Logic and censorship

Can logic help us with arguments about sexual morality, censorship and so on? Only so far it can expose contradictions and fallacies. At some point in any such argument, someone will invoke a principle or universal proposition, and the problem with principles or universal propositions is that they do not allow exceptions. The proposition 'all swans are white' is false so long as there exists one black swan. It's quite binary. So anyone who asserts such a principle cannot allow any exception to it, without modifying it in such a way that it is still a principle, i.e. such that it contains no arbitrary exceptions or modifications or special pleading. For example, the guy arguing here is dangerously close to a principle:

That's how repressive regimes begin. First you start with the sexual content that offends people, then you move on to the religious content, and finally, the political content. Funny how it's always the people screaming "freedom" and "liberty" the loudest who are always trying to curtail it.

This is called the 'slippery slope' argument. As soon as you are on the slope, you will always slide to the bottom, therefore you must not get onto the slope in the first place. In this person's case, being on the slope means having an image filter on Wikipedia, and the universal principle being "You must not filter out content that offends people". But such a principle allows no exception. Would this person not want to 'filter out' content such as child pornography or torture pornography or snuff pornography?

It's not obvious what's obvious

"It ain't obvious what's obvious". Thanks to the Maverick for that insight by Hilary Putnam.  I suppose everyone knows the mathematician's joke about the lecturer how - discussing some result - says 'That's obvious'.  He then pauses, looks down, then goes off for about twenty minutes.  Then he comes back and announces 'Yes, it's obvious'.

Judging from the comments, there's been a bit of misunderstanding about my position on the 'thin conception' of existence.  I don't necessarily agree with the conception.  My question is whether the brief arguments given by Maverick, and which seem as obvious as day to him, really are obvious. Now I think, pace Dr. Putnam, there is a simple test for obviousness. If you can state your position or argument in less than about five sentences, and if the terms are clear or well-defined, or have a common and undisputed meaning, if any assumptions underlying the position are beyond dispute, and if all deductive steps are valid, then  it is obvious. Otherwise it isn't.

Now Maverick's argument, as I understand it, is this:

The thin conception of 'exists' is that 'An F exists' means the same as 'The concept *F* is instantiated'
But if *F* is instantiated, then it is instantiated by an individual that exists
Therefore the thin conception of 'exists' is circular

This is deceptively simple, but fails my test for obviousness.  Why?  The subject of the conclusion is 'the thin conception of exists'.  The predicate is 'circular'.  The predicate of the conclusion is called the 'major term' and it is an undisputed rule of logic that the major term should appear in the premisses. Which of course it doesn't.  This would probably be fine if the idea of a circularity were undisputed and clear, by I have argued elsewhere that it isn't. It is very slippery.

So what is needed is an argument of the following form:

The thin conception of existence is of form X
Any conception of form X is circular
The thin conception of existence is circular.

I would accept any argument of that form as 'obvious'.  And I hope that clears me of any charges of being disingenuous.

A brief history of existence

Yesterday’s post caught a few people by surprise. What is the background to all that? What is the ‘thin’ conception of being? Etc. Of course there is a background to this, and it is large, and it should be part of the baggage of anyone studying modern analytic philosophy. So here is a brief history of the subject.

We start in the fourth century B.C. with Aristotle and his Perihermenias, his treatise on the second operation of the understanding, where two simple concepts are combined to form a proposition. In the tenth chapter he has an obscure paragraph about the verb ‘is’ being predicated as a ‘third elements’. In the scholastic Latin which was used to translate Aristotle’s Greek, this is rendered as tertium adiecens, literally third adjoinment or third adjective. What on earth does that mean? Thomas (in the middle of the thirteenth century) makes a valiant attempt to explain it in his commentary on the work. He says that sometimes the verb ‘is’ is predicated by itself in a proposition, such as in “Socrates is“ i.e. Socrates exists. By this we signify that Socrates really exists. That is predication of ‘is’ as a second element, i.e. existence predicated of itself, existence as a predicate. At other times it is not the main predicate but is joined to the main predicate to connect it to the subject, as in “Socrates is white.” Here we are not asserting that Socrates exists, but rather attributing whiteness to him by the verb ‘is’. Hence, ‘is’ said to be a third element, not because it is a third predicate, but because it is a third element or word in the proposition.

Roll forward to the eleventh century and to Anselm and his so-called ontological argument. This was an argument to prove the existence of God through logic alone, by proving that the concept of God has the concept of existence built into it. He argues as follows

… it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist;. and this being thou art, O Lord, our God. (Proslogion chapter 3).

I won’t go into the tortuous logical details of the argument now, but the argument is generally thought to be invalid, and the reason is generally thought to be treating the verb ‘is’ as a predicate, i.e. as the main predicate in the sentence, rather than as a copula or ‘third element’ which simply joins the real predicate (being wise or being good) to the subject.

