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.

Avicennian logic?

I only just discovered this. It is a Wikipedia 'Request for Comment' or RfC, which is rather like a court where Wikipedia editors pile on to each other, attack and eat their own. This one is quite extraordinary and concerns an editor 'Jagged 85' who has been systematically falsifying material in Wikipedia since he (or she) joined in 2005. The editor had a clear and consistent anti-Western agenda, systematically distorting source material in a way that untruthfully promoted Islamic (and also other non-Western) intellectual achievements, usually by claiming that a scientific developments or invention or discovery was made or anticipated by some non-Western philosopher or scientist.

It highlights a clear set of issues, as follows.

1. There is a large amount of material affected in Wikipedia, which is widely used as a reference work by millions of people, who trust it as a reliable source. The editor contributed to 8,115 pages, making 63,298 edits. Much of the problem material seems still to be there.

2. It demonstrates the role of Wikipedia in disseminating misleading and blatantly incorrect information across the web. The editor began work five years ago in December 2005, hist first edit claiming that "The Indus Valley civilization is in fact recognized as having been the first to develop urban planning. " Because many of his edits are now established, they have been reproduced and cited all over the internet. For example: Google 'Avicennian logic' (including the quotes) and it returns 6,000 sites (the top one being the Wikipedia article on 'Avicennism', where the phrase originates). Yet I am sure there is no formal system of logic known to scholars as 'Avicennian logic'. Avicenna made interesting contributions to logic, certainly, mostly in propositional logic, although this was originally developed by the ancient Greeks. But so did dozens of other middle-Eastern and Western writers, and the innovations of Avicenna do not compare in scale or impact with those of the high middle ages such as supposition theory, 'consequences' and so on. The article on 'Avicennism' says that "Avicennian logic had an influence on early medieval European logicians such as Albertus Magnus". Yet the idea that most influenced these scholars, including Albert, was Avicenna's distinction between essence and existence, which was a genuine innovation, and a departure from Aristotle. This idea had a profound impact, in different ways on Aquinas, Giles of Rome, Henry of Ghent, Scotus and eventually Ockham. But it is a metaphysical idea, not a logical one. As far as I am aware, no medieval writer discusses Avicenna's logic (as opposed to his commentary on the Metaphysics, which they frequently cite). Kneale's great work The Development of Logic mentions Avicenna twice, neither in connection with logic. Bochenski does not mention him at all. None of the articles in the main secondary sources on medieval philosophy mention Avicenna's logic (although they discuss his other achievements at length).

3. It proves a clear weakness in the Wikipedia 'verifiability principle'. The editor always provided reliable sources for their claims. However, examination revealed either blatant misrepresentation of the source, or a selective interpretation that went far beyond the author's meaning. For a long time no editors bothered to check these. The problem was amplified by his frequent use of scholarly works not available on the internet. Most of Wikipedia's editors are amateurs who have no access to a university library. Thus they cannot check a source from a journal, or an old or obscure book that would only be found in a library. Typical of his technique is this edit where he claims that "Avicenna developed an early theory of impetus, which he referred to as being proportional to weight times velocity, which was similar to the modern theory of momentum" citing Aydin Sayili (1987). "Ibn Sīnā and Buridan on the Motion of the Projectile", Annals of the New York Academy of Sciences 500. Yet the source attributes the theory to the fourteenth century French philosopher Buridan, not Avicenna. People trust Wikipedia because they believe the system of 'anyone can edit' allows for cross-checking and verification of references by a large group of users. Clearly, they should get out of this habit.

Thought is quick

"Enthymeme" is a form of argument where one or more of the assumptions is so obvious that it need not be stated. Suppose at a party my wife says "It's past eleven". I know what she means, which can be expressed by the following syllogism.

(Major) If it is past eleven and we are out, then leave now!
(Minor) It is past eleven and we are out
(Conclusion) Leave now!

She does not need to state the major premiss, nor even the conclusion, but I catch her drift. Note both the major and the conclusion contain an imperative. Arthur Prior investigated the logic of arguments containing imperatives in his paper "On Some Proofs of the Existence of God" , published in Papers in Logic and Ethics, Duckworth 1976.

Note also that the minor premiss is an assertion, and must be understood as such for the argument to be valid. If by contrast it meant something like "Would you like another large gin and tonic?" her conclusion would not follow. The point being, "linguistic meaning" is king. If it were not for the meaning we assign to expression types, we would not be able to express ourselves in ways like this, that superficially suggest that meaning constantly fluctuates, and that some expressions have no linguistic meaning.

Thomas Hobbes gives an entertaining example in Leviathan Chapter III (my emphasis).

"For in a discourse of our present civil war, what could seem more impertinent than to ask, as one did, what was the value of a Roman penny. Yet the coherence to me was manifest enough. For the thought of the war introduced the thought of the delivering up the king to his enemies; the thought of that brought in the thought of the delivering up of Christ; and that again the thought of the thirty pence, which was the price of that treason; and thence easily followed that malicious question; and all this in a moment of time—for thought is quick."

The Value of Lawyers

"Great as are the evils which society still owes to lawyers, the lawyer-class has always been a civilizing agency".

Hastings Rashdall, The Universities of Europe in the Middle Ages, Oxford 1895, Vol II Part II, p. 708.

The Prosentential Theory of Truth

In a comment to Vallicella here I mentioned an article on the pro-sentential theory in the Internet Encyclopedia of Philosophy, and said that the theory has 'some affinity' with the 'assertoric' theory of truth I have sketched out here (as well as fiercely defended at Vallicella's place.

Here, I will take some of the claims made for the prosentential theory in that article and compare them with the corresponding claims of the assertoric theory, to see how close the affinity is.

The Assertoric Theory
The assertoric theory of truth is that the copula 'is' of a simple declarative subject-predicate sentence, such as

Tom is running

contains two components. One is the copula, whose function is to join subject and predicate to form the 'content' of the sentence. The content we can signify by a noun phrase such as 'that Tom is running' or the verbal noun 'Tom's running'. The other is the assertoric component, whose function is to signal assertion, i.e. to signal that the person uttering the sentence is saying something capable of being true or false. We can make the internal structure of such a declarative sentence transparent by parsing it as follows:

It is true / that Tom is running

The Prosentential Theory compared to the Assertoric Theory
1. "According to the prosentential theory of truth, whenever a referring expression (for example, a definite description or a quote-name) is joined to the truth predicate, the resulting statement contains no more content than the sentence(s) picked out by the referring expression."

Although the theories are similar, the fundamental difference is that, according to the assertoric theory, the 'truth predicate' (actually the truth operator) operates on a noun phrase signifying the content of the sentence, not the sentence.

2. "The central claim of the prosentential theory is that ‘x is true’ functions as a prosentence-forming operator rather than a property-ascribing locution."

The central claim of the assertoric theory is that 'x is true' functions as an operator on a 'that'-clause that forms a normal sentence (not a 'prosentence'). It claims also that this operator is implicit, though not lexically visible, in a sentence that does not use the words 'is true'.

