Meinong's gambit

In yesterday’s post I argued that not only is the inference

(*) Vallicella is discussing a non-existent thing, therefore something is non-existent

invalid, but that practically everyone will agree it is invalid. Even the most hardened and extreme realist or Meinongian will concede the possibility that nothing is non-existent (even though, as a matter of fact, they believe that some things actually are non-existent). It follows that they cannot use Meinong's gambit to explain intentionality. They can’t explain Bill’s thought as being somehow about a non-existing thing, because they concede that he could have the same thought even if there were no such objects at all.

With this in mind, we can approach the problem which (according to Bill Vallicella here) is central to the phenomenon of intentionality. Bill says that the problem can be expressed in terms of an aporetic triad, saying that while each of these propositions has some claim to plausibility, all three cannot be correct. At least one must be false. Which?

W1. We sometimes think about the nonexistent.
W2. Intentionality is a relation between thinker and object of thought.
W3. Every relation R is such that, if R obtains,then all its relata exist.

I will begin by ‘Ockhamising’ these propositions so that they express the same problem, but in language more acceptable to an Ockhamist. (E.g. I argued here that a term like ‘the nonexistent’ is question-begging).

O1. The proposition ‘Bill is discussing a nonexistent thing’ can be true even when there are no nonexistent things.
O2. The proposition ‘Bill is discussing a nonexistent thing’ expresses a relation between two things.
O3. Every relation is such that if it obtains, all of its relata exist.

With my previous comments in mind, the answer may now be obvious. We can assume that the first proposition is true. The third proposition must also be true. As argued above, the realist cannot plead the ‘nonexistence’ amendment. He can’t argue that the third proposition is false because Bill’s thought may relate him to a nonexistent thing. For the problem remains even when there are no nonexistent things. It is not that we sometimes think of the nonexistent. It is that the predicate "Bill is thinking of ---" may not apply to anything at all, rather than applying to some nonexistent something. Thus, even if there were nonexistent things, this would not explain the problem of intentionality, i.e. the problem that all three propositions above are inconsistent.

It remains that the second proposition must be false. Indeed, isn’t this obvious? The simplest and most economical hypothesis to explain this is that while the proposition ‘Bill is discussing a nonexistent thing’ has grammatically the form of a relation, and is syntactically similar to ‘Bill is meeting his wife’, it does not actually express or signify a relation. What other explanation is there? The second proposition has no claim to plausibility at all.

This explanation involves no recourse to ‘queer objects’ of any kind. The underlying logic of the proposition must be different to the underlying logic of ‘Bill is meeting his wife’. As is manifest and provable, for the latter implies ‘someone is such that Bill is talking to her’. ‘Something is such that Bill is discussing it’.

Distinguishing queer from straight

In my previous post I gave four criteria for distinguishing ‘queer’ from ‘straight’ terms. The most important of these was the last one: a queer term does not refer to or denote anything, and thus does not pick out any category or kind of thing. Bill Vallicella and Peter Lupu are now impatiently challenging me on this. What are the considerations or criteria on the basis of which we decide how to draw the distinction between terms which refer or denote*, and those which do not refer or denote?

There are several techniques used by Ockham throughout Summa Logicae. The one I will use is as follows. Take any proposition p containing a possibly queer occurrence of some term F. Construct a proposition q that uses the term to assert that there are F’s – preferably avoiding the use of ‘exists’ or its cognates, to prevent the realist from driving a wedge between ‘something’ and ‘some existing thing’. Then show, by logical analysis, that p does not entail q, i.e. it is possible that p is true but q false. We can easily do this using an earlier example.

(1) Jake is looking for a gold mine in Surrey, therefore some gold mine is in Surrey.

Even the most hardened realist will agree that the inference is not valid. For it is perfectly possible that the antecedent is true, and that Jake is looking for a gold mine in Surrey, but the consequent false – for there is no gold mine in Surrey, and so ‘some gold mine is in Surrey’ is false. Note my careful use of the categorical sentences ‘some gold mine …’ and ‘no gold mine …’ here, and the avoidance of the word ‘exists’. This is necessary in case the realist argues that there is no existing gold mine in Surrey, i.e. there are gold mines, but they are not ‘existing’ or ‘existent’ ones. We reply: that there is no gold mine in Surrey, not even in this qualified sense. It is not that there is no existent gold mine, as though there could be some non-existent gold mine. That is an abuse of language, and it leads far from the truth. There are no gold mines in Surrey at all.

This reasoning can be confirmed as follows. Consider

(2) Vallicella is discussing a non-existent thing, therefore something is non-existent

The realist cannot explain away the truth of the antecedent, as he might try to do with ‘gold mine in Surrey’, by reference to non-existent things. For he agrees that the inference is invalid, therefore he agrees that the consequent is false, and so nothing is non-existent. It is not merely that the non-existent does not exist (as though there were some things, which happen to exemplify the property of non-existence). It is that nothing - not even a non-existent thing - is non-existent.

Thus I have distinguished a ‘queer’ from a ‘straight’ term by purely logical means. Tomorrow, I shall address Vallicella’s ‘aporetic triad’. We can think of the non-existent; ‘thinking of’ is a relation; a relation must relate existing relata. Does the triad make sense? And if it does, which of the propositions is false?

* I have changed Lupu’s wording from “refers in a way that entails ontological commitments” because I do not understand it. If a term refers, by definition it refers to something, and so there is something to which it refers. By Brentano’s equivalence (i.e. ‘there exists an F’ is convertible with ‘there is an F’), it has existential commitment.

Intentionality: more objections

More objections at Valicella's place. Let's summarise where we are. In the two posts here and here, I gave three criteria for distinguishing 'queer' from 'straight' terms. As follows.

(1) the term is categorial (read ‘noun phrase’). This rules out trivial examples like ‘not’ and ‘the’.
(2) a significant number of people think it does refer or denote. This addresses Bill’s objection about ‘net too wide’. The net is just wide enough to catch the right sort of fish.
(3) the reason these people think it refers is not based on mere empirical considerations. This rules out non-referring/denoting terms like ‘ghost’.
(4) the term, in fact, does not refer or denote.

The next part of the question, which I haven’t answered yet, is what are the sub-criteria by which we address criterion (4)? How do we engage the people picked out by criteria (2) and (3), who will naturally challenge (4)? I will address this shortly. The reason I haven’t addressed it before is so we can be absolutely clear about the form of nominalism I am defending – namely the nominalism defended by Ockham in chapters 49-51 of the Summa Logicae, and throughout the whole section of that book where he discusses Aristotle’s theory of categories. (Ockham argues that the Aristotelian ten categories of being really reduces to two, and that we only really need substance and quality. In chapters 49-51 he is discussing relation, arguing that a relation is nothing absolute and distinct from the terms related, when suitably referred to).

More tomorrow, where I will tie the question back to the thread about 'intentional inexistence'.

More confusion about intentionality

Vallicella has been picking up on some of the issues discussed here over the last week.

His aim to highlight what he thinks is a fundamental confusion in the Ockhamist characterisation of intentionality. It is characteristic of certain mental states (intentional states) to refer beyond themselves to certain items. For example, states of desire refer beyond themselves to items that are not part of the states. In desire something is desired, and so on. Unfortunately (he says) the word 'something' will cause certain people (that's us here) to stumble, leading them wrongly to suppose that “a concrete episode of desire cannot exist unless there also exists, independently of the desire, something that is desired”.

His point seems to be that the inference

(A) Something is desired, therefore there exists something that is desired.

is not valid, but Ockhamists wrongly think it is valid.

This is wrong. (A) certainly is valid. I have argued, particularly here, that when the word ‘something’ occurs in the subject position of a sentence, then Brentano equivalence applies, so that the categorical sentence ‘Some A is B’ is convertible with the existential ‘Some A-that-is-B exists’. Thus there is fundamentally no difference between the following three sentences.

(A1) Something is desired by Tom
(A2) There is something desired by Tom
(A3) There exists something desired by Tom

Thus (A) is valid. If something is desired, then there is something desired. The move from 'something is desired' to 'there is something desired' is a mere grammatical transformation. C.J.F. Williams says that English inherits from Anglo-Saxon the dislike of the verb ‘is’ at the beginning of a sentence, and so we put the word ‘there’ in front. Thus the logical move from ‘Something is desired by Tom’ to ‘is something desired by Tom’ is followed by the grammatical move to ‘There is something desired by Tom’. This in turn is no different from ‘There exists something desired by Tom’.

Brentano equivalence applies when ‘something’ is the subject. It does not apply, as I have argued, when it is the predicate. It is the following inference which is invalid.

(B) Tom desires some F, therefore some F is desired by Tom.

Indeed, the examples given by Vallicella testify to this. He says that ‘Tom wants a sloop, therefore something is a sloop’ is invalid, because Tom may want a sloop even when nothing is a sloop. And the fact that a woman now wants a baby is perfectly consistent with the fact that there are (now) no babies satisfying her want. It is (B), not (A) above, that is the problem.

The question is, why is this a problem?

