Now in the Logic Museum, book I of the Lectura by Duns Scotus. These are Scotus' notes for lectures he gave on Books 1 and 2 of the Sentences as a bachelor theologian at Oxford. It is the only material from his Oxford lectures that were available for some parts of the Sentences, as the Ordinatio (the revised and edited version of the lectures) was never completed. The work is also useful for presenting an earlier and generally simpler and less 'subtle' version of his thought.
As with much of the material in the museum, it is untranslated, I am afraid.
Showing posts with label scotus. Show all posts
Showing posts with label scotus. Show all posts
Sunday, April 29, 2012
Monday, April 02, 2012
More Scotus
Some more Scotus: the Prologue and the first seven distinctions of Book I of the immense Ordinatio. Following the post the other day about actual infinity, note Distinction 2, Question 1 on whether there is an actual infinite, and Question 2 whether some infinite being is per se known to us, such as the being of God.
Sunday, April 01, 2012
Scotus on the actual infinite
Cantor thought that the Scholastics strictly followed Aristotle in rejecting the actual infinite. Aquinas certainly did, but Scotus seemed to have come pretty close to accepting. Here is a passage from Quodlibet 5, where he argues that we can conceive of an actually infinite being. He says that Aristotle ( Physics book III 207a8) defines the infinite as that which for those taking any quantity (i.e. any quantity however large) there always remains something else to take*.
But why can’t we imagine all the parts that could be taken to be actually taken together, so that then we would have an actually infinite quantity, something as great in actuality, as it was potentially? Furthermore, if we can imagine the actual infinite in respect of mere quantity, why not something actually infinite in respect of being? This would be absolutely perfect. For, while an actually infinite quantity has parts which are imperfect (for example, the series of even numbers is imperfect because it lacks the series of odd numbers to make the whole number series), a being that was infinite in being would have perfect parts. According to Scotus anyway, but I didn’t follow the argument. Why would any part of anything be perfect, given that it lacked precisely the remaining bits of the whole in virtue of which it is a part. Isn’t that in the very meaning of the word ‘part’?
Nonetheless, the passage is historically interesting.
*The Latin formulation is “cuius quantitatem accipientibus”, which you can find in at least four places in Aquinas’ Summa: Part I q14 a12 and q86 a2, part IIa q30 a4 and part III q10 a3.
But why can’t we imagine all the parts that could be taken to be actually taken together, so that then we would have an actually infinite quantity, something as great in actuality, as it was potentially? Furthermore, if we can imagine the actual infinite in respect of mere quantity, why not something actually infinite in respect of being? This would be absolutely perfect. For, while an actually infinite quantity has parts which are imperfect (for example, the series of even numbers is imperfect because it lacks the series of odd numbers to make the whole number series), a being that was infinite in being would have perfect parts. According to Scotus anyway, but I didn’t follow the argument. Why would any part of anything be perfect, given that it lacked precisely the remaining bits of the whole in virtue of which it is a part. Isn’t that in the very meaning of the word ‘part’?
Nonetheless, the passage is historically interesting.
*The Latin formulation is “cuius quantitatem accipientibus”, which you can find in at least four places in Aquinas’ Summa: Part I q14 a12 and q86 a2, part IIa q30 a4 and part III q10 a3.
Scotus Quodlibetal Questions
I've been a bit quiet for a few days, which is because I located a source for Scotus' difficult to obtain Quodlibetal Questions. Now in the Logic Museum.
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.
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.
*Shakespeare made extensive use of narratives describing the wreck and redemption of the ship the "Sea-Venture" in Bermuda in 1609, and the events which ensued when the crew made it safely ashore.
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.
*Shakespeare made extensive use of narratives describing the wreck and redemption of the ship the "Sea-Venture" in Bermuda in 1609, and the events which ensued when the crew made it safely ashore.
Thursday, December 15, 2011
A piece of enormously complex polyphony sung over a drone of Aristotelianism and a cantus firmus of revelation
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.
Wednesday, November 30, 2011
The lazy argument for not doing anything
When inspiration fails, I turn to the Maverick’s site to look for easy pickings, and, lo, I find his post from Tuesday about future contingents. Bill starts with a tolerably useful distinction between the two senses of ‘proposition’ that caused so much anguish for Anthony (and me) the other day
Bill continues with a version of the ‘lazy argument’ for not doing anything, as follows.