3. "According to the prosentential theory, the statement ‘p is true’ says no more than the statement ‘p,’

The corresponding claim in the assertion theory is that 'it is true that p' says no more than that p. I.e. 'It is true that Tom runs' says that Tom runs. However, the theory distinguishes between the operator 'it is true that', which operates on a sentence to produce another sentence (of equivalent meaning), the operator 'that' which operates on sentences to produce a noun phrase, and the operator 'it is true' which operates on 'that' clauses to form sentences. This is a crucial feature of the theory which is necessary to prevent the 'substitution problem'. If we substitute the noun phrase 'that Tom runs' for 'p' in 3 above, we get the nonsensical

(*) The statement 'that Tom runs is true' says no more than the statement 'that Tom runs'

which is nonsensical because 'that Tom runs' is not a statement, but a noun phrase. If by contrast we substitute the sentence 'Tom runs', we get

(**) The statement 'Tom runs is true' says no more than the statement 'Tom runs'

which is nonsensical because 'Tom runs is true' is not a well-formed sentence (it would be well-formed if we read it as 'that Tom runs is true', i.e. read the sentence as a that-clause, but then we are not substituting the same thing salva significatione. (To be fair, the IEP article does note the problem of substitution, but does not sufficiently explain how the prosentential theory overcomes it).

4. " The prosentential theory of truth counts as a ‘deflationary’ theory because it denies that any analysis of truth of the form "(x)(x is true iff x is F)" can be given, where ‘x is F’ expresses a property that is conceptually or explanatorily more fundamental than ‘x is true.’ "

The assertoric theory is also a deflationary theory on this criterion. According to the assertoric theory, 'is true' operates on a noun phrase (a that-clause) to form a sentence. This operator is present, explicitly or implicitly, in the main verb of every declarative sentence. It is fundamental to the semantics of the declarative sentence, and no more fundamental explanation is available.

5. "The prosentential theory of truth implies a solution to the liar paradox. Consider the following sentence.- This sentence is false - if it says something true, it is false ... if it says something false ... it is true. [... ] Some attempts to solve the liar paradox involve extreme measures. Tarski, for example, thought that the paradox could be avoided only by eschewing ‘semantically closed languages’ [...] Tarski succeeds in avoiding the basic form of the liar paradox—but only at a very high price. He must content himself with providing an account of ‘true-in-Li’ rather than an account of truth. And, since natural languages like English are semantically closed, Tarski’s theory also has the weakness of applying only to artificial languages. ... According to the prosentential theory, (43) is neither true nor false because it fails to pick up an anaphoric antecedent. Just as I cannot inherit my own wealth, a prosentence cannot inherit its content from itself. "

The assertoric theory solves the Paradox in essentially the same way. 'is true' is fundamentally an operator, not a predicate. When attached to a 'that'-clause, it does not predicate anything or attribute anything to anything named by the clause. It merely signals that the speaker is asserting the content signified by the clause. In the case of the Liar sentence, there is no content to be asserted. According to the assertoric theory, we must analyse every declarative sentence into a content-part, and an assertoric part. Thus the Liar sentence must be analysed as

What this sentence says is false.

where the content part is signified by 'What this sentence says', and the assertoric part to the denial 'is false'. But the sentence says nothing, because the attempt to locate a referent for it fails.

Deflationary theories of Truth

A common objection to deflationary theories of truth is sentences like 'Everything Tom says is true'. Analysing this as

(A) For all p, if he asserts p, then p.

results in incoherence when we attempt to substitute. If we substitute sentences like 'snow is white', we get

(B) If he asserts 'snow is white', then 'snow is white'.

which is nonsense. If we substitute propositional content, signified by a 'that' clause, we get

(C) If he asserts that snow is white, then that snow is white.

which is also nonsense. However, we can evade this difficulty along the lines I have suggested in earlier posts. The first insight is that 'it is true that' is a complex operator built from 'it is true', which operates on 'that' clauses to form declarative sentences, and 'that' which operates on sentences to form 'that' clauses. Then it is coherent to hold that the semantics of any declarative sentence can be represented formally as

(D) |- c

where the operator |- corresponds to the 'it is true' part, and 'c' to a that-clause. I.e. we parse 'it is true that Tom runs' as 'it is true / that Tom runs'. Then the problem sentence 'He is always right' can be analysed as

(E) If he says c, |- c

Suppose for example that he says that Tom runs. then c = that Tom runs (note I substitute a 'that' clause, not a sentence), and |- = 'it is true', as above. This yields

(F) If he says that Tom runs, it is true that Tom runs = if he says that Tom runs, Tom runs

which makes perfect sense.

Why truth is not a predicate

As I have argued below and elsewhere, the copula 'is', as in

(1) Tom is running

has a twofold function. The first is to join subject and predicate together into a single content that is expressible by the sentence. For example 'Tom's running' or 'that Tom runs'. The second - and this is something only a verb can do - is actually to express this content. Thus

(2) Tom's running is the case

or 'That Tom runs is a fact' or 'it is true that Tom runs'. Now as it happens the operator 'it is true' which we attach to the that-clause 'that Tom runs' or 'is the case' which we attach to 'Tom's running' also contains the verb 'is'. But this, I argue, is a grammatical accident. The 'is' in 'is the case' is mere filling. The operator 'is the case' is a unitary element of the sentence. It would be better expressed by a single verb 'isthecase' or 'itistrue'. If it is essentially complex, then of course it contains the verb 'is', and if it functions as a copula, then it will have the twofold function described above. 'the case' would be a predicate that we could attach to the subject 'Tom's running' to form the noun-phrase 'Tom's running being the case'. And we could further assert this to form a new sentence 'Tom's running being the case is the case' and so on ad infinitum.

This is obvious with 'is the case'. We are not tempted into supposing that 'the case' is a predicate that qualifies Tom's running in any way. It is less obvious with 'it is true'. It is more tempting to suppose that the noun-phrase 'that Tom is running' refers to some content, a thing, and that in forming 'that Tom is running is true' we are predicating 'truth' of this content. Bad things lie in that direction.

See also Maverick Philosopher for a different take on why truth is not a predicate

Semantic cancellation

The dispute about assertion continues at William Vallicella's house here. To recap. I hold that every declarative sentence contains an 'assertoric component'. This is part of the semantics of the sentence. Vallicella objects that one token of the same sentence-type may be used to make an assertion, another not. "Therefore, there cannot be an assertoric component in indicative sentence types ... whether there is anything assertoric about a token depends on how it is used in a concrete situation."

My reply to this is that the phenomena Vallicella has in mind can easily be explained by the possibility of 'semantic cancellation' i.e. the use of a sign added to an expression to cancel out part of the semantics of the expression. If we agree that semantics is compositional, and if we agree that verbal composition does not always reflect semantic composition (as in 'Tom runs' = 'Tom is running'), then we allow for the possibility of 'semantic cancellation'.

If we allow for semantic cancellation, we automatically allow that one token may have a different semantics from another of the same type, because of the presence of semantic cancellation in the latter case. For example, in

(A) Tom runs
(B) Sarah believes that Tom runs.