Queer entities and the supernatural

Before I go on to discuss what distinguishes ‘queer’ terms from ‘straight’ ones, I should add a third characteristic of queer terms to the two which I gave in my post yesterday. (The first characteristic was that a queer term does not refer to anything. The second, that it must appear, at least to some people, to refer, even though it doesn’t. This is what makes for its ‘queerness’, that illusory quality that deceives some people into believing it has a reference. Its queerness is the linguistic equivalent of an optical illusion).

A further characteristic is necessary to distinguish queer terms from other non-referring terms like ‘dragon’, ‘goblin’, ‘ghost’ and so on. The reason that some people believe these terms refer is unconnected with the reason that metaphysicians believe that there exist such things as intentional objects, or universals, or haecceities. People believe that ghosts exist because they believe that certain objectively verifiable phenomena are evidence for the existence of ghosts. For example, the photograph on the left undoubtedly exists. It is a real photograph that anyone reading this blog can see. And some people may believe it is evidence for ghosts.

But metaphysicians do not use physical items like photographs, recordings, eye-witness reports or anything which is observable, as evidence for the existence of universals or haecceities or whatever. The only evidence required is an argument or a line of reasoning of some kind. To persuade you of the existence of universals, a metaphysician requires only your time, a modicum of intelligence, the ability to read a text, possibly extending over innumerable volumes, considerable patience with his or her obscurities of expression, and a grain of salt. Nothing else is required. The text can be as old as you like. No specific knowledge of the world is required, other than of language and of technical abstract terms, some of which may be invented by the author. This is the ‘evidence’ of the metaphysician. The only laboratory required is an armchair, the only tool a thick pair of reading glasses.

Thus, the third characteristic of a ‘queer term’ is that the reason for believing that it refers must not consist of observable or empirical evidence. The reason must consist of a text that has no reference to the world except the use of abstract terminology. (I was about to say ‘abstract objects’, but these of course are ‘queer’, and Ockhamists generally avoid using queer terms, although they frequently have to mention them).

In summary, a ‘queer term’ is a categorical term such that

1. It does not refer to or denote anything.
2. Some people (metaphysicians) believe that it does denote or refer
3. Their reason for believing this is not based on empirical observation (or revealed by supernatural agency for that matter).

Ockham's nominalism

At this stage, I should discuss Peter Lupu’s objections (mostly in the extended comment on Vallicella’s blog here) to the nominalist program.

I should first explain what I think the nominalist program is. I am taking my lead from a principle that William of Ockham neatly formulates in his Summa Logicae book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is “to multiply entities according to the multiplicity of terms and to suppose that every term has something real (quid rei) corresponding to it”. He says grumpily that this is erroneous and leads far away from the truth. ('Radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens'). See also an early definition of nominalism here.

What does he mean? Well he says that it is an error. He implies it is a common one, by attributing to the moderns and by the fact he mentions it all. Thus he implies that there exist terms which do not have something real corresponding to them.

If Ockham is correct, the relevant distinction to draw is between queer and straight terms. Straight terms have something real corresponding to them, queer terms don’t. Furthermore, there must at least be some temptation to imagine that queer terms refer to or denote something, otherwise there would be little point in making it.

Which brings me to the main point raised by Peter Lupu, who asks “What are ‘queer-entities’ and how do we determine whether a given entity is “queer” or “straight”? There are two parts to his question. In answer to the first, there are no such things as queer entities, if Ockham is right. There are only ‘queer terms’. These, by definition, are terms that don’t refer to or denote anything, and so by implication there are no ‘queer entities’.

This is what makes any debate with realists difficult. Realists, namely those who think that queer terms refer, will persist in using the queer terms as if they did refer, and so will ask what kinds of thing are referred to, what is their ‘ontological status’ and so on. Ockhamists will naturally refuse to use these terms as if they referred, and refer the names of the terms instead, typically by using real or scare quotes.

There is a similar difficulty in the debate between those who believe in ‘paranormal phenomena’ and those who don’t. Believers talk about ‘the phenomena’ (without scare quotes) as though there were such things as alien abductions, electronic voice phenomena, telepathic radiation and so on. But to use such talk is to presume the existence of such things, as though the only real debate were about their precise nature and properties. Non-believers will rightly refuse to use such terms, and will instead talk about the reports of such things, or of the supposed evidence for them. Reports and evidential phenomena are real enough. The question is whether there exist any things of which they are reports, or evidence.

That deals with Peter's first question. What are queer entities? We can't say, because there are no such things, just as we can't say what kind of things ghosts are. But we can say what 'queer terms' are. These are terms that are categorical, but which (a) have no reference or denotation and (b) appear, or are believed by many, typically on grounds of reason alone, to have a reference or denotation.

Peter’s second point, on how we determine whether given entity is “queer” or “straight”, I will leave for the next post, although clearly the first point applies here also. If the nominalist is right, we cannot ask this question of anything, just as we cannot ask whether a UFO came from Alpha centauri or Betelgeuse. We can only ask whether a given term is queer or straight. More to follow.

Seeking the nonexistent

Yesterday I discussed an apparent problem for the Brentano thesis (that every categorical sentence of the form ‘some A is a B’ is convertible with an existential sentence of the form 'an A-B exists'). The problem is sentences like

(1) Gerald is looking for a gold mine in Surrey

which can be true even though gold mines in Surrey don’t exist.

Such sentences are admittedly a problem, but they are not a problem for the Brentano thesis as such. For (1) above is equally consistent with the following sentence

(2) No gold mine is in Surrey

which is not existential, but categorical. Indeed, Brentano equivalence clearly holds for the conversion of ‘No gold mine is in Surrey’ and ‘no gold mine in Surrey exists’ or ‘a Surrey gold mine does not exist’. The problem is not for Brentano at all, but rather for Aristotle, and the principle of conversion of the particular proposition. According to Aristotle (and according to modern logic, as it happens) ‘Some A is B’ is convertible with ‘Some B is A’. But if ‘Gerald is looking for a gold mine in Surrey’ is true, then by conversion of the particular, the following sentence:

(3) some gold mine in Surrey, is looked for by Gerald,

ought to be true. But surely it isn’t, since it implies that some gold mine (namely the one sought by Gerald) is in Surrey, and we agreed that no gold mine is in Surrey. Is the principle of particular conversion invalid? Or is there something else going on? To me, this is the strongest evidence that there is a deeper logical structure to (1) than the surface grammar suggests. Consider:

(4) Some gold mine, thought by Gerald to be in Surrey, is looked for by him.

which I think is true. And that is roughly equivalent to

(5) Gerald thinks there is some gold mine in Surrey, and he is looking for it.

or

(6) Gerald is looking for a gold mine which he thinks is in Surrey

Thus the quantifier noun phrase ‘some gold mine’ has to be qualified by ‘is thought by’ or some other intentional construction, before the conversion is valid, and thus it is not an ordinary conversion. None of this (pace Vallicella and Lupu) has to do with metaphysics or weird objects or ‘the nonexistent’, except figuratively, but rather it has to do with a more complex logic that underlies our ordinary discourse, and which we need to make visible, if we can.

A problem for the Brentano thesis

As discussed yesterday, a 'Brentano equivalence' holds when we can convert existential sentences of the form 'an A-B exists' and categorical sentences of the form 'Some A is B'. The Brentano thesis is that every such (genuinely) categorical sentence is convertible.

This effectively amounts to the claim that any sentence of the form 'something is such and such' is existential. If anything is such and such, then that thing is an existing thing. The range of our natural language quantifiers 'every' and 'some' covers the entire realm of existence. Every thing is an existing thing.

There are strong arguments for this thesis. But there are strong arguments against, as well, which brings us back to the problem of intentionality. Surely the following inferences are all valid.

• Jake is looking for a gold mine in Surrey, therefore Jake is looking for something (namely a gold mine in Surrey).
• Bill wants a cigarette, therefore Bill wants something (a cigarette).
• Andy is thinking about Pegasus, therefore Andy is thinking about something (Pegasus).

The problem is that any of these antecedents could conceivably be true, the inference seems valid, yet the 'something' in the consequent does not appear to be any existing thing. Clearly Jake can be deludedly looking for a Surrey gold mine, and so looking for a mine, and so looking for something. Yet, as far as we know, there are no gold mines in Surrey. The simple categorical sentence 'Jake is looking for something' can be true, without requiring that the something exists, contra Brentano.

The nonexistent

Sadly, Bill finally had enough of my comments on intentionality. I'm not sure exactly what underlies it, but I suspect it is my persistence on the 'Brentano equivalence'. There is more here and very much more here. Briefly, a Brentano equivalence holds when we can convert existential sentences of the form 'an A-B exists' and categorical sentences of the form 'Some A is B'. There is much evidence that such an equivalence holds in ordinary subject-predicate sentences. Thus 'some buttercups are yellow' is convertible with 'yellow buttercups exist' and 'no buttercups are blue' with 'blue buttercups do not exist'. And as I commented here, there seems little difference between 'Tom's worship has an object' and 'there is an object of Tom's worship' or 'there exists an object of Tom's worship'.