1. Either I will be killed tomorrow or I will not.
2. If I will be killed, I will be killed no matter what precautions I take.
3. If I will not be killed, then I will be killed no matter what precautions I neglect.
Therefore
4. It is pointless to take precautions.
This is a breathtakingly rotten argument. Is it true that I will be killed in France tomorrow, I will be killed even if I take the precaution of not going to France? Surely not. It cannot be true that I will have been killed in France, even though I have not gone to France. The argument is only effective if we believe in truthmakers. For if the proposition ‘I will be killed in France tomorrow’ is true now, then Truthmakerists say it has a truthmaker now, i.e. some state of affairs that ‘makes it’ true. But 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.
The early Duns Scotus has a nice argument against this which I discussed in a post in 2009. Scotus writes
*From a translation I made in 2009, which may be different from the corresponding translation (of Aristotle’s Perihermenias) that is now going through the usual process at CUA publications.
Accordingly, a proposition is the sense of a context-free declarative sentence. A context-free sentence is one from which all indexical elements have been extruded, including verb tenses. Propositions so construed are a species of abstract object. This will elicit howls of outrage from some, but it is a view that is quite defensible.I.e. proposition in the sense the medievals used it is “context-free declarative sentence”. A proposition in the modern sense is the sense (or ‘meaning’) of a context-free declarative sentence. (The medievals sometimes distinguished between a spoken proposition, i.e. context-free declarative sentence, and a ‘mental proposition’, i.e. the sense of a context-free declarative sentence.
Bill continues with a version of the ‘lazy argument’ for not doing anything, as follows.
1. Either I will be killed tomorrow or I will not.
2. If I will be killed, I will be killed no matter what precautions I take.
3. If I will not be killed, then I will be killed no matter what precautions I neglect.
Therefore
4. It is pointless to take precautions.
This is a breathtakingly rotten argument. Is it true that I will be killed in France tomorrow, I will be killed even if I take the precaution of not going to France? Surely not. It cannot be true that I will have been killed in France, even though I have not gone to France. The argument is only effective if we believe in truthmakers. For if the proposition ‘I will be killed in France tomorrow’ is true now, then Truthmakerists say it has a truthmaker now, i.e. some state of affairs that ‘makes it’ true. But 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.
The early Duns Scotus has a nice argument against this which I discussed in a post in 2009. Scotus writes
It must be understood that a proposition about the future can be understood to signify something in the future in two ways. So that the proposition about the future signifies it to be true now that something in the future will have to be true [verum esse habebit] (for example, that ‘you will be white at a’ signifies it now to be in reality so that at time a you will be white). Or it can be understood that it signifies now that you will be white then: not that it signifies that it is now such that then you are going to be white, but that it signifies now that then you will be white. For to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a.*I take it that “signify it to be [the case] now that you will be white at a” means signifying that a truthmaker exists now for ‘will be white at a’.
*From a translation I made in 2009, which may be different from the corresponding translation (of Aristotle’s Perihermenias) that is now going through the usual process at CUA publications.
Saturday, May 21, 2011
Old wine in new bottles
There is an interesting claim by Tim Crane in his paper "The Singularity of Singular Thought" that bears a marked resemblance to something said by Duns Scotus in his Questions on Aristotle's Perihermenias. Crane says
* Book I Question 6 n43. As some readers of this blog will know, I am working with Jack Zupko on an English translation of this early work of Scotus. This may even get published this year, who knows.
What is relevant to generality is not that as a matter of fact the information is true of many things, but the fact that a thinker can make sense of it being true of many things (or of different things in different possible situations). Conversely, what is relevant to singularity is not the fact that the information in one’s file is true of just one thing, but that one cannot make sense of it as being true of many things.Scotus says
Terminus communis secundum quod habet rationem communis est natura prout concipitur sub ratione ‘dicibilis de pluribus’, et ita suppositum est natura concepta apud intellectum sub ratione ‘indicibilis de pluribus.* “A common term, according as it has the nature of the common, is a nature as conceived under the aspect ‘predicable of many,’ and so a suppositum is a nature conceived in the understanding under the aspect ‘incapable of being predicated of many".A suppositum is a technical term difficult to translate, and is often left untranslated. Scotus here often uses it to mean any object that falls within the range of a common term (or the 'value' of a variable, if you like). Thus any man is the suppositum of the common term 'man'.
* Book I Question 6 n43. As some readers of this blog will know, I am working with Jack Zupko on an English translation of this early work of Scotus. This may even get published this year, who knows.
Friday, September 24, 2010
Why haecceity is not repeatable
The difficulty raised by Paasch is as follows. If haecceity involves a form of relation to an individual, the haecceity cannot be prior to the individual which it individuates, and then the individual must be already an individual. The haecceity arrives 'too late'. But if haecceity is absolute, then it is not contradictory for God to create another, numerically different individual with the same haecceity. I will attempt to answer this question. I am using Spade's translation of the Vatican edition of the Ordinatio, section references are also to that edition.