(B) has a different semantics from (A). (A) is true iff Tom runs. But (B) can be true or false whether or not Tom runs. But this is not an argument against the existence of an assertoric component which relates 'Tom' and 'runs'. Semantic cancellation explains this. The operator 'that' cancels out the assertoric component in (A), and converts its semantics into that of a noun-phrase. This phrase is object to 'Sarah believes', where the assertoric component is now located inside the main verb 'believes'. We can further cancel this out by adding another 'that' operator to create another that-clause, as in:

(C) that Sarah believes that Tom runs.

and so on. Note that semantic cancellation can be non-verbal. If I utter 'Tom runs' together with a nod and a wink (meaning that Tom is a lazy fellow who takes no exercise at all), the nod and wink is a cancellation operator on the verbal part of the assertion. I.e. the utterance of the sentence accompanied by the nod and wink is equivalent to

It is not the case that / Tom runs

where 'Tom runs' is the verbal component, and 'It is not the case that' corresponds to the non-verbal nod or wink. Ironic or arch modes of expression can also be used to the same effect ('Tom runs - oh yeah right').

In summary. Vallicella's argument against an 'assertoric component' is that a token of the same sentence-type may be used without making an assertion. My reply to his argument is that this is because of semantic cancellation, which removes the assertoric component. The fact that this componet is removed in the one case, does not prove that it did not exist in the other.

The ultimate goal of this is a nominalistic theory of truth which is a version of the redundancy theory of truth. i.e. a theory which denies the existence of both truthbearers and truthmakers. There is something else at stake also, nothing to do with truthbearing and truthmaking. Vallicella's type-token argument is a general argument against 'semantic determinism'. Semantic determinism is the thesis that the same tokens of a type-identical set of signs will always have the same meaning. If this were not true, it would destroy the possibility of communication. Given that we cannot bring things that are not directly known to speaker and hearer (such as other people's thoughts, or things that are not perceptible to us) into the discussion, we have to use words as symbols of things - nominibus utimur pro rebus notis, quia non possumus nobiscum ferre res ad disputandum. If different tokens of these symbols (or rather sets of symbols) did not have a fixed and constant meaning, how could we communicate at all?

Now I agree that a subset of the symbols we use can change their meaning depending on context. But when we include the whole context, and if we regard the context itself as part of the symbol-set, then I claim that the semantics is deterministic. For example, when I use the word 'this', pointing to an animal, then 'this is a tree' is false. When I point to a tree, the same sentence (i.e. a different token of the type 'this is a tree') is true. So it may appear that the semantics of 'this is a tree' is indeterminate. But if we include the act of pointing, i.e. the gesture, and the tree-appearance, as all included in the symbol-set, then the semantics is determinate. Any token of 'this is a tree' accompanied by the act of pointing, and a representation of the demonstrated object, will have the same meaning (and the sentence will be true when the representation is in fact of a tree, false otherwise).

So, quite a lot is at stake.

The Truth Operator

A modified version of my comment on Maverick Philosopher, about the distinction between truth as a predicate, which as Bill argues seems to commit us to realism about truthmakers, and truth as an operator, which does not appear to lead to such a commitment.

I subscribe to an 'operator' theory of truth. Each sentence has a syncategoric semantic component which corresponds to assertion. This component is always locked inside the main verb of the sentence. The operator 'that', which forms a that-clause from the sentence, strips out this assertoric component to convert the sentence into a categorematic expression signifying a possible object of thought, belief, assert, judgment etc. The operator 'it is true' replaces the assertoric component again to give us back the sentence (although the main verb is now the 'is' of 'it is true' rather than the verb of the operated-on sentence).

Thus the expression 'it is true that' is a sentence-operator that contains two operators, namely 'is true' and 'that'. The operator 'that' operates on sentences to produce a that-clause:a noun-phrase that names a content, a possible object of belief and judgment. It does this by removing the assertoric element from the sentence. The operator 'it is true' operates upon that-clauses, to form whole sentences. Such sentences have the same truth-conditions as the original sentence. Thus:

(1) Snow falls

is a sentence that asserts something, via the assertoric component embedded in the main verb 'falls'.

(2) that snow falls

is a that-clause naming a possible object of judgment or belief, such as in the sentence 'John believes that snow falls', which we parse as 'John / believes / that snow falls' to clarify its relational form 'X believes Y'. Note that in the belief sentence the verb 'falls' is no longer the main verb. The truth or falsity of 'John believes / that snow falls' no longer depends on whether snow does fall or not. Rather it depends on whether John believes this or not. Finally

(3) It is true that snow falls

Gets us back to a sentence with the same truth-conditions as (1), but with a different semantics. The main verb is now the 'is' of 'it is true', and the verb 'falls' is a subordinate verb. The assertoric component of (3) lies in the 'is' of 'it is true', the assertoric component of (1) lies in 'falls'. We can parse (3) as 'It is true / that / snow falls' to make it clear that there are two operators rather than one (Frege's mistake was to think there is only one). Or we can parse it as 'It is true that / snow falls' to make it clear that the combination of 'it is true' and 'that' gives us a further operator.

This may remove the temptation to suppose that there are such things as 'truthmakers'. (Well it won't, I imagine the supporters of truthmaking will continue in the deep error of their ways, but that is the way). The operator approach is of course consistent with a thoroughgoing nominalist program. I wonder whether, if ordinary language had the right synactic structure so that operators and existence-verbs and the like were clearly identified, the users of that language would be so committed to realist semantics. Could we even 'do' metaphysics in such a language?

The meaning of Meinong

Bill Vallicella has an interesting defence of Meinong here. The statement

(1) There are items that have no being

is clearly self-contradictory. This is the reading attributed to Meinong by analytic philosophers (boo!) reading Meinong. But perhaps Meining meant this

(2) Some items have no being.

which (Bill argues) is not self-contradictory.

This argument entirely depends on the meaning of the word ‘being’. Bill’s claim that (1) is self-contradictory suggests he is reading it as expressing what ‘there are’ expresses. I.e. he would regard ‘there are blue buttercups’ as semantically equivalent to ‘blue buttercups have being’. Call this the ‘being/there are’ equivalence thesis. By contrast, his claim that (2) is not self-contradictory suggests he is reading ‘some’ statements as not expressing being. I.e. he would regard ‘some buttercups are blue’ as different both from ‘blue buttercups have being’ and ‘there are blue buttercups’. Call this the ‘some/there are’ non-equivalence thesis.

But what if I say

(3) There are no items that do not have being ?

Am I contradicting one who claims that some items have no being? Apparently not, for if according to Bill we are to read statements beginning ‘there are’ as expressive of ‘being’, then (3) does not deny (2) at all, indeed is perfectly consistent with it. I show this as follows. The statement

(4) ‘There are no X’s that are Y’ is equivalent to ‘any X that is Y does not have being’

follows from Bill's ‘being/there are’ equivalence implied above. I then substitute (4) into (3) to give

(5) Any item that does not have being, does not have being

Thus the statement that there are no items that fail to have being is apparently consistent with the statement that some items fail to have being. But that hardly seems correct. The natural reading of (3) is as the denial of (2), and hence its contradictoru. If one is true, the other is false.

Bill’s error (as I see it) is in denying the equivalence of ‘some’ and ‘there are’ statement. Is there really any logical difference between ‘there are blue buttercups’ and ‘some buttercups are blue’? Or between ‘there is a bridge crossing the river between Barnes and Hammersmith’ and ‘a bridge crosses the river between Barnes and Hammersmith’? I doubt it. But if we uphold ‘some/there are’ equivalence, and we uphold the ‘being/there are’ equivalence, we are led into contradiction again: if (1) is self-contradictory, (2) is.