Hence my objection to Bill's claim that 'We sometimes think about the nonexistent'. 'The nonexistent' is an abstract noun phrases built out of an adjective, like 'the unemployed', 'the French', 'the damned', which appear to refer to a whole class of things (unemployed people, French people, damned souls). If the same is true of 'the nonexistent', then it refers to a whole class of things - things which do not exist - and we can divide all things in reality into those which do exist (mountains, horses, yellow buttercups) and those which do not (golden mountains, unicorns, blue buttercups, four-leaf clovers and so on). You can see the idea in the picture on the left (from the Logic Now and Then symposium in 2008 - I don't remember who the speaker was).

Clearly, no one who divides reality up in this way can consistently hold the Brentano equivalence, according to which any thing is also an existing thing. If 'the nonexistent' refers at all, it refers to nonexistent things. But a nonexistent thing is a thing which does not exist, and so is a thing such that there is no such thing. But there is no such thing. So 'the nonexistent' does not refer. Accordingly, we cannot think of the nonexistent, if the Brentano equivalence is valid.

Clearly there is a problem, as true sentences like 'the Greeks worshipped Zeus' or 'Tom is thinking of Pegasus' suggest. But I will talk about this in the next post.

Ockham and the golden mountain

Reading Valicella’s discussion of Twardowski’s ‘solution’ to the paradox of intentionality brought to mind my old translation of Ockham’s commentary on Aristotle’s Perihermenias. The whole thing is worth a read, but section 9 is particularly relevant.

Replying for those who say that an intentional object is a real being, Ockham argues that 'a chimaera exists in reality' has distinct meanings according to whether 'chimaera' denotes personally, or materially or simply. If it denotes personally (i.e. if it is meant to denote a chimaera itself) it is false. But if it denotes ‘materially’ (i.e. if it stands for the word 'chimaera') or ‘simply’ (it stands for the concept of a chimera), it is true, for the word 'chimaera', and the concept chimaera both exist in reality. Similarly the proposition 'a chimaera is understood' is false, if 'chimaera' is meant to stand for a chimaera, but true, if it stands either for the word itself, or for the concept of a chimaera. (An argument he repeats in Summa Logicae II.72). This solution seems close to the one that Twardowski criticises. When I think about the round square or the golden mountain (in whatever psychological mode) the object of my thought is neither a mental content nor an abstract object. And ‘the golden mountain’ refers to the golden mountain, not, as Ockham’s comment suggests, to the concept of a golden mountain.

Note Ockham’s use of the example ‘golden mountain’ (mons aureus). I can find only one earlier example, in Scotus’ questions on the Metaphysics (q.6), written in the late 1290s, but it must surely be older than that.

Intentional objects

Given that

(*) Tom worships Zeus is true, which of the following, if any, are true?

(1) Tom’s worship is object-directed
(2) Tom’s worship is directed towards an object
(3) Tom’s worship has an object it is directed to
(4) There is an object that Tom’s worship is directed to
(5) There exists an object that Tom’s worship is directed to
(6) The object that Tom’s worship is directed to exists

Ockham on the BBC

Researching ways in which I might write a useful and interesting and improving article on Ockham for the Daily Mail, I found this excellent programme on the life and work and legacy of Ockham, first broadcast 8:00 a.m., Thursday 31 May 2007, on Radio 4. It doesn’t tell us a huge amount that someone familiar with Ockham or that period of medieval thought would not have already known. Its interest lies in the great way it summarises Ockham. Given you have five minutes, twenty minutes or (as in the case of this broadcast) 45 minutes to talk about Ockham, what actually do you say? The Wikipedia article is truly awful (for reasons I explain here, if it is not self-evident from just looking at the article). The article in the Stanford encyclopedia of philosophy is simply not going to be comprehensible to the average Daily Mail reader.

The opening (by Bragg) is picturesque.

The small village of Ockham, near Woking in Surrey, stands a church. Made of
grey stone, it has a pitched roof and an unassuming church tower but parts of it
date back to the 13th century. This means they it have been standing when the
village witnessed the birth of one of the greatest philosophers in Medieval
Europe. His name was William and he became known as William of Ockham. William
of Ockham’s ideas on human freedom and the nature of reality influenced Thomas
Hobbes and helped fuel the Reformation. During a turbulent career he managed to
offend the Chancellor of Oxford University, disagree with his own ecclesiastical
order and get excommunicated by the Pope. He also declared that the authority of
rulers derives from the people they govern and was one of the first people so to
do. Ockham’s razor is the idea that philosophical arguments should be kept as
simple as possible, something that Ockham himself practised severely on the
theories of his predecessors.

That's right! Begin with a picture of where Ockham grew up, and a place he might have seen in some earlier form. Designate him as ‘one of the greatest philosophers in medieval Europe. Say that he ‘fuelled the Reformation’, that he disagreed with his own order, and was excommunicated by the Pope (as was Anthony Kenny, one of the participants in the programme, as it happens). The only thing it is missing is the wonderful “under cover of darkness” from the Stanford article, describing his flight from Avignon for Pisa. Probably the only part of that article that would not have been out of place in the Mail. The programme is well worth a visit. In summary:

• What sort of world did Ockham live in (Kenny, 1:19)


• His early life (Adams 5:50)


• The problem of universals (Adams 7:46). There is a wonderful moment where Adams says “The problem is really a problem about whether similarity is to be grounded in the identity of metaphysical components. If each of us is a human being, we are maximally similar with respect to rational animality. But does that similarity between two individuals ... have to be grounded in a common metaphysical consituent which we all share, and if it does, then would there have to be another constituent which makes us to be the very individuals that we are - the haecceity". Bragg understandably asks her to run that one past him again.


• Ockham on universals. (Adams 9:05) Ockham's view that any explanation in terms of a common nature and an individuating component requires an account of the connection between the nature and the individuator is, and O thinks that any attempt to give an account of this will end in contradiction.


• The Holy Trinity. (Cross - 10:48). This is a wonderful explanation of why Ockham’s view on universals was controversial. If there aren't shared natures, it is hard to explain how there is just one God, where there are supposed to be three divine persons who all share something (the divine nature/essence), plus a distinguishing feature. If in principle there couldn't be a shared essence, it looks as though you have ruled out the Trinity on philosophical grounds. Oh no.


• How Ockham gets round it (Cross, 12:46). Ockham simply thought that theology is an exception. A bit of a sidestep, and an unsatisfactory position for a medieval philosopher, given their program, which had some success, of showing the overall consistency and coherency of Christianity, even if its truth cannot be logically proved.


• Ockham's Razor (Kenny 15:51). “Scotus had grown huge metaphysical fuzzy beard that needed cutting off”. This is how Kenny achieved fame and respect and universal admiration in the philosophical universe. However, he does add that Ockham was the most brilliant philosopher ever to have taught at Oxford, and Kenny taught at Oxford.


• The political period (Cross, 22:40). The spiritual Franciscans, who believed in Franciscan poverty – the use of things, but not the ownership of property - were a bit ‘like hippies’, and also possibly a bit mad. Pope John XXII proclaimed that Franciscans had a right to use things, which Ockham said contradicted a proclamation in 1279 proclamation, since a ‘right to use’ is the same as ownership. Ockham’s finally declared that the pope was a heretic. ‘Quite bold really’, comments Bragg (although Adams adds that it was actually quite common in those days for popes to be denounced as heretics).


• Church and state. (Adams 31:40). Ockham defended a dualist or parallel system of church and state. He had a liberal view of the state - after the fall, you wouldn’t have to have property ownership if everyone would live by natural reason – but not everyone will, so you need the state. The state should stay out of church affairs, the church should stay out of temporal affairs. He also emphasised personal liberty, so clearly was a very modern person.


• Divine right. (Kenny 35:44) The right of monarchs does not derive directly from God. It comes from God to the citizens who then pass it on, if they wish, to the king. Ockham’s significance. (Cross, 37:50) Ockham’s theory is a modern democratic theory, promoting a liberal state. This idea might have reached Hobbes, who had been reading Grotius, who might have been reading someone like Ockham or Marsilius.


• Ockham’s real significance. (Cross 41:10) Ockham was more influential for his logic - not least because early modern philosophers were nominalists.

The programme features host Melvyn Bragg, with experts Anthony Kenny, Marilyn McCord Adams and Richard Cross.

Everything is everything

Peter Adamson from King's College London emailed me to let me know about his series of podcasts here. It currently covers only the pre-Socratics ('Aristotle is some way in the future still'). In one of the pods, Peter talks us through the philosophy of Anaxagoras (who I talked about in an earlier post here) with entertaining humour: "He didn't wind up drinking hemlock, but instead just left town, which is safer"; "We humans get a healthy portion of mind, rocks don't get any".

He also notes that "When soul singers from the 1970s to the present have informed us that everything is everything, they were broadly speaking in agreement with Anaxagoras". Very true, and to bring us up to date here is the excellent rapper Lauryn Hill singing Everything is everything, which contains as an added bonus the philosophical 'what will be will be'.

Ghosts and metaphysics

Peter Lupu makes the following objection to my claim that there are no substantive theses of metaphysics. Claims such as “there are no universals” are substantive metaphysical theses. But it is also a substantive thesis of nominalism, one which I (as a card-carrying nominalist) would surely uphold. The choice is mine!