It is fairly clear that for Scotus, haecceity is not any relation between an individual and something else. This seems clear from his reply to the 'negation' theory of Henry of Ghent discussed in Question 3 (nn 49-56). 'Nothing is absolutely incompatible with any being through a privation in that being, but rather through something positive in it" (n 49). He gives the example (n50) of there being nothing present to sight. This does not produce any incompatibility with the sense of sight. By analogy, if being indivisible were simply a negation like not having anything present to sight, there would be no contradiction or incompatibility in something that is extrinsically indivisible being intrinsically divisible. So individuality is not a form of negation, and by inference not any form of relation. Individuality must be intrinsically a feature of the individual. "It is necessary through something positive intrinsic to this stone … that it be incompatible with the stone for it to be divided into subjective parts. That positive feature will be what will be said to be by itself the cause of individuation. For by 'individuation' I understand that indivisibility - that is, incompatibility with divisibility". (n57)
That leaves the other difficulty raised by Paasch. If haecceity is an absolute, positive, intrinsic feature of this stone, why is not contradictory for God to create another individual with the same haecceity. What specifically about this feature makes it, in Scotus's words 'incompatible with division'?
The answer to this probably lies in the sections of distinction III (nn 48, 76, 165) where he explicitly says what he means by haecceity.
In section 48 he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into (subjective) parts? (See my note on 'subjective parts' here).
In section 76 he says that individuation or numerical unity is not the indeterminate unity by which a species (e.g. man) is said to be one species. A designated unity is a 'this', that which it is inconsistent to divide into subjective parts. The cause is asked not of 'singularity in general' but of this designated singularity, i.e. as it is determinately this.
In section 165 he says that which is a 'this' is such that it is contradictory for it to be divided into several subjective parts, and contradictory for it to be 'not this'. It cannot be divided by anything added to it, for if it is incompatible for it to be divided of itself, it is incompatible with it, of itself, to received anything by which it becomes 'not this'. To say that something can be this and that through something extrinsic that is added is to say contradictory things.
In summary: haecceity for Scotus is an absolute, intrinsic feature of an individual thing. It is the feature whereby we conceive of and signify a thing as this. For any this, anything that does not possess this feature is a not-this, and thus not the same individual. Thus it would be contradictory for God to create another individual from this one with the same haecceity as this one. To have the same haecceity it would have to be this. To be a different individual had would have to be not-this.
Contradiction.
It is fairly clear that for Scotus, haecceity is not any relation between an individual and something else. This seems clear from his reply to the 'negation' theory of Henry of Ghent discussed in Question 3 (nn 49-56). 'Nothing is absolutely incompatible with any being through a privation in that being, but rather through something positive in it" (n 49). He gives the example (n50) of there being nothing present to sight. This does not produce any incompatibility with the sense of sight. By analogy, if being indivisible were simply a negation like not having anything present to sight, there would be no contradiction or incompatibility in something that is extrinsically indivisible being intrinsically divisible. So individuality is not a form of negation, and by inference not any form of relation. Individuality must be intrinsically a feature of the individual. "It is necessary through something positive intrinsic to this stone … that it be incompatible with the stone for it to be divided into subjective parts. That positive feature will be what will be said to be by itself the cause of individuation. For by 'individuation' I understand that indivisibility - that is, incompatibility with divisibility". (n57)
That leaves the other difficulty raised by Paasch. If haecceity is an absolute, positive, intrinsic feature of this stone, why is not contradictory for God to create another individual with the same haecceity. What specifically about this feature makes it, in Scotus's words 'incompatible with division'?
The answer to this probably lies in the sections of distinction III (nn 48, 76, 165) where he explicitly says what he means by haecceity.
In section 48 he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into (subjective) parts? (See my note on 'subjective parts' here).
In section 76 he says that individuation or numerical unity is not the indeterminate unity by which a species (e.g. man) is said to be one species. A designated unity is a 'this', that which it is inconsistent to divide into subjective parts. The cause is asked not of 'singularity in general' but of this designated singularity, i.e. as it is determinately this.
In section 165 he says that which is a 'this' is such that it is contradictory for it to be divided into several subjective parts, and contradictory for it to be 'not this'. It cannot be divided by anything added to it, for if it is incompatible for it to be divided of itself, it is incompatible with it, of itself, to received anything by which it becomes 'not this'. To say that something can be this and that through something extrinsic that is added is to say contradictory things.
In summary: haecceity for Scotus is an absolute, intrinsic feature of an individual thing. It is the feature whereby we conceive of and signify a thing as this. For any this, anything that does not possess this feature is a not-this, and thus not the same individual. Thus it would be contradictory for God to create another individual from this one with the same haecceity as this one. To have the same haecceity it would have to be this. To be a different individual had would have to be not-this.
