing is denoted by the subject. Boethius takes an 'externalist' line, arguing that nothing is true, unless there is a corresponding truth in reality. Every A is B asserts a combination of A and B, i..e a really existing combination, ergo is false when no A exists. Other writers of that school and period thought that the proposition, when 'per se' or 'essential' must be true even when no A exists, and even when nothing exists. The questions by Siger reflect the latter position more.
I will shortly be publishing another related set of questions attributed to Scotus, on the very same topic, but publication was delayed owing to my uncertainty about the attribution (it is supposed to be by Scotus, by I am not so sure).
A Happy New Year to all my readers.
The pieces concern the familiar question of whether universal propositions are true when nothing is denoted by the subject. Boethius takes an 'externalist' line, arguing that nothing is true, unless there is a corresponding truth in reality. Every A is B asserts a combination of A and B, i..e a really existing combination, ergo is false when no A exists. Other writers of that school and period thought that the proposition, when 'per se' or 'essential' must be true even when no A exists, and even when nothing exists. The questions by Siger reflect the latter position more.
I will shortly be publishing another related set of questions attributed to Scotus, on the very same topic, but publication was delayed owing to my uncertainty about the attribution (it is supposed to be by Scotus, by I am not so sure).
A Happy New Year to all my readers.
Saturday, November 24, 2007
Medieval hymns (1)
Fregit Adam interdictum
et reliquit hoc delictum
posteris miseris
poenam culpae veteris;
libera conditio
mergitur in vitio,
viget in natura
conjectura.
o quanta miseria!
Fregit homo pactum dei,
unde sumus omnes rei
patimur, labimur
aeternumque morimur
donec virgo peperit,
quae naturam praeterit
sola praeter morem
pium redemptorem.
o quanta miseria!
Hic adjutor opportunus
a peccato liber unus
exstitit, restitit
hosti, qui nos perdidit;
qui dum petit humilem,
tentat ut vincibilem,
satan enervatur,
vincit, qui temptatur.
o quanta victoria!
et reliquit hoc delictum
posteris miseris
poenam culpae veteris;
libera conditio
mergitur in vitio,
viget in natura
conjectura.
o quanta miseria!
Fregit homo pactum dei,
unde sumus omnes rei
patimur, labimur
aeternumque morimur
donec virgo peperit,
quae naturam praeterit
sola praeter morem
pium redemptorem.
o quanta miseria!
Hic adjutor opportunus
a peccato liber unus
exstitit, restitit
hosti, qui nos perdidit;
qui dum petit humilem,
tentat ut vincibilem,
satan enervatur,
vincit, qui temptatur.
o quanta victoria!
Tuesday, November 13, 2007
Thursday, November 08, 2007
Summa Theologiae I 84 - 89
Questions 84 to 89 of the great Summa Theologiae now in Logic Museum II here.
Thursday, October 18, 2007
Saturday, August 18, 2007
Every man is an animal
But is 'Every man is an animal' true when there are no men? Some new pages in the Logic Museum on the medieval dispute about this question. The main page outlines the controversy (which lasted from the early thirteenth to the late sixteenth century). The first subpage contains new translations (and Latin sources fresh to the web) of early writings on the subject. Much more to follow.
Friday, July 20, 2007
The Ontological argument
A new page here in the Logic Museum on the ontological argument. Kicks off with Aristotle's proof of the existence of God from the Metaphysics, and Descartes argument from Meditations V. Coming later will be Augustine's argument (from On Free Will), Anselm's version of the ontological argument proper, Aquinas comments on Anselm's argument, and Scotus' very complex version of the cosmological argument.
Saturday, July 14, 2007
Originals and Covers, Covers and Originals
When the Levee Breaks. The cover by Zeppelin, and the original by Memphis Minnie.
Fields of Gold. Eva Cassidy's version, and the original by Sting.
Crossroads. The original by Robert Johnson, and a cover by Clapton.
Fields of Gold. Eva Cassidy's version, and the original by Sting.
Crossroads. The original by Robert Johnson, and a cover by Clapton.
Is 'every man is an animal true' when there are no men?
A splendid new page in the Logic Museum here.
Sunday, July 01, 2007
The Square of Opposition
Just to draw attention to the page in the Logic Museum on the famous square. Plenty of material there, and plenty coming up, particularly of relevane to my dispute with Terence Parsons about the semantics of the O proposition.
Thursday, December 07, 2006
Buridan on Individuation
Here is a splendid passage from the 14C logician John Buridan. The Latin you can find on Peter King's website, here, of which my hasty English translation is below. The passage is interesting because, while logicians like Ockham anticipate Russell's idea of scope distinction (i.e. between ~ the F is G and the F is ~ G), Buridan here also anticipates the idea that proper names are telescoped definite description. (Buridan uses the wonderful Latin word circumlocutio). Note also the examples of 'teacher of Alexander' (magister Alexandri) and 'student of Plato' (discipulus Platonis) as the relevant circumlocutio of 'Aristotle'. These are familiar from Kripke, but he just got them from Frege, who had a good German classical education, and probably got them from some unknown scholastic source.
Another familiar idea is that genuinely singular terms are really demonstrative. Buridan says that a proper name is a circumlocution, but that a truly singular term is used in the presence ('prospect') of something, whose function is not to indicate similarity, but to indicate that it can belong to no other thing.
See also the following pages in the Logic Museum.
Aquinas on the name 'God'.
Ockham's Theory of definite descriptions.
Another familiar idea is that genuinely singular terms are really demonstrative. Buridan says that a proper name is a circumlocution, but that a truly singular term is used in the presence ('prospect') of something, whose function is not to indicate similarity, but to indicate that it can belong to no other thing.
See also the following pages in the Logic Museum.
Aquinas on the name 'God'.
Ockham's Theory of definite descriptions.
'But if you say, how can I conceive Aristotle in a singular way, when he was never in my prospect? In reply, I say that it is not possible for you, properly speaking, because you do not conceive him differently from other men except according to a sort of circumlocution, such as 'the greatest philosopher', 'the teacher of Alexander', 'the disciple of Plato', who composed the books of philosophy which we read &c. Now although this description does not in truth belong to anyone but him, yet it is not properly a singular term (terminus singularis) - Although it does not belong to anyone except him alone, it is not inconceivable (repugnat – fudge) that in this way of signifying or imposition that it may belong to many and stand (supponat) for many, and if there were another God similar, the name 'God' would belong to him and would stand for him without a new imposition of the word – and so if there were another who were the greatest philosopher and the master of Alexander and the disciple of Plato &c, the said description would belong to him and would stand for him.
'For thus it is not a term that is absolutely and properly singular. Because if this thing in my prospect I call 'Socrates' by a proper name, it is not because he is such and such but because the name 'Socrates' would never belong to those other things insofar as they are similar – unless from another imposition [that name] were imposed to signify that other thing, and thus equivocally'.
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