I reply: is the thesis that there are no such things as ghosts, a substantive thesis in the theory of ghosts? No. Because it is not a thesis about ghosts. Any thesis in the theory of ghosts is about ghosts. But the thesis that there are no ghosts is a substantive theory not about ghosts, but about the world. Namely, that the world contains no ghosts. Not being a thesis about ghosts, it is not part of the theory of ghosts.

Analogously, the nominalist holds that there are no universals. His thesis is a substantive one, to be sure. But it is not part of the theory of universals. Rather, it is a substantive part of the theory of the world, that it contains no such things as ‘universals’.

Album fuit disputaturum

Vallicella continues here. What I find puzzling is how he continues with trifling, even frivolous objections to the extreme version of Ockhamism that I have proposed here and there, without picking up on any of the really serious objections to it.

So let’s talk about one possible objection here. Extreme or ‘London’ Ockhamism is the view that relations can only relate things. There are no ‘non-existent relata’. Where the Stanford Realist talks about ‘non-existent relata’, as apparently required by ‘Tom is thinking about Pegasus’, the Ockhamist sees only things. ‘Tom is thinking about Pegasus’ relates Tom to nothing (for Pegasus is not a thing). Thus ‘Tom is thinking about Pegasus’ is a linguistic relation only

Londonists allow present relations. Thus ‘Cameron is colleague of Clegg’ is true, and relates two things. Londonists also allow past relations. Thus ‘Churchill met Roosevelt’ is true, since it expresses a relation which was between two things, although now between no things.

The problem occurs when the relation is between something in the present, and something in the past, or when there is no time at which the relation could possibly have been between two things. Consider ‘Churchill (who died in 1965) died before Cameron (who was born in 1966) was born’. At no time when Churchill was something, was Cameron something. For when Churchill was something, Cameron was not born. And when Cameron was born, and so was something, Churchill was nothing. Thus at no time did ‘Churchill died before Cameron was born’ relate any two things.

The medieval philosophers discussed a similar problem in the sophisma ‘Album fuit disputaturum’ (a white person was going to argue). Assume Socrates was white, before he went into the Mediterranean sun. And assume that he only argued after acquiring a Mediterranean suntan. Thus ‘a white (i.e. untanned) person is arguing’ was never true (at least, in respect of Socrates). Thus ‘Album fuit disputaturum’ apparently relates the person of whom the subject is true (untanned and unarguing Socrates) with the person of whom the predicate is true (tanned and arguing Socrates). How is that possible?

Aquinas on Aristotle's Posterior Analytics

Just out in the Logic Museum. Thomas's very accessible and highly recommended commentary on Aristotle's Posterior Analytics.

Intentionality and semantics

Bill Vallicella comments: "One cannot eat without eating something, and indeed something that exists. And one cannot desire without desiring something -- but in this case the thing desired needn't exist." But then we have the problem of 'something desired which doesn't exist', which seems contradictory. Is the problem about ontology at all?

Consider

(1) Jake is searching for a gold mine near Cripple Crow Creek.
(2) There are no gold mines near Cripple Crow Creek.

There is not even even a whiff of contradiction or paradox here, and we are not tempted to posit 'non-existent objects' or suchlike. Of course, if we try to analyse them in terms of predicate calculus, we do get a contradiction:

(1a) For some x, [x is a gold mine near Cripple Crow Creek, and Jake is searching for x].
(2a) Not for some x, [x is a gold mine near Cripple Crow Creek].

The first sentence logically implies 'for some x, x is a gold mine near Cripple Crow Creek', which directly contradicts the second. But that suggests a problem with the analysis of (1) into an inappropriate formalisation such as (1a), rather than any question of 'ontology'. As soon as we even ask the question about the 'ontological status' of the sought-for gold mine, we are already on the metaphysical sandbank. E.g. we might try resolve the contradiction between (1a) and (2a) by replacing (2a) with

(2b) Not for some x, [x is an existent gold mine near Cripple Crow Creek].

This resolves the contradiction. But by now we are well into the Meinongian jungle. This is entirely a problem of language and logic, as I see it. What is the deep structure or logical analysis of sentence (1) which makes it transparently clear that it is not inconsistent with (2)? Note that we do get inconsistency if we turn the grammatically active sentence (1) into a passive without getting 'existential implication'.

(1b) Some gold mine near Cripple Crow Creek is sought for by Jake.

In its most natural reading, this contradicts (2). So, what is the true semantic structure of sentence (1)? That is the real question, and it has nothing to do with metaphysics. As a suggestion, consider

(3) Jake says that there is a gold mine near Cripple Crow Creek.

which we can analyse into

(3a) Jake says that for some x, x is a gold mine and x is near Cripple Crow Creek.

This, unlike (1a) above, is not inconsistent with (2a) above, since it does not imply that for some x, etc. Could there not be some analogous analysis of (1) into

(1c) Jake is searching-that-there-is a gold mine near Cripple Crow Creek ?

Could it be that 'searching for' has an embedded that-clause which invalidates the inference to 'for some x there is ...', but which is not visible at the surface level of the sentence? That seems a much cleaner way to resolving the difficulty than all this intentional objects nonsense. For nonsense it is.

Brentano and the convertibility of ‘exists’

Brentano held that a thought must have an object. Did he mean to qualify this by ‘existing object’? According to at least one important thing he said, he would not have drawn any distinction between ‘object’ and ‘existing object’. According to what is now called the Brentano-Venn analysis of propositions, every categorical proposition (one of the form ‘A is B’) is convertible with an existential proposition ‘An A-B exists’. He says, for example

The categorical proposition "Some man is sick", has the same meaning as the
existential proposition "A sick man exists" or "There is a sick man".

It follows from this that 'some hobbit is thought about by some man' is convertible with 'some hobbit thought by some man exists' or 'there is a hobbit thought about by some man'. I have more to say on the history of this here.

Can a relation have non-existent relata?

Can a relation have non-existent relata, asks Bill Vallicella. Surely not. For we have to ask what kind of relation it is – one-termed, two-termed, three-termed, or whatever. Let’s suppose it is two-termed, i.e. it has two relata. If one of those were destroyed, i.e. made non-existent, it would only have one relatum. If both destroyed, none. Frege said it well: that the number zero represents the denial of existence. If the number of Fs is zero, then there are no Fs: no Fs exist.

Thus if a relation has two relata, it has two existing relata.

Intentionality II

In my first post yesterday, I asked us to accept the following definition, for the sake of argument.

(1) Intentionality: the existence of some thoughts depends on the existence of external objects

Note my comment 'for the sake of argument'. As Bill Vallicella has commented on this post here, this definition does not coincide with Franz Brentano's definition. But then Brentano's use of the term does not coincide with the medieval usage, which is different again. The thesis I am trying to capture here is what Stephen Neale has called the 'object-dependence' of certain thoughts: that certain thoughts are intrinsically 'about' an object. Note also that by 'external' I mean genuinely separable and distinct from the person thinking: such that it could exist (in some sense) without the person thinking about it, but also such that if it did not exist, the thought could not exist.

I am exploring the reasons that some philosophers have given for believing the thesis of intentionality or 'object dependence' as I am characterising here. The first step is to characterise thought in terms of the language expressing it, in a way that implies (1) **, as follows.

(2A) A thought is the same as the signification of the proposition* expressing that thought
(2B) The signification of some propositions (namely singular propositions) depends on the existence of external objects

This doesn't get us that far, but it focuses the discussion. It takes us from 'thought', which in a wide sense could include any mental phenomenon such as an emotion, a musical phrase, an idea or mental image, to something narrower whose structure and composition is closely related to the structure and composition of language. This move was crucial in the development of modern analytic philosophy (in the hands of Russell, Wittgenstein and others). It was also taken for granted by the late 13th century modist philosophers who held that thought is presupposed by signification (significare praesupponit intelligere).

*I am using the term 'proposition' in its traditional sense, i.e. as signifying an indicative sentence, rather than the meaning of an indicative sentence.

** Note that, in this and all subsequent posts, I will be giving premisses that support the contentious premiss of the previous post, in terms of a (to me) uncontentious premiss labelled 'A', and a contentious premiss labelled 'B'.

Is there a problem of intentionality?

Is there a problem of intentionality? That depends what intentionality is. Let's accept the following definition, for the sake of argument.

(1) Intentionality: the existence of some thoughts depends on the existence of external objects

Is that a problem? Yes, and for two reasons.

First, a psychological reason. It is intuitive that thoughts, which are part of our mind, don't depend on the existence of objects external to our mind. If they did, we would automatically know whether there objects corresponding to them are not. For example, I can wonder whether the Antichrist exists, and I can have thoughts about the Antichrist. Or at least it seems to me that I can think about the Antichrist. And if it seems to me that I think p, that I do think that p (this is the 'Cartesian intuition' - I cannot be mistaken about the existence and nature of my own thoughts). But if a thought about the Antichrist requires that the Antichrist exists, and if I am thinking about the Antichrist, then the Antichrist exists. But that is absurd, for my thought is to question whether the Antichrist exists at all. Therefore my thought about the Antichrist does not require that the Antichrist exists.

