Tuesday, November 30, 2010

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.

Monday, November 29, 2010

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.

Saturday, November 27, 2010

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.

Thursday, November 25, 2010

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

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.

Tuesday, November 23, 2010

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.

Monday, November 22, 2010

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.

Sunday, November 21, 2010

Aquinas on the Perihermenias

Just out, Thomas Aquinas' commentary on Aristotle's Perihermenias (also known as De Intepretatione). the commentary was probably written between 1269 and 1271, following his other 'Aristotelian' commentaries such as on the Posterior Analytics and on the Metaphysics. There are some notes on the Perihermenias, together with links to other commentaries (including this one) here.

I see Charles Freeman has just commented on an earlier post - welcome Charles. There were dozens, if not hundreds of medieval commentaries on this logical work by Aristotle. Many of them were written before the thirteenth century - Abelard's being the most notable of those.

Tuesday, November 16, 2010

The problem of Aristotle

I have just noticed The Closing of the Western Mind by Charles Freeman. The thesis is that after Constantine declared Christianity the state religion in 312, the church successfully quashed any challenges to its religious and political authority, in particular any challenges arising from the tradition of Greek rationalism and (in effect) held up human development for a thousand years until the Renaissance.

The difficulty with any such view is that it must face up to the 'problem of Aristotle'. If there really was a 'spirit of Greek rationalism', why did Greek science and philosophy apparently not advance much beyond Aristotle, writing in the fourth century BC, and Constantine in 312 (that's about 700 years)? And if Christian dogma was really that stifling, how was it that Western science developed from the rediscovery of Aristotle's work at the end of the 12th century to the scientific revolution in the 17th century (that's about 500 years)?

It is particularly difficult to explain given that (as I noted here, and as everyone knows) Aristotelian science is so spectularly wrong. Nearly all his scientific views are false, indeed spectacularly and obviously false, and in a way that the simplest experiment would confirm. How did the Greeks did not notice this? As Hannam notes (God's Philosophers chapter 11), simple observation of the trajectory of an arrow or of a ball thrown through the air, noted by Albert of Saxony as early as the 14th century, would have refuted a considerable part of Aristotle's physics.

Why and how was it that the medieval West eventually progressed well beyond Aristotle's science, when Greek culture did not? Constantine's state religion seems completely irrelevant.

Sunday, November 14, 2010

Hasty generalisation?

After a demanding and sometimes painful week with Longeway I am taking it relatively easy with James Hannam's Gods of the Philosophers. "With an engaging fervour, James Hannam has set about rescuing the reputation of a bunch of half-forgotten thinkers, and he shows how they paved the way for modern science" says Boris Johnson, no less.

It is an engaging and entertainingly written book, whose purpose is to show the extent of scientific progress in the Middle Ages, and to dispel some prevalent and persistent myths about the period. I can't find serious fault so far (I have reached the 'condemnations' of 1277). While it has no news for students of the period, being mostly taken from (generally reliable and authoritative) secondary sources, the subject desperately needs a popular audience, and Hannam has succeeded brilliantly

Yet it has attracted fierce criticism. Charles Freeman, author of The Closing of the Western Mind, attacked the book in an essay in New Humanist, arguing that it presents a distorted view of the medieval period.

God’s Philosophers is ... poorly structured, without a
coherent argument and often misleading, either through making assertions for
which there is no, or contrary, evidence or by omitting evidence that would
weaken its case. The review that called it “a spirited jaunt” was spot on. It
catches the mood of serendipitous ramblings, anecdotes and asides that make it
an easy read but hardly a serious contribution to our understanding of medieval
and sixteenth century science. Its success is mystifying.
Hannam replied, and Freeman followed with a further critique.