Contradiction.
Monday, September 20, 2010
Indivisibility and Unrepeatability: Subjective Parts
Before I attempt an answer to Paasch's question there is a preliminary notion that needs to be clarified, as it is crucial to Scotus' account of individuation, and it is also one of those medieval ideas that are obscure to us schooled in the thought of the modern predicate calculus.
In book II, d3 section 48 (Vatican edition) he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into subjective parts?
A 'subjective part' is a term that would have been familiar to any scholastic logician. Peter of Spain explains it [1], together with the notion of 'integral part', in his Treatise on Logic, a standard textbook of the time. "The [term] 'whole universal', as taken in this way, is anything superior and substantial, taken in respect of its inferior. For example, animal to man, man to Socrates. A 'subjective part' is said of any inferior, taken under the whole universal. […] The 'whole integral' is is a composite of parts having quantity, and its parts are called 'integral parts'. An integral part is what, taken with the other parts, gives the quantity of the whole'.
Walter Burley explains it [2] by definition as well as by example, saying that an individual is a subjective part of a species, because the species is directly predicated of the individual, and for the same reason the species is a subjective part of the genus, because the genus is directly predicated of the species, and this is the difference between an integral part and a subjective part, because the whole is directly predicated of a subjective part, but is not directly predicated of an integral part, but only indirectly. And so 'a hand is a man' is false, or 'a head is a man'.
The distinction probably comes from Porphyry's introduction to Aristotle's Categories, where he says that that individual is a part of the species, and the species by the genus, so that genus is a sort of whole, the individual is a part, and species both whole and a part.
Thus (returning to Scotus) we have the sense in which an Socrates is indivisible or 'individual'. The genus 'animal' can be divided into subjective parts such as man, giraffe, grasshopper and so on. The species 'man' can be divided into subjective parts such as Socrates, Plato and so on. But these cannot be divided in the same way. Socrates is not like a species having some member x of which we can truly say that x is Socrates. This conception of division is fundamentally different from modern logic. We predicate 'animal' or 'man' of some x (e.g. Socrates). But the subject is always an individual. We have man(Socrates) and animal(Socrates). We do not and cannot have animal(man), for as Geach notes, modern predicate logic assumes a fundamental distinction between the relation of class-inclusion (man to animal) and the relation between individual and class (Socrates to man, Socrates to animal). Thus we cannot even understand Scotus' conception of individuation unless we drop an idea that is part of the language of thought for modern analytic philosophers. The idea may be wrong and misguided, even incoherent (as Geach cogently argues). But we cannot even begin to 'get inside the head' of the medieval logician unless
This should also clarify the distinction between the modern notion of individuation as 'unrepeatability' and notion of it as indivisibility. Repeatability is another idea of modern predicate calculus. A predicate is repeatable when it be 'instantiated' more than once. An instance of F is an x such that Fx, another instance is a y such that Fy, and x <> y. Note that the instance must be an individual x or y, not another predicate. We can have man(Socrates) and man(Plato), but not animal(man), animal(giraffe), or at least not when the function-argument notation is understood as in standard predicate logic. But divisibility, as Scotus and other medieval logicians understand it, is fundamentally different. Animal is divisible because it is (as it were) instantiated by man or giraffe. 'Man' is repeatable because it can be instantiated, in exactly the same sense, by Socrates and Plato. But Socrates cannot be further instantiated.
Hence there is not really a problem of individuation for modern logic. The argument to a propositional function is guaranteed to be individual because anything other than a sign for an individual in the argument place (or a variable representing it) will make the expression ill-formed. Scotus, by contrast, has to explain why the Porphyrian tree comes to an abrupt halt with individuals such as Socrates and Plato, because he is assuming that the relation between Socrates and his species is fundamentally the same as that between the species and its genus. If the relation between Socrates and man is essentially like the relation between man and animal, why is it that we can't repeat Socrates into subjective parts, the way that we can repeat animal into subjective parts such as man and giraffe.
So, you can either argue that the problem of individuation is a silly problem that can't even be stated in modern logic. Or you can take it seriously, as I will try to do in a later post. More later.
[1] Totum universale, ut sic sumitur, est quodlibet superius et substantiale, sumptum ad suum inferius, ut animal ad hominem, et homo ad Socratem. Pars subiectiva dicitur quodlibet inferius, sub toto universali sumtum . . .Totum integrale est, quod est compositum ex partibus, quantitatem habentibus, et pars eius dicitur pars integralis. Pars integralis est, quae cum aliis partibus reddit quantitatem totius.