Second, a psycho-physical reason. It seems plausible that the existence and nature of our thoughts depends upon the existence and nature of certain biological processes (i.e. in the brain). But the existence and nature of biological processes is in theory independent of things that exist outside. Therefore the existence and nature of our thoughts is independent of what exists outside.

Therefore there is a problem of intentionality. Many philosophers have tackled the problem by questioning whether we have 'Cartesian intuitions', or by theories of mind that are consistent with (1). I shall not be approaching the problem this way. The intentionality thesis, as expressed by proposition (1), seems to me fundamentally false. Instead, I shall be making a series of posts looking at the arguments for (1). More later.

Is there an English philosophy?

Some subjects are independent of the culture that first developed them. Thus, we can't really talk about German or French mathematics, except in referring to the history of their respective development. Other subjects are strongly dependent on their culture. Think poetry. Think of Shakespeare or Goethe.

Philosophy is oddly in-between. On the one hand, it is supposed to deal with eternal verities and perpetual and necessary truths. So it ought to belong with mathematics and logic or biology. On the other hand, there are so many varieties of opposing philosophical positions (Platonic realism vs nominalism, physical realism vs idealism, and so on), and many more possibly combinations of such positions, that philosophy appears almost as subjective as poetry or painting. C.S. Peirce below gives a persuasive argument that nominalism is essentially English.

From very early times, it has been the chief intellectual characteristic of the
English to wish to effect everything by the plainest and directest means,
without unnecessary contrivance. In war, for example, they rely more than any
other people in Europe upon sheer hardihood, and rather despise military
science. The main peculiarities of their system of law arise from the fact that
every evil has been rectified as it became intolerable, without any
thoroughgoing measure. The bill for legalizing marriage with a deceased wife's
sister is yearly pressed because it supplies a remedy for an inconvenience
actually felt; but nobody has proposed a bill to legalize marriage with a
deceased husband's brother. In philosophy, this national tendency appears as a
strong preference for the simplest theories, and a resistance to any
complication of the theory as long as there is the least possibility that the
facts can be explained in the simpler way. And, accordingly, British
philosophers have always desired to weed out of philosophy all conceptions which
could not be made perfectly definite and easily intelligible, and have shown
strong nominalistic tendencies since the time of Edward I, or even earlier.
Berkeley is an admirable illustration of this national character, as well as of
that strange union of nominalism with Platonism, which has repeatedly appeared
in history, and has been such a stumbling-block to the historians of philosophy.

Peirce is discussing Berkeley here. I will turn to William of Ockham later, to whom a similar point applies. Can we say that Ockham is an essentially English philosopher? Who are the other English philosophers of whom we would say, as we say of Shakespeare or Chaucer or Milton, that they are represent Englishness, or English thinking, or English tendencies?


* Peirce, C.S., "Fraser's The Works of George Berkeley", North American Review 113 (October 1871): 449-72. Review of The Works of George Berkeley, by Alexander Campbell Fraser, 1871.

The first Wikipedia philosophy article

Joseph Reagle has managed to reconstruct one of the earliest versions of Wikipedia (dating from 2001). As he says, it is a weird mixture of philosophy, geography, the United States and a huge collection of articles on Atlas Shrugged. I have copied the original article on philosophy below, probably written by Larry Sanger. It is an interesting question whether the article is better or worse than the one that exists now. While the present article has many more lists and extensive cross-references, the original article tries to get to the heart of what philosophy really is. Sanger mentions two standard theories about this. The first is that philosophy is essentially a priori. The natural habitat of the philosopher is the armchair, rather than the laboratory, or a field trip, or a museum. I think this is correct. The second is that the scope of philosophy has got ('gotten') much narrower over time. As problems got solved, they got moved out of philosophy and into the departmental sciences, until what is left is a core of apparently intractable problems (some or all of which may be solved in time, just as the problems of physics and psychology have been 'solved'). I don't think think this is correct. And more later, as I like to say.

Consider first how to distinguish philosophy from science -- from disciplines
like physics and chemistry. Well, it?s not part of philosophy to do
experiments. Experiments play little, if any, role in the solution of
philosophical problems. Now someone might object to this, if he knows much
about the intersection of philosophy and science. He might say, "But
philosophers are often referring to and interpreting the scientific work of
physicists, who do experiments about space and time and quantum mechanics.
And they are often referring to experimental work done in psychology when they
discuss philosophy of psychology."

There?s no doubting that
philosophers sometimes interpret and refer to experimental work of various kinds
-- especially in the philosophies of the different sciences. For example,
in philosophy of physics, or philosophy of psychology. But that?s not
surprising of course: the purpose of those branches of philosophy, branches like
philosophy of physics, is to help interpret the philosophical aspects of
experimental work. But at any rate it?s not the philosophers, in their
capacities as philosophers, who do the experiments.

There is a
basic historical reason why philosophy is not experimental. Originally,
"philosophy" meant simply "the love of wisdom." The "philo-" part comes
from the Greek word philein, meaning to love, and the "-sophy" part comes from
sophia, or wisdom. Originally the scope of philosophy was all abstract
intellectual endeavor. Even up until early modern times, the people we now
call "scientists" were referred to as "natural philosophers," i.e., philosophers
who study nature. Over the years, the scope of philosophy has gotten
smaller and smaller, as different sciences have spun off and become independent
disciplines in their own right. Some relatively early "spin-offs" were
physics and chemistry; more recently, just within the past 100 years, psychology
has spun off.

So of course one might wonder how thinkers knew or
sensed that a new discipline was to be treated as independent from
philosophy. The answer is that the discipline began to be prosecuted using
rigorous methods of observation and experimentation. Philosophy in its
core sense, the sense that remains today, is essentially something that one
should be able to do from one?s armchair, surrounded, at most, by some books
that scientists write. But be careful thinking about this. I
emphatically do not mean that philosophy is totally non-observational, or
non-empirical. Certainly philosophy makes use of, in a really essential
way, observations about the world. But they are, we might say, very
general observations -- observations like "It seems to me I make free choices"
and "It seems to me that killing another person, if ever necessary, requires a
really good excuse." Observations like this take a great deal of
investigation to make; they require careful attention. But most (not all)
philosophical topics require no more specialized knowledge than the average
educated person has; except perhaps specialized knowledge about philosophy
itself.

So philosophy is not experimental and its observations are
only very general, broad observations. And that is what makes it different
from natural sciences like physics, and social sciences like psychology.
So mind you, some people confuse philosophy and psychology, but they are
different. Philosophy does study the mind (and it also studies other
things besides the mind, too), just as psychology does. But the study of
the mind involved in doing psychology involves careful, specific observation of
particular mental phenomena, and experimentation; philosophers think about more
general aspects of the mind, questions like, "What is consciousness? What
is the mind itself?"

The London Greyfriars

More strange goings-on at Wikipedia. The article on the London Greyfriars, which had never existed until this week, has been put up for deletion. The reason: simply because the author was someone that Wikipedia didn't like.

The London Greyfriars has a fascinating history, not least the connection with Ockham and Chatton (and their feud, of which more should be said).

If any of you have Wikipedia accounts, you are free to vote on the matter. Even if you don't, you can easily create one, it being the 'Encyclopedia that anyone can edit'.

Internal and external time

I am still thinking about Brightly's objection to my arguments here and elsewhere. Is the impossibility of a Cantorean transfinite consciousness - a conscious moment preceded by an infinite number of conscious moments before that - simply down to the length of time such a consciousness would require? One simply cannot wait for so long. Or is it as I maintain, that the discontinuity between the transfinite consciousness and the finite one is such that the traversal of such a sequence is impossible?

Every conscious moment leads to the next, but that 'next moment' must be finitely far away. For conscious time and physical time are fundamentally different. I cannot 'cheat' infinity by sleeping for an infinite number of days then waking up on the infinitieth day. The physical time is irrelevant, for in my consciousness the passage of an infinite number of days goes unnoticed. The infinitieth day is indistinguishable from any other day in the finite series. Therefore (I would like to argue) in order to get to the infinitieth day, it is essential to be conscious of every one of the previous days. Every conscious moment (i.e. every moment of my consciousness) must be either (a) conscious of some previous moment or (b) conscious of nothing previous, in which case it is my first conscious moment, and nothing of mine preceded it.

Augustine (in the Confessions, e.g., see here) made a similar distinction between 'internal' (conscious) and 'external' (physical) time, holding that only internal time is real.

For if there are times past and future, I desire to know where they are. But if
as yet I do not succeed, I still know, wherever they are, that they are not
there as future or past, but as present. For if there also they be future, they
are not as yet there; if even there they be past, they are no longer there.
Wheresoever, therefore, they are, whatsoever they are, they are only so as
present. Although past things are related as true, they are drawn out from the
memory, -- not the things themselves, which have passed, but the words conceived
from the images of the things which they have formed in the mind as footprints
in their passage through the senses. My childhood, indeed, which no longer is,
is in time past, which now is not; but when I call to mind its image, and speak
of it, I behold it in the present, because it is as yet in my memory. Whether
there be a like cause of foretelling future things, that of things which as yet
are not the images may be perceived as already existing, I confess, my God, I
know not. This certainly I know, that we generally think before on our future
actions, and that this premeditation is present; but that the action whereon we
premeditate is not yet, because it is future; which when we shall have entered
upon, and have begun to do that which we were premeditating, then shall that
action be, because then it is not future, but present. (Confessions XI.18.23).