Alternatively we could deny the ‘being/there are’ equivalence. But then we have the difficulty of what ‘being’ statements mean. We have no difficulty understanding ‘there are’ statements. You know what I mean when I say ‘there is a bridge crossing the river between Barnes and Hammersmith’. If you are stuck in Barnes and want to get to Chiswick via Hammersmith, it is very helpful to learn that statement is true, and you can act upon it accordingly. But ‘a bridge crossing the river between Barnes and Hammersmith has being’ is obscure, and not one a motorist can readily deal with. He either interprets it as meaning *there is* a bridge crossing the river. But that is no different from ‘some bridge crosses the river’ or ‘at least one bridge crosses the river’, and it follows a simili that (2) is self-contradictory. Or he regards it as altogether mysterious, and it follows that Meinong’s claim is mysterious and obscure. That is the dilemma.

The Theory of Descriptions according to Wikipedia

So Peter Smith couldn't help correcting Wikipedia's entry about the Theory of Descriptions here. I am not sure if his point is entirely fair. (Certainly there are far worse things on Wikipedia philosophy and logic he could have tried to fix, e.g. this abomination).

It depends on what problem the Theory of Descriptions is intended to fix. The medieval Latin philosophers faced a similar problem and they arrived at a substantially similar solution to Russell, but they didn't have a distinction between 'a' and 'the' (which is the focal point of Peter's correction). So logicians such as Ockham were no wiser than Wikipedians?

The problem that Ockham (and the early Scotus, Robert Kilwardby and many others) were trying to fix was that 'Chimera is white' and 'Chimera is not white' are both false. But Aristotle says that de quolibet dicitur affirmatio vel negatio vera - either the affirmation of any sentence is true, or its negation is. Ockham argues that the second sentence is not really a negation of the first, for it can be unpacked as 'Chimera is something and it is not white'. The real negation, by contrast, is 'Chimera is not something or it is not white'. (Ockham like the other medievals was not worried here about uniqueness claims).
If the problem to be solved is not a 'non denoting description' but rather the one outlined above, namely that '[the] present King of France is bald' '[the] present King of France is not bald' are both false, then the original Wikipedia entry is not off the rails entirely.

Or perhaps he is objecting to something else, namely that unpacking 'chimera is white' into 'chimera is something-white' leads to an infinite regress. The medievals discussed this problem too. They saw that if 'Caesar est homo' = 'Caesar est ens homo', i.e. 'est' always unpacks into 'est ens', then this leads to an infinite regress, 'Caesar est ens homo' = 'Caesar est ens ens homo' and so on. Nicholas of Paris, Robert Bacon (not to be confused with Roger) discussed this in the early 13th century. But that is something else.

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

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.

Andrew of Cornwall

A link to my article about Andrew of Cornwall here in an attempt to discover why Google seems consistently to favour Wikipedia. I created a smaller version of the same article in Wikipedia (which I will not link to for obvious reasons), but Google sadly ignores it.

Snow in London

Alan Rhoda has been defending the idea that there must be some necessary connection between the present and the future in order for propositions about the future to be true or false. I restate his argument as follows. A true proposition depends on what exists - a 'state of affairs' - for its being true. The state of affairs that makes the proposition true at some particular time must exist also at the same time. Accordingly, it cannot be true now that there will be snow in London tomorrow, unless this truth 'supervenes upon present reality', i.e. there is some existing state of affairs which makes this proposition about the future true. Which is absurd. Why should snowing in London tomorrow be logically connected with any state of affairs existing today?

The mistake lies in his assumption that what makes a proposition true at some time must exist at that same time. Certainly there is a connection between truth and existence. This was recognised by the scholastic philosophers of language. Unumquodque sicut habet esse, ita et veritatem "As each thing is in respect of being, so it is in respect of truth", taken from Aristotle Metaphysics book 2 (993b 31). A proposition signifying that some state of affairs exists, is true or false depending on whether that state of affairs exists or not.

A corollary of this is what I shall call the Adequacy Principle: that the state of affairs signified to exist by the proposition can be no more (and no less) than what makes the proposition true. Otherwise, suppose a proposition signifies the existence of more than what is required to make it true, e.g. suppose that it signifies the existence of X and Y, but Y alone is sufficient to make it true. Then so long as Y exists, the proposition will be true, even if X does not exist, and even though the proposition signifies that X does exist. This is impossible, therefore a proposition can signify the existence of absolutely no more than what is sufficient to make it true. (A similar argument proves that a proposition can signify the existence of no less than what is necessary to make it true, but that is not relevant here).

From the Adequacy Principle it follows that a proposition in the future tense, signifying that some state of affairs Y will exist, depends for its truth on the future existence of Y, and nothing else, particularly nothing else in the present. The proposition 'It will snow in London' can be analysed as

* Snowing in London will be the case

which signifies that the future state of affairs 'snowing in London' will exist. It signifies no more than that, in particular, it does not signify that some state of affairs X exists now. Why should it? It may be that some present state of affairs (large cold front sweeping in from Siberia) will be the cause of the snow. But the proposition in the future tense has nothing to say about cold fronts.

Ayn Rand: lost in translation

The strange arguments continue in my comments box below and I continue to be mystified. One of the 'objectivists' there claimed that

1. If the premises [of an argument] are known to be false, are arbitrary, or from revelation, then even if the logic is valid, the proof [i.e. the conclusion] is indeed not a claim about reality.

To which I immediately objected

2. God can reveal to me the truth of a mathematical theorem, which is a claim about reality, therefore (1) is false.

This is a standard form of argument used in philosophy. Someone claims 'if p then q'. If you are able to give an example of 'p and not-q' that is obviously true, then you have refuted them. Since (1) is equivalent to the claim that no conclusion revealed by God is about reality, it is clearly refuted by (2).

This argument (which as I say is a standard type of argument you learn early on when you study philosophy) drew a number of objections. The first was

3. If you can suddenly prove a mathematical theorem, which can be validated to all fair rationals in the world, you are within your rights to say you got it from God if you wish.

This is not an objection to my argument. I am arguing that (1) above is false, because according to (1), it is impossible for the premisses of an argument to be true, and for the conclusion to be about reality, i.e. for the conclusion to be true. But the example (2) clearly demonstrates that it is possible for true premisses to be derived from revelation. It might be questioned whether I knew the conclusion to be true, because I was relying on revelation and not mathematical understanding. But a true proposition is unquestionably true, whether I know it or not. The next objection was

4. Your (hypothetical) revelation from God is no demonstration of its truth. If the content of the revelation, once examined in real world terms, is found to be true, then logic prevails from the latter reasoning, not from the former.

The argument here is that because the conclusion is not demonstrably true (because its truth is revealed), therefore it is not true. This is false again, and seems to rest on a confusion between truth and demonstrable truth. If a proposition is true, it is true, even if it is not demonstrably true. The next objection was

5. Even if metaphysically factual, the mathematical revelation is not epistemically true.

I don't understand what are meant by 'metaphysically factual' or 'epistemically true'. The latter probably means 'is not known to be true'. To be sure: if God reveals a true proposition to me, without my understanding why it is true, I probably cannot be said to know it. But that does not show it is not true.