[2] Expositio super librum Porphyrii: De genere quidem et specie. Recapitulans dicit quod intelligendum est quod individuum est pars subiectiva speciei, quia species predicatur de individuo in recto; et propter eandem causam species est pars subieciva generis, quia genus predicatur in recto de specie; et hec est differentia inter partem integralem et partem subiectivam, quia de parte subiectiva vere predicatur suum totum in recto, sed de parte integrali non vere predicatur totum in recto, sed in obliquo. Manus enim et caput sunt partes integrales hominis, quia integrant hominem. Et ita hec est falsa: ‘manus est homo’, vel ‘caput est homo’. Text from here.
In book II, d3 section 48 (Vatican edition) he says that we must not ask what it is by which such a division is formally incompatible to an individual (since it is formally incompatible by incompatibility), but rather what it is by which, "as by a proximate and intrinsic foundation", the incompatibility is in it. What is it in this stone by which, as by a proximate and intrinsic foundation, it is absolutely incompatible with it to be divided into subjective parts?
A 'subjective part' is a term that would have been familiar to any scholastic logician. Peter of Spain explains it [1], together with the notion of 'integral part', in his Treatise on Logic, a standard textbook of the time. "The [term] 'whole universal', as taken in this way, is anything superior and substantial, taken in respect of its inferior. For example, animal to man, man to Socrates. A 'subjective part' is said of any inferior, taken under the whole universal. […] The 'whole integral' is is a composite of parts having quantity, and its parts are called 'integral parts'. An integral part is what, taken with the other parts, gives the quantity of the whole'.
Walter Burley explains it [2] by definition as well as by example, saying that an individual is a subjective part of a species, because the species is directly predicated of the individual, and for the same reason the species is a subjective part of the genus, because the genus is directly predicated of the species, and this is the difference between an integral part and a subjective part, because the whole is directly predicated of a subjective part, but is not directly predicated of an integral part, but only indirectly. And so 'a hand is a man' is false, or 'a head is a man'.
The distinction probably comes from Porphyry's introduction to Aristotle's Categories, where he says that that individual is a part of the species, and the species by the genus, so that genus is a sort of whole, the individual is a part, and species both whole and a part.
Thus (returning to Scotus) we have the sense in which an Socrates is indivisible or 'individual'. The genus 'animal' can be divided into subjective parts such as man, giraffe, grasshopper and so on. The species 'man' can be divided into subjective parts such as Socrates, Plato and so on. But these cannot be divided in the same way. Socrates is not like a species having some member x of which we can truly say that x is Socrates. This conception of division is fundamentally different from modern logic. We predicate 'animal' or 'man' of some x (e.g. Socrates). But the subject is always an individual. We have man(Socrates) and animal(Socrates). We do not and cannot have animal(man), for as Geach notes, modern predicate logic assumes a fundamental distinction between the relation of class-inclusion (man to animal) and the relation between individual and class (Socrates to man, Socrates to animal). Thus we cannot even understand Scotus' conception of individuation unless we drop an idea that is part of the language of thought for modern analytic philosophers. The idea may be wrong and misguided, even incoherent (as Geach cogently argues). But we cannot even begin to 'get inside the head' of the medieval logician unless
This should also clarify the distinction between the modern notion of individuation as 'unrepeatability' and notion of it as indivisibility. Repeatability is another idea of modern predicate calculus. A predicate is repeatable when it be 'instantiated' more than once. An instance of F is an x such that Fx, another instance is a y such that Fy, and x <> y. Note that the instance must be an individual x or y, not another predicate. We can have man(Socrates) and man(Plato), but not animal(man), animal(giraffe), or at least not when the function-argument notation is understood as in standard predicate logic. But divisibility, as Scotus and other medieval logicians understand it, is fundamentally different. Animal is divisible because it is (as it were) instantiated by man or giraffe. 'Man' is repeatable because it can be instantiated, in exactly the same sense, by Socrates and Plato. But Socrates cannot be further instantiated.
Hence there is not really a problem of individuation for modern logic. The argument to a propositional function is guaranteed to be individual because anything other than a sign for an individual in the argument place (or a variable representing it) will make the expression ill-formed. Scotus, by contrast, has to explain why the Porphyrian tree comes to an abrupt halt with individuals such as Socrates and Plato, because he is assuming that the relation between Socrates and his species is fundamentally the same as that between the species and its genus. If the relation between Socrates and man is essentially like the relation between man and animal, why is it that we can't repeat Socrates into subjective parts, the way that we can repeat animal into subjective parts such as man and giraffe.
So, you can either argue that the problem of individuation is a silly problem that can't even be stated in modern logic. Or you can take it seriously, as I will try to do in a later post. More later.