I won't attempt any serious analysis of these, except to note Freeman's frequent accusation of Hannam's 'sweeping assertions'. Generalisation is difficult to avoid when you are attempting to cover nearly a thousand years of intellectual history in 300 pages. So far, Hannam has avoided it very well. His main arguments is are from example. He gives many stories and accounts, all sourced, showing the extent of medieval innovation. Many of them are simply intended to debunk myth and prejudice (I was particularly struck by the revelation that the synthesis of hydrochloric, sulphuric and nitric acid first occurred in the West in the thirteenth century, and not earlier in the Middle East). The only hint of generalisation I have found so far is on page 105. Hannam writes:
The condemnations [of 1277 when 219 propositions were banned in Paris] and
Thomas's Summa Theologiae had created a framework within which natural
philosophers could safely pursue their studies. The framework first defined
clear boundaries between natural philosophy and theology. This allowed the
philosophers to get on with the study of nature without being tempted to indulge
in illicit metaphysical speculation. Then the framework laid down the principle
that God had decreed the laws of nature but was not bound by them. Finally, it
stated that Aristotle was sometimes wrong [...] and if Aristotle could be wrong
about something that he regarded as completely certain, that threw his whole
philosophy into question. The way was clear for the natural philosophers of the
Middle Ages to move decisively beyond the achievements of the Greeks (God's
p. 105).
The passage is not sourced, and Hannam does not explain clearly the logic for his assertion. It is one of at least three views which Hyman and Walsh summarise it as follows.
Most scholars agree that these condemnations had a profound effect on the
history of medieval thought, but they disagree as to the nature and significance
of that effect. The condemnations have been called [1] a brutal victory
Augustinianism over Aristotelianism, but Aristotle flourished in the schools
after as well as before. It has been said [2] that by freeing the later Middle Ages
from the domination of a rigid Averroistic Aristotelianism, the way was opened
for the development of natural science as the inquiry into nature rather than
the dogmatic reiteration of the Aristotelian corpus. But surely this exaggerates
the monolithic character of the acceptance of Aristotle even by masters such as
Siger of Brabant, and underestimates the continued influence of Aristotle and
Averroes on the development of natural science. A more general and widely
accepted view [3] is that with the Condemnation of 1277, the scholastic effeort to
inforporate and renovate philosophy came to an end. But this surely
underestimates the philosophical advances, especially the methodological ones,
of the later period.
But it is a recognised view for all that. So far there is very little of distortion or falsification. I recommend the book.

Saturday, November 13, 2010

Ockham: the founder of European empiricism

I am finally getting to the meaty parts of Longeway's book*. He says at the beginning (p.2), and in the 'Ockham and his [medieval] predecessors approached some of the most fundamental problems of a scientific empiricism, both ancient and modern'and that 'Ockham may reasonably be regarded as the founder of empiricism in the European tradition'. This is strong and heady stuff and was a clinching reason for buying the book. After 100 pages, we are getting towards some of the reasons.

I understand Longeway's argument as follows. According to Ockham (Summa I.26), there are three kinds of definition. (1) A nominal definition is a way of setting the meaning of the defined term, and so a is true in virtue of the meaning of the term. E.g. 'a bachelor is an unmarried man. (2) Two kinds of real definition. A metaphysical definition indicates genus and difference, for example 'a man is a rational [differentia] animal [genus]'. (3) A natural definition (Spade translates this as physical definition) is one which signifies obliquely essential parts of the thing defined. For example, 'a triangle is a figure contained by three straight lines'.

Ockham argues (Summa II.ii.35, cited in Longeway p. 112) says that any attempted demonstration will depend upon either the nominal definition of the attribute, and so beg the question, or a metaphysical definition, which is essentially inexplicable and provides no scientific assistance, or a natural definition. Only demonstration using natural definition is truly scientific.

Let's flesh this out. The Aristotelian model for scientific demonstration is as follows.

A B is a C
An A is a B
Therefore, an A is a C

To explain why A is C, Aristotle says we must find a 'middle term' B which is common to A and C. But it is clearly not enough for B simply to be synonymous with C, otherwise the syllogism would beg the question. For example

An unmarried man is a bachelor
John is an unmarried man
Therefore, John is a bachelor.

To understand the term 'batchelor' you have to understand that it means 'unmarried man'. Thus the conclusion moves us no further than the minor premiss 'John is an unmarried man' It expresses the same thing in different terms, having the same meaning, and the 'reasoning' is trivial. Nor is a 'metaphysical definition' of any assistance. We can have a direct intellectual grasp of a thing, but only of its genus, as a whole, 'without any insight into its metaphysical structure' (p.114). 'A demonstration rooted in a grasp of metaphysical definition of the primary subject of an attribute can only occur after this life'.