When I suggested that 'objectivists' tend to make claims about truth and logic and metaphysics as though they were experts on the subject, which turn out to be nonsensical or silly, or ill-thought out, it was objected that this is because non-objectivists use concepts 'loosely'. This contradicts my impression that objectivists (or at least the ones here) use concepts loosely. It seems to me that they confuse the notions of truth and validity, of truth and knowledge of truth, of proofs and statements. These are all concepts used by logicians and which have a clear meaning that is carefully taught in elementary logic classes. I put it to the objectivists that it is not logicians who 'use concepts loosely'.

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:

For a proposition to be true, what it represents as being the case must
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]

Scotus 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:

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 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.

It 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.

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.

The supporters of Ayn Rand

I was going to follow up the previous post on Rand with a few comments but Triablogue beat me to it. There are also some excellent comments on the post made by Dominic Tennant in the course of a running argument with someone called John Donohue. Tennant leaves me with very little to say on Rand's 'existence exists' axiom. But fortunately it leads me to another thought that had been in the back of my mind, about supporters of Rand. I judge the worth of a writer by reading them. But also instructive to read what their supporters say. Supporters of Rand, in my experience, tend to be shrill, and philosophically and logically illiterate. Perhaps that tells us something about Rand?

Tennant points out the 'Existence exists' is incoherent - existence is commonly regarded as a second-order property. Not by everyone, I should point out, but certainly Frege's view that existence is a second-order predicate is accepted by nearly all those in mainstream analytic philosophy. Nor is Donohue's restatement, "whatever exists exists" in any way useful, because it is either merely tautological and doesn't tell us anything, or it is equally incoherent (for it dubiously assumes that existence is a first-order predicate).

Donohue objects "All truth discovered by Objectivism is through induction, and all induction is consistent with the constraint that all existents named/claimed in the induction must actually exist in objective reality". Tennant immediately objects that if the entire worldview is inductively inferred, there is no certainty in it, for induction is an informal fallacy. Donohue objects that induction is not a fallacy, and that its goal is to deploy reason with greater and greater precision until a given proposition/claim achieves a position of "true" and "certain" within the context of human knowledge. Tennant objects that he cannot be serious. Induction is an informal fallacy—it is a kind of logically invalid inference which may nonetheless yield true results. "In logic, a type of nonvalid inference or argument in which the premises provide some reason for believing that the conclusion is true. Typical forms of inductive argument include reasoning from a part to a whole, from the particular to the general, and from a sample to an entire population. Induction is traditionally contrasted with deduction. Many of the problems of inductive logic, including what is known as the problem of induction, have been treated in studies of the methodology of the natural sciences. (Britannica Concise Encyclopedia, 'induction'.)"

As Tennant correctly points out, what Donohue is describing here —"greater and greater precision"—is characterized by deduction. Induction works in the opposite direction: from greater precision and certainty towards less and less of the same. How can Donohue not be familiar with the problem of induction? How can he not be aware that absolute certainty is not guaranteed by merely inductive inference? Perhaps this is because Donohue has only read Rand, which does seem consistent with his ignorance of basic logical concepts. "Next time, take a Logic 101 course and read some introductory philosophy before you head out into the real world and try to pontificate on a blog published by people who have a clue and can call your bluff."

All very true, and remember that Donohue is one of the more articulate supporters of Rand. This began with problems at the Wikipedia article on Rand. Rand supporters turn up in large numbers to make sure that any 'objective' assessment of Rand's work is impossible, and they wear out the more logically-minded editors with this endless logically illiterate ranting. There is nothing in Wikipedia's policies that prevents this happening. Everything on Wikipedia is done by 'consensus', even if that is a consensus of idiots. This would not have mattered in the days when Wikipedia was a tiny website run by a dedicated band of enthusiasts. Now it really is used by everyone on the planet. If only it really were the sum of all human knowledge. Governments are now forcibly taking over banks. Why can't they forcibly take over Wikipedia?

Ayn Rand and Wikipedia

Was Ayn Rand a philosopher? That is the question now being taken to the important mediation committee of Wikipedia. There is currently a disagreement about whether the article about her should qualify her as a 'popular' or 'commercially successful' philosopher, or an 'amateur philosopher' (as Anthony Quinton did in his article on popular philosophy in the Oxford Companion to philosophy), or whether she is a philosopher without qualification.

This involves many difficulties, the main one being that Wikipedia has no concept of 'expert opinion'. We simply cannot ask Anthony Quinton or Ted Honderich or any of the philosophical establishment to weigh in on this important question. The question must be settled by whoever of the anonymous and mostly unqualified editors who turn up at the article talk page to thrash out a consensus. Which is not as bad as it sounds. Wikipedia has strict rules about 'reliable sources' and an entire manual devoted to citation. The rules are orientated towards mainstream academic consensus, and against 'original research' and using duff sources. This means you should use primary sources, however good, to support a claim. You should avoid using a blog or other self-published sources. Reliable and authoritative secondary sources are the preferred method of citation. Thus articles like Wittgenstein can be pretty good. The prose is often awkward and amateurish, and you have to put up the usual slavish political correctness of Wikipedia. But the results are not nearly as bad as you might have expected.

The difficulty is to assess writers like Rand, who have been so marginalised by the academic establishment that it is hard to find any reliable sources dealing with her, or her work. Who was Rand? That is the first question that non-American readers are likely to ask. I had not read any of her work until last week, and had only heard of her through Quinton's passing reference in the Oxford Companion. Well, read the article linked to above, which gives you a flavour of her work. There is a helpful lexicon on a pro-Rand website here, which contains samples of her writing. Otherwise there a few reliable sources which give a critical assessment of her work. Try these posts by the philosopher William Vallicella, who has a good explanation here of how Rand fails to understand Kant, and here where he points out some elementary - really elementary - logical errors in her work.

My view, based on a cursory reading of her actual writing, was that she lacked even a basic understanding of the essentials of the subject. I was particularly intrigued by her views on existence. But that is a personal view which, despite my qualifications, counts for nothing in Wikipedia. More about this later.

Meanwhile, let the excellent Brandon have the last word. He shows well how it is possible to combine sympathy with frankness (something the Wikipedia article should aim at, in my view). "Is she a bit of a hack when it comes to philosophy? Definitely. But I think what we see in Rand is someone of considerable native talent and ability whose reason never underwent the sort of discipline that would have made that talent genuinely shine."

Commentaries on the Perihermenias

A new set of pages in the Logic Museum (index here) consisting of Boethius' translation (from Greek to Latin) of Aristotle's 'On Interpretation', and three commentaries on them: Boethius' own, Abelard's and Aquinas'. The commentaries are both excellent introductions in their own right to Aristotle's work, and a useful insight into the medieval conception of logic.

Endorsement

Wow, great page [Logic Museum]. I'm a philosophy student and have had a long and abiding interest in the medieval period and especially in the history of logic. As you say this history is severely misrepresented to the average student which I gradually became aware of as an undergraduate by reading outside class from various medieval histories and journals on the era. Thanks so much for your site.

David

[Any time - Ocham]

Azzouni and equivocation

There is a very fine argument in Ockham's Summa Logicae book II, chapter 4. He is objecting to the claim that the verb 'to be' is ambiguous in certain arguments. But this is completely irrational, he says " for it amounts to destroying every argument form. For whenever it pleases me, I will say that 'to be' is equivocal in the premisses, and I will ascribe at will a fallacy of equivocation to every syllogism".