The whole issue was extensively discussed in the late thirteenth century, but this is rarely if ever mentioned in modern philosophy courses because of the assumption that all philosophy began in the early modern era as a byproduct of the glorious enlightenment process. Thus students tend to hear about the ontological argument in the context of Descartes, rather than Anselm or thirteenth century philosophers. Descartes writes in his Meditation V:

… the existence can no more be separated from the essence of God, than the idea of a mountain from that of a valley, or the equality of its three angles to two right angles, from the essence of a [rectilinear] triangle; so that it is not less impossible to conceive a God, that is, a being supremely perfect, to whom existence is awanting, or who is devoid of a certain perfection, than to conceive a mountain without a valley.

Note that Descartes was writing in Latin, another fact that is sometimes overlooked. This is because we associate the enlightenment process with the modern romance languages rather than Latin, which belongs to the dark ages before the early enlightenment.

Roll forward again to Kant, the glorious eighteenth century philosopher of the high enlightenment, who famously tells us (in The Critique of Pure Reason, A 598/B626) that existence is not a ‘real predicate’. This was a period when all good philosophers wrote in German (Sein* ist offenbar kein reales Praedikat).  'Existence' is not a determining predicate which enlarges the concept of the subject to which it is added, in the way that ‘white’ enlarges the concept ‘man’ by increasing its intension but reducing its extension. When philosophers talk about existence not being a predicate, it is usually Kant’s discussion they have in mind. (Maverick has strong views about this, but I’ll pass over those for now).

Kant had little influence on modern logic, however. The main development of the question whether ‘existence is a predicate’ comes in the middle of the nineteenth century. I have a bit about the history in a discussion of Brentano here, and see also this contemporary paper here. Brentano argued that we can always translate any sentence containing the verb ‘exists’ into one that does not contain it. Thus ‘a sick man exists’ translates to ‘some man is sick’. This idea is the direct ancestor of the modern view, often associates with Quine, that existence is what the existential quantifier expresses. It is uncertain how it got into modern predicate logic, as there are at least three contenders, namely Brentano, Frege and the American Charles Peirce. Probably it was Peirce via the German logician Ernst Schroeder. I wrote a short piece on this for Wikipedia years ago, which is still there (permalink).

So the issue of detail is whether the verb ‘is’ is simply a copula that joins subject to predicate. This is essentially the view embedded into modern predicate calculus and the use of ‘existential’ quantifier. The general and important position that it underlies is whether we can prove the existence of God, or not. If existence is merely ‘someness’, i.e. if ‘existing thing’ is equivalent to ‘something’, the ontological argument does not get off the ground. But if it is something larger or ‘thicker’, the argument at least stands a chance. Thus large things sometimes hang on small things.

One day I should write this history up properly. Every discussion I see has some part of the history, without taking a view of the whole.

*I literally just noticed that Kant is using the German 'sein', which is the infinitive of the German verb 'to be'.  English philosophy tends to follow Latin philosophy in using the distinct verbs 'to be' (esse) and 'to exist' (existere). That distinction is a subject in its own right, which I will pass over for now.

Not proven, not guilty

I have been leafing through Ueberweg's System of Logic, which is an interesting nineteenth-century and Teutonic look at that subject.  Very few logic text books would now mention Hegel's logic, for example.  He has an interesting discussion of the principle of Excluded Middle, the one that says any sentence, or its negation must be true.  He claims (p. 263) that the principle may be invalid in certain instances. For example, 'not proven' fills an obvious gap between 'guilty' and 'not guilty'.

Surely not.  What does 'not proven' mean?  It means not proven to be guilty.  'It is proved that' is an operator on the proposition 'x is guilty', not a third truth value filling the gap between sentence and negation. What an elementary mistake, or have I missed something?

Kilwardby on the usefulness of logic

As I argued before, Ockham's nominalism is not simply about whether universals exist or not.  It is more radical than that: problems in philosophy and theology arise from misunderstandings and disagreements about logic.  This is not an idea that originated with him, as the following quote* from the mid thirteenth-century theologian Robert Kilwardby shows.

The origin of this science [i.e. logic] ... was as follows.  Since in connection with philosophical matters there were many contrary opinions and thus many errors (because contraries are not true at the same time regarding the same thing), thoughtful people saw that this stemmed from a lack of training in reasoning, and that there could be no certainty in knowledge without training in reasoning.  And so they studied the process of reasoning in order to reduce it to an art, and they established this science by means of which they completed and organised both this [science] itself and all others; and it is the science of the method of reasoning on all [subject] matters.

Note that 'logic' in the medieval period covered more than formal logic, and covered metaphysics, semantics, informal and demonstrative reasoning as well. Nor did symbolic logic exist.  Medieval logic is the logic of natural language, as ordinary people use it in argumentation.