The only case where true demonstration is possible is in the case where the middle term involves a natural definition. And this can only happen where the subject is something composite. Longeway cites (p. 113) the example of a triangle, with spatial parts arranged in such a way that an analysis of its structure will tell us that it has the attribute in question. This is what happens in geometry and mathematics.

This means that there can be no true scientific explanation of things which are essentially simple. Ockham thinks we cannot explain heat, for example, because we cannot explain it in terms of of composition and mathematics. As Longeway explains it "The natural definition of an attribute is of no assistance here for the straightforward reason that a simple quality such as heat has no variety or structure of essential parts, but is rather uniformly alike in every one of its parts. No mechanism by which heat heats is there to uncover. It just heats. And this can only be known from experience" (p. 113)

We can only apply mathematical techniques to things in nature which they are composite, and which can be defined in terms of their material parts. Thus (for Ockham) we cannot have a scientific explanation of substance. Ockham still holds to the Aristotelian view that the causal properties of a substance cannot be explained in terms of the substance's parts. According to Aristotle, substances are essentially simple. Their properties follow from their substantial form (the essence of a substance, corresponding to a species). A substantial form is what is signified by the definiens of a definition. A substantial form is a universal (since only universals are definable - see Metaphysics Z8 1034a6-8). A substantial form is immaterial (because a substance is a combination of material and form). A substantial form is simple (Metaphysics Z12). If the properties of a species could be explained by composition, a substance would not be an essential unity, and so would not be a substance, but a collection of substances.

This is interesting, but doesn't really explain why we should regard Ockham as the founder of European empiricism. As Longeway points out, real progress only began when Descartes and Boyle "insisted on mathematical-mechanical modes of explanation connecting one accident of material substance to another, rather than explanations of the first attributes of material substance". (p.115) One of the essential ingredients of modern science is the rejection of the Aristotelian doctrine of substantial forms. (See Locke about this here, especially section 10). Since Ockham did not reject substantial forms, why should we regard him as the founder of modern science?

Longeway gives no convincing reply to this line of reasoning, except for suggesting that once Ockham has shown the impossibility of scientific explanation using metaphysical definition, it is tempting to look for explanations in terms of natural definition.

we know that early modern scientists were so tempted, and Descartes and others
rejected the assujmption immaterial substantial forms underlying biological
properties precisely because such an assumption did nothing to provide an
understanding why animals and plants have the properties in question. (p 115)
Since our only tool for understanding why is analysis in terms of material parts and the application of mathematics, it would be natural to be tempted by materialist reductionism in biology.

* Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio.

Tuesday, November 09, 2010

The end of the first of the second

The last questions of Prima Secundae, the first part of the second book of Summa Theologiae. Questions 106-108 and Questions 109-114 now available.

Is it cruel to believe in Hell?

Is the belief cruel? You might say that God is cruel. But is the person who believes this of God also cruel? Why? If God does not exist, no one has or will be punished, and so no one is hurt. If God exists, but does not intend to punish souls in this way, the same applies. Cruelty can only exist when there is an object of cruelty.

But if God exists and does intend punish souls in this way, then that is the fact of the matter. There is nothing that the believer can do to prevent the suffering.

David Hume had the interesting theory that all professed believers are really atheists. He says that all Catholics condemn the St Bartholomew's massacre as cruel and inhumane. Yet these are the same people, he says, who condemn non-Catholics to eternal torment 'without scruple'.

Currently being discussed at the Quodlibet forum.

Wikipedia admits plagiarism

Yesterday's post saw a burst of traffic from Wikipedia, of all places. The fuss over this particular incident will down, but there are two important principles to be gathered from this.

The first is that most of the people now on the project do not possess the skills to develop an accurate and comprehensive reference work. As we just saw, a senior person on the project has defended his outright plagiarism by admitting he cannot write. Another of his colleague agrees, making the extraordinary statement that "plagiarism … is not only rampant, it is a standard editorial practice throughout the project". Crowdsourcing doesn't work.