Absolutely right. The verb 'is' is implicit in every proposition. If this verb is ambiguous, we can disprove any argument whatever at will, by appealing to this ambiguity or equivocation. But that is irrational, and amounts to destroying all logic. For logic is about the form of arguments, and not about what we can 'ascribe at will'. If we can challenge the validity of any argument 'at will', you destroy all logic.

This claim that Ockham objects to is precisely the claim that Jody Azzouni appears to be making when he argues against the 'triviality thesis', which is the thesis that the existential quantifier just means 'there is', and 'there is' just carries ontological commitment. Azzouni argues that the triviality thesis is wrong since there are assertions of the form 'there are Fs' that do not always carry ontological commitment.

If Azzouni is correct, it really does amount to destroying all logic. I have already argued this in my objection to William Craig's claim that there is no contradiction in 'some x's are numbers and no numbers are created' and 'all x's are created by God', by reason of equivocation on the existential quantifier. If an argument as basic as this is invalid, all argument is invalid.

Here are two more arguments for this.

1. Meinongians say there are fictional entities. Nominalists say 'there aren't'. Regardless of what is the correct position, this disagreement could not take place at all unless both sides were agreed on the meaning of 'there are' and 'there aren't'. When the nominalist says that there aren't any fictional entities, he is denying exactly what the Meinongian asserts when she says that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.

2. Azzouni might argue that (for example) 'there are hobbits in Tolkien' is true, but 'there are hobbits in Jane Austen' is false. But this is not an argument that 'there is' is equivocal. On the contrary, it means exactly the same in both cases. What is asserted is different, for in one case we say there are hobbits in Tolkien, in the other, that there are hobbits in Jane Austen. It is the qualifying 'in Austen' or 'in Tolkien' that changes the assertion. But in both cases 'there are' means the same. If it doesn't mean the same it amounts, as Ockham says, to the destruction of all logic.

Cicero in the Logic Museum

Another parallel translation in the Logic Museum: Cicero's commentary on Aristotle's Topics

The Toils of Metaphysics

Here are three quotations on the nature of philosophy (or 'metaphysics') that have something in common. They are all from the eighteenth century (Isaac Watts, known to members of the Anglican communion from the many hymns he wrote, David Hume and Thomas Reid). They all defend philosophy in some way while conceding its defects.
Watts criticises the 'subtlety' of scholastic metaphysics, and like Hobbes, disparages the tendency of philosophers to invent meaningless names.

Both Hume and Reid underscore their point with a staggering variety of metaphors. Both compare idle speculation to a net. Hume speaks of the 'intangling brambles' of religious fears and prejudices. Reid warns against being 'intangled in metaphysical toils'. Hume invokes Locke's comparison to the robber's den. Reid speaks of the 'bogs and quagmires' into which philosophy may entice us, and at the end compares Philosophy to a fair but wayward lady, whom he must trust until he finds 'infallible proofs of her infidelity'.

"In order to make due Enquiries into all these and many other Particulars which go toward the compleat and comprehensive Idea of any Being, the Science of Ontology is exceeding necessary. This was what was wont to be called the first part of Metaphysicks in the Peripatetick Schools. It treats of Being, its most general Nature, and of all its Affections and Relations. I confess the old popish Schoolmen have mingled a Number of useless Subtleties with this Science; they have exhausted their own Spirits, and the Spirits of their Readers in many laborious and intricate Trifles, and some of their writings have been fruitful of Names without Ideas, which hath done much Injury to the sacred study of Divinity. Upon this Account many of the Moderns have most unjustly abanded the whole Science at one, and thrown abundance of Contempt and Raillery upon the very name of Metaphysicks; but this Contempt and Censure is very unreasonable, for this Science separated from some Aristotelian fooleries and scholastic Subtleties is so necessary to a distinct Conception, solid Judgment, and just Reasoning on many subjects, that sometimes it is introduced as a Part of Logic, and not without Reason. And those who utterly despise and ridicule it, either betray their own Ignorance, or will be supposed to make the Wit and Banter a Refuge and Excuse for their own Laziness." [Isaac Watts - Logick, or the Right use of Reason, I. 6. ix]

"But this obscurity in the profound and abstract philosophy, is objected to, not only as painful and fatiguing, but as the inevitable source of uncertainty and error. Here indeed lies the justest and most plausible objection against a considerable part of metaphysics, that they are not properly a science; but arise either from the fruitless efforts of human vanity, which would penetrate into subjects utterly inaccessible to the understanding, or from the craft of popular superstitions, which, being unable to defend themselves on fair ground, raise these intangling brambles to cover and protect their weakness. Chased from the open country, these robbers fly into the forest, and lie in wait to break in upon every unguarded avenue of the mind, and overwhelm it with religious fears and prejudices. The stoutest antagonist, if he remit his watch a moment, is oppressed. And many, through cowardice and folly, open the gates to the enemies, and willingly receive them with reverence and submission, as their legal sovereigns.

"But is this a sufficient reason, why philosophers should desist from such researches, and leave superstition still in possession of her retreat? Is it not proper to draw an opposite conclusion, and perceive the necessity of carrying the war into the most secret recesses of the enemy? In vain do we hope, that men, from frequent disappointment, will at last abandon such airy sciences, and discover the proper province of human reason. For, besides, that many persons find too sensible an interest in perpetually recalling such topics; besides this, I say, the motive of blind despair can never reasonably have place in the sciences; since, however unsuccessful former attempts may have proved, there is still room to hope, that the industry, good fortune, or improved sagacity of succeeding generations may reach discoveries unknown to former ages. Each adventurous genius will still leap at the arduous prize, and find himself stimulated, rather than discouraged, by the failures of his predecessors; while he hopes that the glory of achieving so hard an adventure is reserved for him alone. The only method of freeing learning, at once, from these abstruse questions, is to enquire seriously into the nature of human understanding, and show, from an exact analysis of its powers and capacity, that it is by no means fitted for such remote and abstruse subjects. We must submit to this fatigue in order to live at ease ever after: and must cultivate true metaphysics with some care, in order to destroy the false and adulterate. Indolence, which, to some persons, affords a safeguard against this deceitful philosophy, is, with others, overbalanced by curiosity; and despair, which, at some moments, prevails, may give place afterwards to sanguine hopes and expectations. Accurate and just reasoning is the only catholic remedy, fitted for all persons and all dispositions; and is alone able to subvert that abstruse philosophy and metaphysical jargon, which being mixed up with popular superstition, renders it in a manner impenetrable to careless reasoners, and gives it the air of science and wisdom." [David Hume, An Inquiry concerning Human Understanding, section I].

"In the meantime, the unprosperous state of this part of philosophy [epistemology] hath produced an effect, somewhat discouraging indeed to any attempt of this nature, but an effect which might be expected, and which time only and better success can remedy. Sensible men, who never will be sceptics in matters of common life, are apt to treat with sovereign contempt everything that hath been said, or is to be said, upon this subject. It is metaphysic, they say: who minds it? Let scholastic sophisters entangle themselves in their own cobwebs; I am resolved to take my own existence, and the existence of other things, upon trust; and to believe that snow is cold, and honey sweet, whatever they may say to the contrary. He must either be a fool, or want to make a fool of me, that would reason me out of my reason and senses.