*De ortu scientarum, ed. Albert G. Judy, London, The British Academy, 1976, chapter 53.

Street of straw

I gave an example in this post from June 2010 of the odd little details of a man’s life that occasionally obtrude from otherwise serious and impersonal work. I just found another in Buridan’s Summulae de dialectica Book I c. 7. Gerardus est cum Buridano; ergo ipse est in vico Straminum. What is he on about? Well, the Vicus Straminis or street of straw – so-called from the straw-strewn floors of the schools, was in the area still known as the Latin Quarter, the centre of the Arts schools of Paris. Petrach calls it the strepidulus straminum vicus, the noisy street of straws, presumably because of the incessant noise of the disputation going on. This was where Buridan would have conducted his lectures in the 1330s, and presumably spent so much time there that if Gerard is with Buridan, then he is in the Vicus Straminis.

The street is now called the Rue du Fouarre – there’s a bit about it in the French Wikipedia, but seems to have retained little of its former scholastic glory. The article quotes Balzac, who says that it was once the most famous street in Paris in the thirteenth century. But now (that is, in Balzac’s day), it is the poorest one.

Traditional logic at the Mises Institute

"Jake" writes to me at the Logic Museum saying that David Gordon at the Mises Institute recently held an online logic course in which he used Joyce's Principles of Logic as the class's primary text. "Very intriguing and delightful to see that text being used for a 250-plus-person class in 2011". I doubted Jake for a second, but it seems absolutely genuine. Why would anyone teach a subject that appears outdated and outmoded ever since the famous developments of Frege and Russell and Godel and all the rest? Perhaps the key is Gordon's remark that "The course will emphasize ordinary language reasoning rather than mathematical logic". And he writes

It was not always this way. Logic used to be a key component [of] liberal education: it was part of the classic “trivium”. Being able to masterfully wield logic in debate enabled Peter Abelard to advance medieval philosophy past the Neoplatonic rut it was mired in, and made him the closest thing in his day to a rock star. The School of Salamanca used scholastic logic to give birth to economic theory. Even after scholasticism was unfairly discredited, logic was still widely studied by schoolboys throughout the west. The Austrian School used logic to rigorize and advance economic science. However, the rise of positivism rang the death knell for the widespread study of logic.

And rightly so. While mathematical logic is excellent mathematics, it doesn't capture everything about human reasoning using ordinary language. In particular, as I have emphasised repeatedly here, it captures hardly anything of the interesting and difficult bits. Thank you Dr Gordon.

Some of Joyce's Logic is available at the Logic Museum here.

Logic and scientific reasoning

This is a follow-on from my earlier post about whether Aristotle's account of scientific reasoning truly captures what scientific reasoning is. He describes two forms: propter quid where we reason from cause to effect, and quia, where we reason from effect to cause.

Propter quid
Being an A is the cause of anything being a B
This X is an A
This X is a B

Quia
Being an A is the only cause of anything being a B
This X is a B
This X is an A

Neither of these captures the process of geniune scientific reasoning or discovery. In propter quid, the major premiss cannot be known unless the causal connection 'A causes B' has already been established. Since proof of the causal connection is the end-product of scientific reasoning and methodology, rather than the beginning, Aristotle's syllogism captures nothing useful. The same objection applies to the quia form, with the additional objection that the 'only' qualification cannot be established with any certainty at all. Scientific reasoning involves constructing a model of reality that explains the observed effects. It is difficult to establish that such a model is the only one. Ptolemy's model of the solar system (where the earth is at the centre) explained the observations available to ancient scientists. Copernicus' model (sun at the centre, circular orbits) explains the same observations, but in a different way. Kepler's model (sun at the centre, elliptical orbits) is different again. Further changes and refinements to this model continued into the twentieth century. It is difficult to prove that any model is the only explanation of the observed effects.

And in any case, how could such a simple syllogism as Aristotle's capture the essence of what is essentially a complex reasoning process that could take many forms?

See also Thomas Reid on the utility of logic.

"The art of syllogism produced numberless disputes, and numberless sects who
fought against each other with much animosity, without gaining or losing ground,
but did nothing considerable for the benefit of human life. The art of
induction, first delineated by Lord Bacon, produced numberless laboratories and
observatories, in which nature has been put to the question by thousands of
experiments, and forced to confess many of her secrets that before were hid from
mortals: and, by these, arts have been improved, and human knowledge wonderfully
increased.

"In reasoning by syllogism from general principles, we descend to
a conclusion virtually contained in them. The process of induction is more
arduous, being an ascent from particular premises to a general conclusion. The
evidence of such general conclusions is probable only, not demonstrative: but
when the induction is sufficiently copious and carried on according to the rules
of art, it forces conviction no less than demonstration itself does."

On whether 'induction' is any improvement on Aristotelian 'deduction', more later.

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.