[1] Totum universale, ut sic sumitur, est quodlibet superius et substantiale, sumptum ad suum inferius, ut animal ad hominem, et homo ad Socratem. Pars subiectiva dicitur quodlibet inferius, sub toto universali sumtum . . .Totum integrale est, quod est compositum ex partibus, quantitatem habentibus, et pars eius dicitur pars integralis. Pars integralis est, quae cum aliis partibus reddit quantitatem totius.
[2] Expositio super librum Porphyrii: De genere quidem et specie. Recapitulans dicit quod intelligendum est quod individuum est pars subiectiva speciei, quia species predicatur de individuo in recto; et propter eandem causam species est pars subieciva generis, quia genus predicatur in recto de specie; et hec est differentia inter partem integralem et partem subiectivam, quia de parte subiectiva vere predicatur suum totum in recto, sed de parte integrali non vere predicatur totum in recto, sed in obliquo. Manus enim et caput sunt partes integrales hominis, quia integrant hominem. Et ita hec est falsa: ‘manus est homo’, vel ‘caput est homo’. Text from here.
Sunday, September 19, 2010
Paasch on haecceity
I put J.T. Paasch (Blog: Boring Things - "nothing but fun") on my visiting list some time ago. But then it was not updated for some time and I neglected to visit, and so missed a fine series of posts about Scotus and 'haecceity'. List below.
This is something to return to. I have been struggling with Scotus' account of haecceity for years. The standard place is the six questions in Distinction III of book II of his Ordinatio (Opera omnia, ed. C. Balic and others (Rome, 1950-), vol. 7, p. 458ff). There is a very similar discussion in the earlier questions on the Metaphysics (Quaestiones super libros Metaphysicorum Aristotelis, Libri VI–IX, edited by G. Etzkorn, R. Andrews, G. Gál and others, Opera Philosophica 4 (St. Bonaventure, N.Y.: The Franciscan Institute Press, 1997).
Scotus' argument, as far as I can make it out, is that there exists an identity less than numerical identity (minor unitate numerali). This is the identity of a species, the one of "man is one species, giraffe is another". But a species is essentially repeatable. If you can have one man, you can have another man, another individual of the same species.
But the same is not true of individual identity. We cannot repeat Socrates as we can repeat man. One of Scotus' targets here is the theory of Porphyry, that an individual is defined by a collection of differentia. We start with the most general genus, i.e. being of some kind, then descend to living being, then animal, then rational animal. As we get more specific, the number of features required to define the species increases. Finally we get to the most specific species, namely the individual - descendentibus nobis per divisionem a generalissimus ad specialissima iubet Plato quiescere. Scotus rightly argues against this. Being individualised can't be like being the most highly specified species at the bottom of the tree of being. Being a species is essentially to be divisible into further species. "... the nature of the most specific species is not of itself this, just as something divisible is not from its nature of itself this, so that it is of itself repugnant to it to be divided into parts, because then it could not receive something through which formally such division would belong to it".
It is not clear what Scotus' haecceity is - he practically defines it as what it is not. Paasch is concerned with the question of whether a haecceity really can be unrepeatable. More later.
Thursday, August 26, 2010. "Are Scotus's haecceities really unrepeatable?"
Friday, August 20, 2010 "What makes a haecceity unrepeatable?"
Saturday, August 14, 2010 "What are haecceities?"
Saturday, August 7, 2010 "Scotus: haecceities must be some positive entity"
Friday, July 30, 2010 "Individuation is a question of the formal cause"
Meanwhile, I see that according to his Facebook page, Paasch is working on a PhD in philosophy and theology at Oxford, when he is not working as a bartender, introducing his favorite customers to excellent vintage cocktails he has dug out of old cocktail books. Well then! Mine's an Old Fashioned please.
Since I went on the wagon I'm
certain drink is a major crime,
For when you lay off the liquor
You feel so much slicker -
Well that is, most of the time.
But there are moments sooner or later,
When it's tough, I've got to say, not to say, "Waiter
Make it another old fashioned please".
My favourite drink. More information on Wikipedia.
This is something to return to. I have been struggling with Scotus' account of haecceity for years. The standard place is the six questions in Distinction III of book II of his Ordinatio (Opera omnia, ed. C. Balic and others (Rome, 1950-), vol. 7, p. 458ff). There is a very similar discussion in the earlier questions on the Metaphysics (Quaestiones super libros Metaphysicorum Aristotelis, Libri VI–IX, edited by G. Etzkorn, R. Andrews, G. Gál and others, Opera Philosophica 4 (St. Bonaventure, N.Y.: The Franciscan Institute Press, 1997).