"I confess I know not what a sceptic can answer to this, nor by what good argument he can plead even for a hearing; for either his reason is sophistry, and so deserves contempt; or there is no truth in human faculties - and then why should we reason? If, therefore, a man find himself intangled in these metaphysical toils, and can find no other way to escape, let him bravely cut the knot which he cannot loose, curse metaphysic, and dissuade every man from meddling with it; for, if I have been led into the bogs and quagmires by following an ''ignis fatuus'', what can I do better than to warn others to beware of it? If philosophy contradicts herself, befools her votaries, and deprives them of every object worthy to be pursued or enjoyed, let her be sent back to the internal regions from which she must have had her original.

"But is it absolutely certain that this fair lady is of the party? Is it not possible she may have been misrepresented? Have not men of genius in former ages often made their own dreams to pass for her oracles? Ought she then to be condemned without any further hearing? This would be unreasonable. I have found her in all other matters an agreeable companion, a faithful counsellor, a friend to common sense, and to the happiness of mankind. This justly entitles her to my correspondence and confidence, till I find infallible proofs of her infidelity. " [Thomas Reid, An Inquiry into the Human Mind, works, introduction, ''ibidem'' p. 105]

Ontological dependence

My argument again. The following formally expressed statements are inconsistent.

1. (E x) number(x)
2. (x) number(x) implies not created(x)
3. (x) God created x

If (1) some x is a number, then (2) that x was not created. But (3) for all x, God created x, so God created that x. Contradiction.

Given this, it doesn't help to say that existentially quantified statements such as (1) don't really express or imply existence, or that (1) has no 'ontogical commitment'. This is irrelevant. Even if (1) is true of some x's to which we have no ontological commitment, it still logically follows that (3) is true of all x's, and so (presumably) is true of x's to which we are not ontologically committed. This is no way out.

Azzouni argues that our criterion for existence should be 'ontological independence'. If an object's properties depend wholly upon us (as in the case of fictional objects) then that entity does not exist. If our method for establishing the truth about an object is trivial (as in the case of mathematics) then it is ontologically dependent upon us. Accordingly, mathematical objects do not exist.

This does not help with the theological problem above. Even if (1) is true of ontologically dependent objects, there is still a contradiction, because there is nothing to prevent the universal quantifier ranging over such objects. If God created all things, then he made ontologically dependent things. But according to (2) some ontologically dependent things (numbers) are not created. Contradiction.

And Azzouni's suggestion creates another problem. I can meaningfully ask whether there are such things as 'ontologically dependent' objects. If yes, then why does Azzouni say that such objects do not exist? If not, in what sense is Azzouni offering any kind of solution at all? More on this later.

Azzouni on Ontological Commitment

Deflating Existential Consequence: A Case for Nominalism. Jody Azzouni, New York: Oxford University Press, 2004

I haven't got hold of a copy of this book yet, but the next best thing is a review. Three below.

Mark Colyvan
Thomas Hofweber
Joseph Melia

Did God create all things?

Vlastimil Vohanka has drawn my attention to an article by the American theologian William Lane Craig, which deserves a separate post. Craig, despite the fact he tends to include rather creepy-looking pictures of himself in his published work, is an admirable writer, who generally manages the trick that is essential to good philosophy, of being both clear and difficult at the same time. Here, he raises the question of whether numbers could have been created by God. He says that Christian theology requires us to say that everything that exists apart from God was created by God (John 1:3). But numbers, if they exist, are necessary beings. They thus would seem to exist independently of God. And (simplifying his point somewhat) the number 3 must have existed prior to God’s creating the number 3, which is impossible! "I remember the sense of panic that I felt in my breast when I first heard this objection raised at a philosophy conference in Milwaukee. It seemed to be an absolutely decisive refutation of theism. I didn’t see any way out."

First of all, I'm not sure this raises any genuinely theological issues. Craig should have read Augustine, who says (On the Literal Exposition of Genesis IV, c. 7) 'Six is a perfect number, not because God completed all things in six days, but rather, conversely, the reason God completed things in six days, was because that number is perfect, which would be perfect even if those things did not exist'. Moreover the second part of the verse from John which Craig quotes ("Through him all things were made; without him nothing was made that has been made") leaves open the possibility that there are some things which weren't made or created at all.

In any case, the solution that Craig comes up with does not do the trick. His solution is to propose some half-way house between being a thing of any sort whatever, and being a thing to which we are 'ontologically committed' (a favourite expression of his). Thus he agrees that we can 'quantify over' numbers, i.e. admit that there are such things as numbers, but not admit that numbers 'really exist', or that we are 'ontologically committed' to them.

There is a lot I could say about this, including how this is a good example of how pretensions to formal logic completely obscure something that should be quite simple. Here, I will briefly note that this manoeuvre does not resolve the difficulty at all. The first part of John's verse says nothing about real existence, or about 'ontological commitment'. It simply says 'God created all things'. Whether we are ontologically committed to numbers or not, whether they 'really exist' or not, Craig agrees that numbers are things, i.e. that some things (perhaps things that are fictional, or which don't really exist in any strong sense) are numbers. In which case, it logically follows that God created numbers.

Ironically, he says that "The existential quantifier simply serves to facilitate logical inferences." Quite. But then logical inference is what guarantees the move from 'God created all things, and some things are numbers' to 'God created numbers', and that is precisely the inference that creates his problem.

Note that Craig mentions a book by Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism which I mean to read one day, and which will deserve a post or two when I have.

Part I of the Summa Theologiae

Questions 106-110, Questions 111-114, and Questions 115-119 of Part I of the Summa now available in the Logic Museum. This brings us to the end of the First Part of the work. Only Part II, I and II, and Part III to go. This is the only parallel Latin-English version on the Internet. Also the only complete one. There are a number of missing bits of the internet versions currently available.

The Frozen Present

I am translating Scotus' questions on Aristotle's On Interpretation (the Peryhermenias) and have reached the part where he discusses the problem of future contingents. Scotus' take on this is interesting and I will discuss it in a future post. Meanwhile I am reading around the subject. I dusted off Gilbert Ryle's Dilemmas, which was one of the first philosophy books I read, a discussion by Prior in a paper called 'It was to be', and older discussions by Boethius, Abelard. Today it is Aquinas. He writes (in his commentary on the Peryhermenias, I l 15. n2).

Omne quod est necesse est esse quando est, et omne quod non est necesse est non
esse quando non est. Et haec necessitas fundatur super hoc principium:
impossibile est simul esse et non esse: si enim aliquid est, impossibile est
illud simul non esse; ergo necesse est tunc illud esse. [my emphasis]

I.e. everything that is the case, is necessarily the case, when it is the case. This is because (he argues) it is impossible that the same thing should be the case, and not be the case at the same time. At first sight his argument seems absurd. It is sunny now. Might it not be sunny now? Of course. And this doesn't involve supposing a contradiction, because although 'it is sunny' is true now, to suppose that it were not sunny now involves supposing that 'it is sunny' is not true now. So no contradiction is involved. Aquinas seems to be confusing the possibility of its being p, but being possibly not-p, i.e.

possibly( p and possibly not-p)

which does not involve a contradiction, with the possibility of being p and not-p, i.e.

possibly( p and not-p)

which does involve a contradiction.