On this view, however, it seems difficult to explain the passage of time.

Books not bombs

I came out of a meeting at Mallet Street and behold, there was a large demonstration. I remember demonstrations from the 1970s, gradually dissipating the energy of the 1960s. This was like, and unlike, anything I had seen before. There were many similarities. There was the ‘Socialist Workers Party’ out in force. This is one of a few relics of organisations that survive from the old days. Oddly titled: what is this idea of ‘workers’? They were handing out hundreds of flags stapled onto sticks, no doubt assembled in some third world sweatshop. There were young people with stuff painted on their faces: a hippy custom that survived in the backwaters of Glastonbury and has always been there, really, without us realising what it really was in its essential nature. There were people lecturing the crowd in that odd Sid James/Ben Elton old-fashioned ‘workers’ accent that no young Londoner actually speaks . And lots of banging on drums and stuff. All this was familiar from the 1970s

But the scale and energy of it was beyond anything I had experienced. I stayed for ten minutes to listen to the speeches. Short, compressed angry sentences, followed by swelling angry noises from the crowds. Grandiose sentiments (one of them calling for an immediate general strike). Although I was only there for a short time, at the beginning of the march, it was clear it was going to be very big (as indeed it was). And though I am too old to be a victim of naïve sentiment, I succumbed to naïve sentiment. The rise in tuition fees takes the expense of education to impossible levels. Education will suffer. In particular, the classics, medieval studies, all the stuff that is not obviously ‘vocational’ will suffer. So, books are good. Bombs are bad. Support books.

Aquinas on the Metaphysics - books V and VI

Book V and Book VI of Thomas's commentary on the Metaphysics just out in the Logic Museum. Let me remind you again of the hyperlinkish wonder of the Web. I have nearly completed a translation of one of Burley's questions on the Perihermenias (which will itself shortly end up in the Museum). He says (though I don't claim fully to understand this)

[...] certain persons say that being is not the essence of a thing, but
nonetheless proceeds from the essential principles of a thing of which it is the
being, and is in the same genus by reduction with the thing of which it is the
being, just as motion is of the same genus by reduction with a finishing point.
Therefore the being of a substance is a single actuality in the genus of
substance by reduction, and is neither substance nor accident. And Thomas and
Giles hold this opinion.

The footnote in Stephen Brown's edition, (Fran. Stud. 34 (1974) 200-295) refers us to Thomas commentary on book IV, IV, lect. 2 n. 558. In the old days you would have to look for some old book, probably in some university library. Now you can just follow the link. And it doesn't end there, because the commentary is linked right back to Aristotle's text.

What Thomas says is as follows. As I said, I don't claim to understand it fully.

Latin

English

Sed in primo quidem non videtur dixisse recte. Esse enim rei quamvis sit aliud ab eius essentia, non tamen est intelligendum quod sit aliquod superadditum ad modum accidentis, sed quasi constituitur per principia essentiae. Et ideo hoc nomen ens quod imponitur ab ipso esse, significat idem cum nomine quod imponitur ab ipsa essentia.

558. But in regard to the first point he does not seem to be right; for even though a thing’s existence is other than its essence, it should not be understood to be something added to its essence after the manner of an accident, but something established, as it were, by the principles of the essence. Hence the term being, which is applied to a thing by reason of its very existence, designates the same thing as the term which is applied to it by reason of its essence.

Anaxagoras and the argument from design

Anaxogoras (500-428 BC) seems to have been the first to suggest that ‘blind’ causation and deterministic mechanical features of the world cannot explain the order and harmony we see in the universe. Many or all of the operations of nature seem to be directed towards specific ends. Anaxogoras – apparently reacting to contemporary atomistic theories that deterministically explained everything in terms of fixed laws of the motion of elementary particles – thought that such design was evidence of an agency which was rational and non-physical. This idea clearly appealed to Aristotle, and may have been an influence on his thought. He speaks approvingly:

When one man said, then, that reason was present - as in animals, so throughout
nature - as the cause of order and of all arrangement, he seemed like a sober
man in contrast with the random talk of his predecessors. We know that
Anaxagoras certainly adopted these views, but Hermotimus of Clazomenae is
credited with expressing them earlier. Those who thought thus stated that there
is a principle of things which is at the same time the cause of beauty, and that
sort of cause from which things acquire movement. [Metaphysics book I, 984b18

Without doubt, the idea became influential as a result of Aristotle. He argues (in Book 12 of the Metaphysics) that the world is moved by an eternal prime mover who is the source of all process and change, while not itself subject to process or change. This substance does what is the highest form of life ought to do, namely to think. ‘The rule of many is not good; one ruler let there be.’ Thomas Aquinas finally unified Catholic and ancient Greek with this idea at its centre.

Sed pluralitas principatuum non est bonum. Sicut non esset bonum quod essent
diversae familiae in una domo, quae invicem non communicarent. Unde relinquitur
quod totum universum est sicut unus principatus et unum regnum. Et ita oportet
quod ordinetur ab uno gubernatore. Et hoc est quod concludit, quod est unus
princeps totius universi, scilicet primum movens, et primum intelligibile, et
primum bonum, quod supra dixit Deum, qui est benedictus in saecula saeculorum.
Amen. [Commentary on the Metaphysics, book 12]

*Note (quick advertisement for the Logic Museum) that the Museum is still, AFAIK, the only place on the internet where you can link to Aristotle via Bekker numbers. The coverage and scope of Aristotle, and the medieval writers who cited his work, is increasing all the time.

Cantor's Angel

The brief argument I gave here needs expanding. I wrote:

Every day I wake up from sleep, that 'little slice of death', and become
conscious. Imagine the following thought-experiment. I wake up an infinite
number of times. Could I have a conscious moment after that infinite sequence?
Is it possible that there could be a waking moment belonging to my consciousness
such that there are an infinite number of waking moments before that? Surely
not. I can't think of an argument to prove it, rather, it seems an irreducible
part of my idea of consciousness that I cannot conceive of an actual or
'completed' infinity of conscious moments.

Imagine the following thought-experiment. My soul is in hell, and I am being tormented by a demon dentist who is removing my teeth by drilling through their nerves in an exquisitely painful way. My agonising screams are echoing through the halls of the inferno. After all my teeth are removed, they are supernaturally replaced, and the whole process begins again. I understand that this process is to continue infinitely. (There is a colourful depiction of the infinity of hell by James Joyce here).

While I am waiting for the demon to replace my teeth, a Cantorean angel whispers to me. I must not despair. After this process has been repeated infinitely many times, my soul will enter a transfinite Cantorean paradise. I will still be conscious of every one of the infinite moments that has passed in hell. But those moments will now be behind me. They have all happened, infinitely many of them, an infinite number of teeth drilled out and replaced.

Now I ask. Does the pronouncement give me any hope? Surely not. I cannot hope ever to escape this infinite painful process; I have no hope. But if the consciousness in the Cantorean paradise were my consciousness, I would have such a hope. Therefore the consciousness in the Cantorean paradise cannot be my consciousness.

My consciousness is a set of conscious moments tied together by their belonging to a single consciousness. Any future moment must be such that I can hope or expect to experience it by the process of waiting. Thus no future moment of the same consciousness can be such that it is preceded by an infinite number of such moments belonging. For I cannot hope or expect the experience of such a moment. I would be waiting for and expecting something that will never happen to me. (I concede it is logically possible that such a moment could happen to someone else, who was remembering my conscious moments as if they were my own, but more on that later).

Completion and consciousness

Of course the argument I gave yesterday is a blatant fallacy. We have

• Achilles will not reach the tortoise before the sequence is completed
• The sequence is never completed.

but the word 'complete' is being used in different senses in the two propositions, and so the one does not imply the other. In the first sense it means 'happened', and since it seems possible for every event in the infinite sequence to have happened, it is therefore possible for the sequence to be 'complete' in that sense. In the second sense it means something like 'terminated', and in that sense the second proposition seems false. If the sequence were terminated at some point, then Achilles will not reach the tortoise, but we have no argument that it will not be terminated.

But the idea of completion suggests another argument. Every day I wake up from sleep, that 'little slice of death', and become conscious. Imagine the following thought-experiment. I wake up an infinite number of times. Could I have a conscious moment after that infinite sequence? Is it possible that there could be a waking moment belonging to my consciousness such that there are an infinite number of waking moments before that? Surely not. I can't think of an argument to prove it, rather, it seems an irreducible part of my idea of consciousness that I cannot conceive of an actual or 'completed' infinity of conscious moments. (Complete in the first sense of 'already happened').

You object: what if I failed to wake at some point, an infinite number of days passed, and then I woke up? I reply: physical time and conscious time are different. If I go to sleep on Saturday, and an infinite number of days pass, and I wake up, it is no different for me than if I had woken up on Sunday. I cannot conceive of a sequence of infinite waking moments that I can ever 'escape from', in the sense that every one of those moments was behind me. Perhaps there could be some consciousness after such a sequence, but it would not be my consciousness.