The second is the lengths the adminstration will go to stifle any legimitimate criticism of the project. An editor (not me) who raised an earlier alarm about plagiarism was promptly blocked by the same person who said that plagiarism is now standard practice. The edit history of the plagiarist has been erased - if you click on the links in my previous post you will see they no longer work. Any discussion of the incident has been stifled. A long-term content contributor complained about this and was promptly blocked as well . More details here.

Of course, all organisations have the tendency to stifle debate and legitimate criticism. But Wikipedia takes this to extremes, which is especially ironic given its commitment to 'free culture' and 'open source'. Or is it? When being free and open really means stealing, it's difficult to be free and open, isn't it?

Sunday, November 07, 2010

Plagiarism now and then

I've commented before that many of Wikipedia's articles are plagiarised from out of date sourceslike the Catholic Encyclopedia and Encyclopedia Britannica. Actually a lot of them are plagiarised from more current sources. The table below compares the article on an American Buddhist temple written by a member of the prestigious Arbitration committee with the source where he apparently obtained it from. He has since left ‘the project’ after similar concerns raised by other users, and left this touching message on his talk page. This includes the bizarre statement “I asked many people for help because I know I’m not good at writing”.

The first formal meeting was held on August 25, 1996 in York County, Virginia and was attended by many local Thais, Laotians, and Cambodians.The first formal meeting was held on August 25, 1996at the Thai Erawan Restaurant in York County, Virginia. The meeting was very successful with many local Thais, Laotians, Cambodians attended.
After the meeting, the first newsletter was published and distributed.After the meeting, the first newsletter was published and distributed.
PhraMaha Surasak Jivanando, the Abbot of Wat Thai Washington, D.C., provided advice to the group throughout the process to get the new temple functioning.PhraMaha Surasak Jivanando, the Abbot of Wat Thai Washington, D.C., who is widely known for his wisdom, kindness, and well respected, provides unending support and advice to the group.
On September 8, 1996, members of the Thai Buddhist community went to Wat Thai and had the first formal meeting with PhraMaha Surasak.Seeking his advice, on September81996, members of the Samukee Group went to Wat Thai Washington, D.C. and had the first formal meeting with PhraMaha Surasak again on November 19, 1996.
The association's first formal president, Dr. Tawatchai Onsanit, guided the organization through the first two years.The association first formal president, Dr. Tawatchai Onsanit, guided the organization through trouble water during the first two years.
Rental properties for religious functions were scarce and thus the association looked for a property to buy.It was also obvious that the rental property for religious functions were scarce. Consequently, probability of succeeding with purchase option was far greater.
The first priority was to have a place where one or two monks could reside in the Tidewater area and provide continuous spiritual leadership. The search committee finally found an affordable place in Carrolton, Isle of Wight County, Virginia.[1]… the first priority was to have a monks' residence such that one or two monks could reside in the Tide Water area and could provide continuous spiritual leadership. The search committee finally found an affordable place at 14289 Chapman's Lane in Carrolton, Isle of Wight County, Virginia.
On September 28, 1997, PhraMaha Taweepong Tawiwongso, PhraMaha Putthachak Buddhisaro, and PhraMaha Saman Methawee were invited to a local celebration of the "Sarth Thai" Day and to visit the place of interest. All monks agreed that was a perfect place for a monks' residence and a meditation center as it was rural and located in a wooded setting.On September 28, 1997, PhraMaha Taweepong Tawiwongso, PhraMahaPutthachak Buddhisaro, and PhraMahaSaman Methawee were invited to a local celebration of the "Sarth Thai"Day and to visit the place of interest. All of the monks agreed that was a perfect place for a monks' residence and a meditation center.
Upon consensus among its members, the Association presented to PhraMaha Surasak Jivanando a proposal to formally establish a monks' residence and requested that two monks reside at the place and act as local religious leaders.Upon consensus of the its members, the Association presented to PhraMaha Surasak Jivanando a proposal to formally establishing a monks' residence and requested that two monks are to reside at the place and to be local religious leaders.
On December 31, 1997, The Buddha Samukee Association bought the said parcel on Chapman's Lane for the sum of 50,000 dollars with the owner agreeing to hold a $40,000 mortgage note. The parcel consists of 6.35 acres of wooded land and a house.On December 31, 1997, The Buddha Samukee Associationbought the said parcel on Chapman's Lane for the sum of 50,000 dollars with the owner agreed to hold a $40,000 mortgage note. The parcel consists of 6.35 acres of wooded land and a house.
In January 1998, Phra Maha Surasak and other monks from Wat Thai Washington D.C. graciously accepted the invitation to visit the place and to give a blessing and a name of 'Wat Pa Santidhamma'.[1]On January 1998, Phra Maha Surasak and other monks from Wat Thai Washington D.C. were graciously accepted the invitation to visit the place and to give a blessing and a name of 'Wat Pa Santidhamma'