Or does he mean something else? Is he denying the sort of 'instantaneous counterfactual' that we take for granted in modern philosophy? In everyday life, we take it for granted that the realisation of any possibility takes time. Might it not be sunny? Only if the clouds pass in front of the sun. But when the clouds pass in front of the sun, it will not be now, and the qualification 'when it is sunny' no longer applies. Time must pass in order to realise the possibility. Perhaps this is the meaning of Aquinas qualification 'when it is p' (quando est). This would be consistent with Augustine's view that God cannot change the past, because would be to turn what was the case, into what wasn't the case. For the same reason, he cannot change the present. For if it took take time to do that, it would no longer be the present. If it did not, this would be turning what is the case, into what isn't. See The Frozen Past.

According to the Bible

Here is a case where the position I have argued for seems to be uncontroversially true. Consider

(A) The earth was created around 6,000 years ago.
(B) According to the Bible, the earth was created around 6,000 years ago.

Fundamentalists will say that (A) is true, non-fundamentalists that it is false. But both agree, indeed everyone who is familiar with the Bible agrees, that (B) is true. According to the Bible, the earth was created at a certain point in human history.

In this case, no one is tempted to say that the Bible is about some parallel Biblical world, such that all the statements in the Bible are by their nature true of that parallel world. On the contrary, both fundamentalists and non-fundamentalists agree that the statements in the Bible are about our world, and that (B) is not a statement about some Bible-world, but about what the Bible says.

Given the existentially conservative explanation works in this case, what reason is there to suppose it should not work in the case of fiction?

Existential Conservatism

Tanas objects: “Not sure I understand what existential conservativism would amount to. Wouldn't you agree that there is a detective in A.C.Doyle' stories?”. Agreed. A classic problem for theories of fiction, particularly ‘existentially conservative’ ones, is to explain how there can be true statements such as ‘Sherlock Holmes was a detective’.

But I should clarify what I mean by ‘existential conservatism’. Suppose someone says ‘Louis XIV had an adviser called D’Artagnan’. Without qualification, that is false. As far as we know, that French King had no such advisor. It is true that, in his "Muskeeters" stories, the novelist Dumas says the French King had such an adviser. And we say that ‘In the stories, Louis had an adviser called D’Artagnan’, or ‘According to Dumas &c’. I'm sure everyone agrees that the fictional statement is not true in an unqualified sense, and requires some qualifying statement such as ‘according to …’ or ‘in the story …’

So we agree up to this point. We disagree, I imagine, on the explanation of these qualifying statements. According to the conservative, the logical form of ‘According to S, p’ is ‘S says that p’. This can be true, even though p is false, for we are truly reporting that someone (or some story says) that p, not reporting that p itself. Thus ‘Sherlock Holmes is a detective’ is false without qualification. In a qualified sense, i.e. as meaning ‘According to the Holmes stories, Holmes is a detective’ it is true. Similarly ‘There are such things as hobbits’ is false, without further qualification. Taken as meaning ‘In Tolkien’s world’, or ‘According to Tolkien’ it is true.

According to existential liberals, on the other hand, the qualifying phrase directs us to a story-world or fictional universe, which really exists, in some sense, and which the story is truly about. Thus ‘there are hobbits in Tolkien’s world’ says of a really existing, but parallel fictional world described by Tolkien, a race of creatures called hobbits exist.

Who is right? According to the conservative, there is no argument evidence or evidence to support the existence of fictional worlds or fictional creatures or people, beyond the need of explaining the truth of statements like ‘Hobbits have furry feet’ or ‘Holmes was a detective’. But given we can explain the truth of such statements in terms of ‘S says that p’, which does not require the positing of an extra universe of things, we should prefer the more conservative explanation, which does not multiply things according to the multiplicity of terms. Or so the original Ockham would have argued.

[edit] By extraordinary coincidence, if it is that, Peter Smith is dealing with a very similar issue here.

On Fiction - The real Ockham speaks

Following Brightly's point in the last post, here is a link to a translation of a work by William of Ockham (the other one) that I made some time ago. Not available in English anywhere else, as far as I know. It is all good stuff, but especially interesting in the current context is section 7 ('A probable opinion: affections of the soul are effigies or fictions')

Here Ockham discusses a view he seems to favour. An intention of the soul, or a concept or affection of the soul is nothing other than a predicable or 'subjectible' in a proposition in the mind, to which there corresponds a predicable or subjectible in utterance, and, generally, affections of the soul, whether intentions of the soul or concepts, are propositions in the mind, or syllogisms, or parts of them. These mental terms and propositions are 'effigies' or 'fictions'. They are not true qualities of the mind, and are not real beings existing subjectively in it, but they are certain things thought by the mind whose being is nothing other than being thought. They exist in the sense that a building designed by an architect really exists, which exists in virtue of being designed or made-up, and so does not exist in reality. This made-up thing can also be called an 'intention', because it is not real, and has intentional being, i.e. being thought of in the soul.

The view is not entirely clear. If a thing has being by being thought, is this not a kind of being? But what kind of being? Ockham himself notes the difficulty of supposing that anything can be understood by us, which does not exist in reality, nor any part of it, and which is neither a substance nor a property of anything.

Brandon: reply on fictional creation

Brandon (who has an excellent and praiseworthy internet residence called Siris) asks whether "Does writing [a fiction about a planet) miraculously create a fictional object the size of Jupiter?" should not really be "Does this describe a fictional miraculously created object the size of Jupiter?"

A good and Brandonesque objection. Well, the question is whether fictional statements (as opposed to merely false ones) 'bestow' properties on fictional objects. If so fictional statements have to be true.

(1) The statement that A is B 'bestows' B upon the fictional A, according to the theory.

(2) So A now has B.

(3) Since the fictional statement 'A is B' now corresponds to the fictional reality, the statement 'A is B' is true as a result.

This raises the question of when the fictional A begins to exist. I suppose it could coherently be held that A always existed, because the author was going to write about A, but that doesn't altogether make sense. What if the world were to turn out otherwise? What happens to the fictional object in a possible world where no one wrote about 'it'?

More plausible (plausibility being relative) is that the fictional object is created just as soon as I talk or write about it. It doesn't possess any properties until I 'bestow' them by making the fictional claim. So why shouldn't we suppose that the existence of the object is also bestowed at the point of writing. Another argument for this is that it is absurd for the the object to exist before it has any properties 'bestowed' upon it, so that there exists an object without any properties whatsoever (except perhaps of existence). Another problem is that this view requires existence being a property, so does it possess this property before the author has said that exists, i.e. bestows existence upon it?

Summa days

Questions 103-5 of the Summa in parallel Latin-English now available in the Logic Museum Annex.

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.

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.

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.

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."

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

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.

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.

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.

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.

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!

The Nature of Truth

by Harold Joachim. Is here.

Summa Theologiae I 84 - 89

Questions 84 to 89 of the great Summa Theologiae now in Logic Museum II here.

The City of God

Now available in parallel Latin-English, in the Logic Museum annex.

First book is here.

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.

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.

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.

Is 'every man is an animal true' when there are no men?

A splendid new page in the Logic Museum here.

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.