Thus any two waking consciousnesses of mine must be connected by a series of finite waking moments. Which leads to the following paradox. Given that every moment of my consciousness is in a sense a waking moment - the only difference being the lapse of physical time which we assume occurs during sleep, and which we assume does not occur when we are waking - and given that any series of conscious moments belong to my consciousness must be finite, how is it that are consciousness also appears continuous. i.e. there are no obvious gaps or 'flickers' in consciousness such as we see in the early movies? How can consciousness be both discrete and continuous?

Two masters of the beat

Joe Morello from 1961, John Bonham from 1971. The influence is clear. Mick Wall recounts

The best thing Bill [Harvey, a friend of Bonham's in the early sixties] ever did
for you was to introduce you to the Dave Brubeck quartet, whose drummer Joe
Morell was famous for his finger control technique - this weird bloody thing he
did with his fingers, tapping on the snare drum in a way that made it sound
like a lion's roar one minute, then doing something else that made it sound like
a bow and arrow the next. You couldn't get over the idea of using your bare
hands on the drums. You thought it was the best thing since sliced bread. Then
Bill showed you another 'great pattern' from a Humphrey Lyttleton recording he had
called 'Caravan', where the drummer played floor-toms with his hands. You
couldn't get over it and begged Bill to show you how it was done. 'Forget it',
he'd said. But you bloody well did, mate. You bloody fucking well did!
(Mick Wall, When Giants Walked the Earth , 2008, p/36)

It's easy to forget the influence that jazz (as well as folk) had on the development of modern rock music in the 1960s.

The essence of Socrates

I am whiling away the time by working on a translation of Burley’s Questions on the Perihermenias. The question on essence and existence is fascinating, but it is almost a parody (and thus a self-parody) of a scholastic quaestio. A sample:

‘Socrates is the essence of Socrates’ is false – for if Socrates and
his essence were the same, whatever were a part of Socrates would be a part of
the essence of Socrates, and then the foot of Socrates would be a foot of the
essence of Socrates, and belonging to the essence of Socrates.

Completing Zeno

Let's restate the Zeno argument as follows.

(1) At time t2 Achilles reaches a point where the tortoise was at t1, at t3 he reaches the point where the tortoise was at t2, at t4 he reaches the point where the tortoise was at t3, and so on.

(2) Achilles will not reach the tortoise before the sequence outlined in (1) above is completed,

(3) The sequence is never completed.

(4) Achilles will never reach the tortoise.

Unlike the IEP version I referenced below, the conclusion appears to follow logically from the premisses. Furthermore, it does not rely on assumptions like 'cannot do infinitely many things in a finite time'. It relies simply on the definition of an infinite sequence as one which is endless, not terminated, not completed.

Well it appears valid, but is it? More tomorrow, and comments welcome.

De Hebdomadibus

Boethius logical-theological work De Hebdomadibus now in the Logic Museum, in the usual parallel Latin-English layout.

More on Zeno

I asked earlier how the four premisses of Zeno's argument given in the IEP imply the conclusion that Achilles never reaches the tortoise.

Clearly there are other assumptions that have to be made. There is the ‘and so on’ of premiss 4. But how does that work? Suppose Achilles aims at the exact spot Y where he is going to overtake the tortoise. Clearly when he has reached that spot, he will have reached the tortoise. If he reaches any spot X before that, he will have not reached the tortoise. So all the ‘argument’ appears to be saying, it seems, is that if we take any point X before Y, then there is some distance to go. And if we take any spot X’ between Y and X, there is still some distance to be ‘and so on’. But this ‘and so on’ doesn’t prove anything. It proves simply (or rather, it assumes that) we can take any distance whatever, and cut it somewhere. How does that prove ‘Achilles will never reach the tortoise’?

Graham Priest has a slightly different version of the argument. He says (I paraphrase) In order to get from a to b, you must first get to each point between a and b. But there are infinitely many points between a and b. Hidden premiss: to get to something = to do something. Therefore to get from a to b in a finite time, you must do infinitely many things. But you can’t do infinitely many things in a finite time. Therefore etc. But there is much to challenge there. Is the hidden premiss correct? Is ‘getting to’ a point the same as ‘doing something’? Can we actually ‘get to’ a mathematical point? How? We can cross such a point, of course. But then the argument amounts to this: there are infinitely many collections of finite distances between a and b, and we can traverse any such collection in a finite time. Indeed, clearly we can, for the total length of any such collection will be the length between a and b.

Aristotle mentions the argument several times in the Physics, arguing that we must distinguish the ‘actual’ from the ‘potential’ infinite, but this distinction is not very clear. I don't have the book to hand, so will post something later.

Is Zeno's Paradox a Paradox?

Brandon Watson has a discussion on Zeno's Paradox here. He refers to a version of the argument given at the Internet Enyclopedia, but I don't follow it. The salient points are listed below. I can see that 1-4 are true. But why is 5 true? How are 1-4 supposed to imply 5?

1. The tortoise has a head start, so if Achilles hopes to overtake it, he must run at least to the place where the tortoise presently is
2. But by the time he arrives there, it will have crawled to a new place.
3. So then Achilles must run to this new place.
4. But the tortoise meanwhile will have crawled on, and so forth.
5. Achilles will never catch the tortoise, says Zeno.

A philosophical scandal

Freddoso writes:

It is something of a philosophical scandal that most of the major works of
William of Ockham, himself an Englishman, have yet to be translated into
English. The Summa Logicae, which contains Ockham's most
extensive treatment of logic and philosophy of language, is a case in point.
Even given the translation of part II found here and Michael Loux's recent
translation of part I, more than half of the Summa Logicae remains
untranslated [Ockham's Theory of Propositions, Indiana 1998] .

Freddoso was writing in 1998, and since then the second part of Part III has been translated by John Longeway (and discussed here in a number of posts). But still (as far as I know) there is no translation of the first part of III (on syllogisms, which covers Aristotle's Prior Analytics) and the third part (on consequences, which broadly cover the Topics). There is also much of the Ordinatio that remains.

This is partly explained by the fact that Ockham has had no 'champions'. Aquinas' work has received attention since the nineteenth century because of his role in the intellectual history of the Catholic church. Scotus has always received the support of the Franciscans (although there is less of Scotus in English than Aquinas). Because of Ockham's perceived apostasy, and perhaps because he was perceived as a 'Catholic philosopher' by the early moderns, has received no such attention.

But it is still a scandal that the works of one of England's greatest philosophers have never been completely translated into English.

Faith, understanding and apostasy

The second of the second part of Summa Theologiae now available in the Logic Museum. Questions 1-7 on the object of faith; the virtue of faith; the cause and effects of faith; questions 8 and 9 on understanding and knowledge, and questions on unbelief, heresy, apostasy and blasphemy.

Augustine on Adam's sin

Advent is nearly here and I shall try to revive my custom of publishing a seasonal Latin hymn. Here is one from three years ago (actually from as long ago as the 12th century). It begins Fregit Adam interdictum – Adam broke God’s commandment, and left the punishment of his sin to all his descendants. One of the themes of Advent is the reminder of this original sin, as well as what follows from it – the hope for a saviour, the virgin birth, the defeat of sin and the Devil.

Below is a passage from Augustine’s City of God, which proves that original sin exists. The evidence for it is the ‘host of cruel ills’ which the world is filled with. These can be restrained by laws and punishments, but law and punishment is itself a means of restraining the evil desires that we are born with. Even great innocence is not a sufficient protection against the evil of this world, for God permits even young infants to be tormented in this life, teaching us ‘to bewail the calamities of this life, and to desire the felicity of the life to come’.

At the end he observes that as well as the gift of grace, there is also the gift of philosophy which – he cites Cicero with apparent approval – is the greatest gift that the gods have given to man.

“That the whole human race has been condemned in its first origin, this life
itself, if life it is to be called, bears witness by the host of cruel ills with
which it is filled. Is not this proved by the profound and dreadful ignorance
which produces all the errors that enfold the children of Adam, and from which
no man can be delivered without toil, pain, and fear? Is it not proved by his
love of so many vain and hurtful things, which produces gnawing cares, disquiet,
griefs, fears, wild joys, quarrels, lawsuits, wars, treasons, angers, hatreds,
deceit, flattery, fraud, theft, robbery, perfidy, pride, ambition, envy,
murders, parricides, cruelty, ferocity, wickedness, luxury, insolence,
impudence, shamelessness, fornications, adulteries, incests, and the numberless
uncleannesses and unnatural acts of both sexes, which it is shameful so much as
to mention; sacrileges, heresies, blasphemies, perjuries, oppression of the
innocent, calumnies, plots, falsehoods, false witnessings, unrighteous
judgments, violent deeds, plunderings, and whatever similar wickedness has found
its way into the lives of men, though it cannot find its way into the conception
of pure minds?