Scotus' argument, as far as I can make it out, is that there exists an identity less than numerical identity (minor unitate numerali). This is the identity of a species, the one of "man is one species, giraffe is another". But a species is essentially repeatable. If you can have one man, you can have another man, another individual of the same species.
But the same is not true of individual identity. We cannot repeat Socrates as we can repeat man. One of Scotus' targets here is the theory of Porphyry, that an individual is defined by a collection of differentia. We start with the most general genus, i.e. being of some kind, then descend to living being, then animal, then rational animal. As we get more specific, the number of features required to define the species increases. Finally we get to the most specific species, namely the individual - descendentibus nobis per divisionem a generalissimus ad specialissima iubet Plato quiescere. Scotus rightly argues against this. Being individualised can't be like being the most highly specified species at the bottom of the tree of being. Being a species is essentially to be divisible into further species. "... the nature of the most specific species is not of itself this, just as something divisible is not from its nature of itself this, so that it is of itself repugnant to it to be divided into parts, because then it could not receive something through which formally such division would belong to it".
It is not clear what Scotus' haecceity is - he practically defines it as what it is not. Paasch is concerned with the question of whether a haecceity really can be unrepeatable. More later.
Thursday, August 26, 2010. "Are Scotus's haecceities really unrepeatable?"
Friday, August 20, 2010 "What makes a haecceity unrepeatable?"
Saturday, August 14, 2010 "What are haecceities?"
Saturday, August 7, 2010 "Scotus: haecceities must be some positive entity"
Friday, July 30, 2010 "Individuation is a question of the formal cause"
Meanwhile, I see that according to his Facebook page, Paasch is working on a PhD in philosophy and theology at Oxford, when he is not working as a bartender, introducing his favorite customers to excellent vintage cocktails he has dug out of old cocktail books. Well then! Mine's an Old Fashioned please.
Since I went on the wagon I'm
certain drink is a major crime,
For when you lay off the liquor
You feel so much slicker -
Well that is, most of the time.
But there are moments sooner or later,
When it's tough, I've got to say, not to say, "Waiter
Make it another old fashioned please".
My favourite drink. More information on Wikipedia.
Tuesday, June 08, 2010
Burley on empty names
I have been reading the early fourteenth century writer Walter Burley. He was working at the same place (Oxford) and the same time (late 1290s) as Scotus, and I wanted to understand how Burley approaches certain questions mentioned by Scotus. In his Questions on the Perihermenias, written in 1301, edited by Stephen Brown (Franciscan Studies 34 (1974) 200-295), question 4, Burley considers the question of whether existence is the same as essence, and in part of that question (4.44) he considers whether propositions like 'Caesar is a man' and 'a man is an animal' are eternally and necessarily true (even if Caesar no longer exists, and even if no man were existing).
He claims that nothing is actually in a real genus, unless it actually exists (nihil est in genere reali actualiter nisi actu exsistat). This (he says) follows from what Aristotle says in Metaphysics 6 at the end, where he divides being into being outside the mind, and a sort of diminished being in the mind, which he excludes from consideration. True being is divided into the ten categories, and so every category of being is true being outside the mind. Thus 'Caesar is a man' is false. He also mentions an argument that Scotus considers in his questions on the Perihermenias, namely Averroes' dictum that in substantial change, a thing loses its name and definition.
He considers the objection (4.54) that every proposition in which genus is predicated of species is necessary, such as 'A man is an animal' and 'a rose is a substance'. He replies that such propositions do not have to be necessary, nor true, unless the species necessarily has being. If 'man exists' is necesary and always true, then 'a man is an animal' is necessary and always true. Otherwise not.
This is opposite to the Scotus' conclusion. Scotus finds that 'Caesar is a man' is true, and he holds that essential propositions (which are sort of our 'analytic propositions') are eternally and necessarily.
Whether the two men met, we do not really know. One source (article "Walter Burley", by Mary Sommers, Blackwell Companion to Philosophy in the Middle Ages) claims that Walter attended Scotus' lectures in 1298, but does not identify her source (beyond the three secondary sources mentioned in the article, I am following these up).
On the question of whether existence and essence are the same, Walter agrees with the opinion of Godfrey of Fontaines (a writer that Scotus was certainly familiar with). Perhaps more about Godfrey later, when I finally track down the elusive De Wulf editions of his work.
He claims that nothing is actually in a real genus, unless it actually exists (nihil est in genere reali actualiter nisi actu exsistat). This (he says) follows from what Aristotle says in Metaphysics 6 at the end, where he divides being into being outside the mind, and a sort of diminished being in the mind, which he excludes from consideration. True being is divided into the ten categories, and so every category of being is true being outside the mind. Thus 'Caesar is a man' is false. He also mentions an argument that Scotus considers in his questions on the Perihermenias, namely Averroes' dictum that in substantial change, a thing loses its name and definition.