These are indeed the crimes of wicked men, yet they
spring from that root of error and misplaced love which is born with every son
of Adam. For who is there that has not observed with what profound ignorance,
manifesting itself even in infancy, and with what superfluity of foolish
desires, beginning to appear in boyhood, man comes into this life, so that, were
he left to live as he pleased, and to do whatever he pleased, he would plunge
into all, or certainly into many of those crimes and iniquities which I
mentioned, and could not mention?

But because God does not wholly desert those whom He condemns, nor shuts up in His anger His tender mercies, the human race is restrained by law and instruction, which keep guard against the ignorance that besets us, and oppose the assaults of vice, but are themselves full of labor and sorrow.

For what mean those multifarious threats which are
used to restrain the folly of children? What mean pedagogues, masters, the
birch, the strap, the cane, the schooling which Scripture says must be given a
child, "beating him on the sides lest he wax stubborn," Sirach 30:12 and it be
hardly possible or not possible at all to subdue him? Why all these punishments,
save to overcome ignorance and bridle evil desires-these evils with which we
come into the world? For why is it that we remember with difficulty, and without
difficulty forget? learn with difficulty, and without difficulty remain
ignorant? are diligent with difficulty, and without difficulty are indolent?
Does not this show what vitiated nature inclines and tends to by its own weight,
and what succor it needs if it is to be delivered?

Inactivity, sloth, laziness, negligence, are vices which shun labor, since labor, though
useful, is itself a punishment.But, besides the punishments of childhood,
without which there would be no learning of what the parents wish,-and the
parents rarely wish anything useful to be taught,-who can describe, who can
conceive the number and severity of the punishments which afflict the human
race,-pains which are not only the accompaniment of the wickedness of godless
men, but are a part of the human condition and the common misery,-what fear and
what grief are caused by bereavement and mourning, by losses and condemnations,
by fraud and falsehood, by false suspicions, and all the crimes and wicked deeds
of other men? For at their hands we suffer robbery, captivity, chains,
imprisonment, exile, torture, mutilation, loss of sight, the violation of
chastity to satisfy the lust of the oppressor, and many other dreadful evils.
What numberless casualties threaten our bodies from without,-extremes of heat
and cold, storms, floods, inundations, lightning, thunder, hail, earthquakes,
houses falling; or from the stumbling, or shying, or vice of horses; from
countless poisons in fruits, water, air, animals; from the painful or even
deadly bites of wild animals; from the madness which a mad dog communicates, so
that even the animal which of all others is most gentle and friendly to its own
master, becomes an object of intenser fear than a lion or dragon, and the man
whom it has by chance infected with this pestilential contagion becomes so
rabid, that his parents, wife, children, dread him more than any wild beast!
What disasters are suffered by those who travel by land or sea! What man can go
out of his own house without being exposed on all hands to unforeseen accidents?
Returning home sound in limb, he slips on his own doorstep, breaks his leg, and
never recovers. What can seem safer than a man sitting in his chair? Eli the
priest fell from his, and broke his neck. How many accidents do farmers, or
rather all men, fear that the crops may suffer from the weather, or the soil, or
the ravages of destructive animals? Commonly they feel safe when the crops are
gathered and housed. Yet, to my certain knowledge, sudden floods have driven the
laborers away, and swept the barns clean of the finest harvest.

Is innocence a sufficient protection against the various assaults of demons? That
no man might think so, even baptized infants, who are certainly unsurpassed in
innocence, are sometimes so tormented, that God, who permits it, teaches us
hereby to bewail the calamities of this life, and to desire the felicity of the
life to come. As to bodily diseases, they are so numerous that they cannot all
be contained even in medical books. And in very many, or almost all of them, the
cures and remedies are themselves tortures, so that men are delivered from a
pain that destroys by a cure that pains. Has not the madness of thirst driven
men to drink human urine, and even their own? Has not hunger driven men to eat
human flesh, and that the flesh not of bodies found dead, but of bodies slain
for the purpose? Have not the fierce pangs of famine driven mothers to eat their
own children, incredibly savage as it seems? In fine, sleep itself, which is
justly called repose, how little of repose there sometimes is in it when
disturbed with dreams and visions; and with what terror is the wretched mind
overwhelmed by the appearances of things which are so presented, and which, as
it were so stand out before the senses, that we can not distinguish them from
realities! How wretchedly do false appearances distract men in certain diseases!
With what astonishing variety of appearances are even healthy men sometimes
deceived by evil spirits, who produce these delusions for the sake of perplexing
the senses of their victims, if they cannot succeed in seducing them to their
side!

From this hell upon earth there is no escape, save through the
grace of the Saviour Christ, our God and Lord. The very name Jesus shows this,
for it means Saviour; and He saves us especially from passing out of this life
into a more wretched and eternal state, which is rather a death than a life. For
in this life, though holy men and holy pursuits afford us great consolations,
yet the blessings which men crave are not invariably bestowed upon them, lest
religion should be cultivated for the sake of these temporal advantages, while
it ought rather to be cultivated for the sake of that other life from which all
evil is excluded. Therefore, also, does grace aid good men in the midst of
present calamities, so that they are enabled to endure them with a constancy
proportioned to their faith. The world's sages affirm that philosophy
contributes something to this,-that philosophy which, according to Cicero, the
gods have bestowed in its purity only on a few men. They have never given, he
says, nor can ever give, a greater gift to men. So that even those against whom
we are disputing have been compelled to acknowledge, in some fashion, that the
grace of God is necessary for the acquisition, not, indeed, of any philosophy,
but of the true philosophy. And if the true philosophy-this sole support against
the miseries of this life-has been given by Heaven only to a few, it
sufficiently appears from this that the human race has been condemned to pay
this penalty of wretchedness. And as, according to their acknowledgment, no
greater gift has been bestowed by God, so it must be believed that it could be
given only by that God whom they themselves recognize as greater than all the
gods they worship.

Ockham's Razor

"Ockham's Razor" is a misnomer. The phrase itself was not coined until 1852 by Hamilton. The modern formulation of the princple, 'Entities should not be multiplied without necessity', is not found in exactly this wording in the medieval literature, and it seems to have originated with the Scotist Commentator, John Ponce of Cork in 1639. The medieval wording, used by both Scotus and Ockham, was 'Pluralitas non est ponenda sine necessitate' - 'plurality is not to be posited without necessity', and 'Frustra fit per plura, quod potest fieri per pauciora' - 'it is vain to make through several, that which can be made through fewer'.

Neither of these capture Ockham's nominalism - a realist may agree that entities should not be multiplied without necessity, but he (or she) will argue against the nominalist that universals re necessary. Ockham neatly formulates a principle that captures his nominalism in Summa book I, chapter 51, where he accuses 'the moderns' of two errors, and says that the root of the second error is to multiply entities according to the multiplicity of terms and to suppose that every term has something real corresponding to it. He says grumpily that this is erroneous and leads far away from the truth. ('Secunda radix est multiplicare entia secundum multitudinem terminorum, et quod quilibet terminus habet quid rei; quod tamen abusivum est et a veritate maxime abducens').

There is more about the myth of the Razor here.

Reply to Freeman

Charles Freeman has commented on my last post in a way that misunderstands my point so fundamentally that it probably needs stating again, more clearly. It was as follows.

1. Many of Aristotle's scientific explanations are obviously wrong.

2. On the assumption that Greek science ended in the 4th century, Greek science had about 700 years to correct these obvious errors. But it didn't (in the sense that it did not arrive at a consensus of where Aristotle was wrong).

The first point is not simply that Aristotle was wrong. It was that he was obviously wrong. For example, he states in De Caelo (tr. Guthrie, Cambridge 1960 pp. 49-51) that if a weight falls a certain distance in a given time, a greater weight will move faster, with a speed proportional to its weight. This is obviously wrong: obvious in a way that his statement about why glass is transparent is not obviously wrong. To refute his theory about glass requires instrumentation and a complex atomic theory, neither of which was available to Aristotle. So while his transparency theory is wrong, it was not obviously wrong. But to refute his theory about falling bodies requires only a few simple experiments. In the 6th century A.D., loannes Philoponus challenged this as follows.

But this [i.e. Aristotle's theory] is completely erroneous, and our view may be
corroborated by actual observation more effectively than by any sort of verbal
argument. For if you let fall from the same height two weights of which one is
many times as heavy as the other, you will see that the ratio of the times
required for the motion does not depend on the ratio of the weights, but that
the difference in time is a very small one." [M. R. Cohen and I. E. Drabkin, "A
Source Book in Greek Science" (McGraw Hill. N.Y.) 220 (1948) - my emphasis].

So my first point stands: some of Aristotle's scientific observations are obviously wrong, in a way that the technology and understanding of the time could easily have shown. On my second point, that Greek science did not correct these obvious mistakes, the history shows that clearly enough. You may object that Philoponus was Greek, and that he spotted at least one obvious error. I reply: Philoponus' observation does not amount to a scientific consensus. We make progress in science when we arrive at a view that is not necessarily correct, but which is accepted by a majority, or a significant majority, of the scientific community. This was not properly achieved until Galileo. And note also that Philoponus was writing somewhat later than Freeman's 'cutoff point' of 381 AD. Moreover, he was a Christian thinker.