He considers the objection (4.54) that every proposition in which genus is predicated of species is necessary, such as 'A man is an animal' and 'a rose is a substance'. He replies that such propositions do not have to be necessary, nor true, unless the species necessarily has being. If 'man exists' is necesary and always true, then 'a man is an animal' is necessary and always true. Otherwise not.
This is opposite to the Scotus' conclusion. Scotus finds that 'Caesar is a man' is true, and he holds that essential propositions (which are sort of our 'analytic propositions') are eternally and necessarily.
Whether the two men met, we do not really know. One source (article "Walter Burley", by Mary Sommers, Blackwell Companion to Philosophy in the Middle Ages) claims that Walter attended Scotus' lectures in 1298, but does not identify her source (beyond the three secondary sources mentioned in the article, I am following these up).
On the question of whether existence and essence are the same, Walter agrees with the opinion of Godfrey of Fontaines (a writer that Scotus was certainly familiar with). Perhaps more about Godfrey later, when I finally track down the elusive De Wulf editions of his work.
Sunday, March 01, 2009
Priscian's Institutiones Grammaticae
Priscian's Institutiones Grammaticae now available (Latin version only) in the Logic Museum annex. I had ignored Priscian before, thinking of him as a grammarian. Which he is, mostly, but there are interesting philosophical and logical insights in this enormous work. Such as that the present time is that of which part is past, part is future (Book 8, p. 414). Scotus uses this to explain how a sentence in the present tense (e.g. "Robert is just passing through the door") may be true even when the event it refers to may just be over.
Praesens tempus est cuius pars praeteriit, parsque futura est
Praesens tempus est cuius pars praeteriit, parsque futura est
Sunday, February 22, 2009
Osmund Lewry
A link here to an article in the new Logic Museum about Osmund Lewry, a Dominican who made some outstanding contributions to the history of logic in England, particularly in Oxford, in the thirteenth century. The article is part of the new Medievalists category which is designed to remedy the poor coverage of scholarly bibliography on the web.
I am trying to find a copy of Lewry's often-cited PhD thesis - "Robert Kilwardby's writings on the logica vetus studied with regard to their teaching and method". There are copies in the Bodleian and in the British Museum but previous experience suggests that this will be a painful and time-consuming process. The academic world still has to come to grips with the Internet and the concept of 'Open Access'.
I shall keep my regular readers amused with the story of my progress.
I am trying to find a copy of Lewry's often-cited PhD thesis - "Robert Kilwardby's writings on the logica vetus studied with regard to their teaching and method". There are copies in the Bodleian and in the British Museum but previous experience suggests that this will be a painful and time-consuming process. The academic world still has to come to grips with the Internet and the concept of 'Open Access'.
I shall keep my regular readers amused with the story of my progress.
Thursday, January 22, 2009
Scotus on future contingency
I mentioned in this post last year that I was working on Scotus' discussion of the problem of future contingents, in his Questions on the Perihermenias, and I said I would discuss it in the future. Alan Rhoda's post on 'alethic openness' has finally got me round to doing so. Alan writes:
I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."
See also my discussion of rain tomorrow.
For a proposition to be true, what it represents as being the case mustScotus discusses a claim very similar to this in Book I of the Questions, qq 7-9. He disputes the claim apparently made by Rhoda above, namely that the truth of a proposition about the future must correspond in some way to 'present reality'. He writes:
correspond to reality, to what is the case. Likewise, for a proposition to be
true now, what it represents as being the case must correspond to present
reality, to what is the case now. [my emphasis]
It must be understood that a proposition about the future can be understood toIt rather hangs upon what Rhoda means by 'true now'. Scotus argues for something like a redundancy theory of future truth. A proposition that says that S will be P so is (now) true iff it will be P, and false if it will not be P. If you mean by 'is now true' something like 'something exists now in reality that makes the proposition true' then Scotus would disagree (and so probably would I). If you mean that 'now' simply indicates the present tense of the 'is' in 'is true', then this is harmless and trivially true.
signify something in the future in two ways. So that the proposition about the
future signifies it to be true now that something in the future will have to be
true [verum esse habebit] (for example, that ‘you will be white at a’ signifies
it now to be in reality so that at time a you will be white). Or it can be
understood that it signifies now that you will be white then: not that it
signifies that it is now such that then you ought to be white, but that it
signifies now that then you will be white. For to signify it to be [the case]
now that you will be white at a, signifies more than to signify that you will be
white at a.
I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."
See also my discussion of rain tomorrow.
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