Thursday, November 04, 2010

The best way for a pressure group to spend its time

"The more I think about it, the more it occurs to me that this [Wikipedia] is the best way for a pressure group to spend its time" Daniel Hannan. I pointed out as much here.

Indifference to science

A few things have reminded me of philosophers' indifference to actual science. The first was my own fault. I linked to this explanation of why glass is transparent, but after second thoughts and a bit longer on Google, the explanation seems completely wrong. I suspect the explanation (if you can follow it) in Wikipedia is the correct one, although (as I constantly remind my readers) you should beware of anything you read in Wikipedia. The second reminder is the supply of amusing and interesting scientific explanations by medieval authors quoted in Longeway's book. All of them are wrong. Grosseteste gives an explanation of thunder that involves hot and cold air mixing, expanding and producing flame, then quenching the flame with an audible explosion (the thunder). Any explanation of thunder that does not involve electricity (and the associated concepts of charge) is clearly wrong. And how about this wonderfully dodgy piece of neuroscience (from Albertus Magnus, quoted in Longeway p.56).

(1) In everyone in which there is an appetite for pain in what opposes him, there is an accession of blood to the heart from the evaporation of gall;
(2) in someone who is angry there is an appetite for pain in what is opposed to him;
(3) therefore, in one who is angry there is an accession of blood to the heart from the evaporation of gall.

The science mentioned by philosophers is often very bad. That in itself does not mean they are indifferent to science, but I believe they are indifferent as well. They are philosophers, and the actual science does not affect any philosophical point being made. I can easily change the example given in my earlier post as follows

Propter quid
Light passes through any substance which neither reflects it nor absorbs it
Glass neither reflects nor absorbs light
Therefore light passes through glass.

I will leave the construction of the corresponding quia form as an exercise. Note also that you would need to combine this with further syllogism involving an account of why glass neither reflects nor absorbs light (a substance absorbs light when its electron orbitals are spaced such that they can absorb a quantum of light (or photon) of a specific frequency, and does not violate selection rules). But none of that matters. The philosophical point is the same. Similarly, we could alter Albert's example to use a favourite example (probably equally dodgy) of modern philosophers of science as follows.

In everyone in which there is an appetite for pain in what opposes him, there is an appropriate stimulation of c-fibers in the hypothalmus
in someone who is angry there is an appetite for pain in what is opposed to him;
therefore, in one who is angry there is an appropriate stimulation of c-fibers in the hypothalmus

Aristotle's point is that every scientific explanation involves interposing a 'middle' B between some empirical truth of the form 'A is C', so we get a demonstration of the form

All B is C
This A is B
Therefore this A is C

which is meant to explain why the empirical truth is really true. All scientific demonstration involves 'finding a middle', and this point can be illustrated whether or not the scientific truth 'All B is C' is bad science or not. This is all about the philosophy of science, not science itself.

Which raises a further interesting point. Given that these medieval philosophers (Grosseteste, Albert, Aquinas, Ockham) were doing philosophy of science, not science itself, does that mean that all the medieval writing about 'science' was really philosophy of science? Which raises the difficult question of whether there really was a scientific revolution in the thirteenth century. And raises yet another question: do we need the philosophy of science, or an approach resembling the one adopted by the Aristotelian philosophers, in order to explain the most fundamental and difficult problems of science? Recall the Aristotelian definition of science: knowledge arrived at by demonstration. What kind of demonstration explains the phenomenon of anger? How do we explain anger in terms of the mechanical stimulation of 'c-fibres'? What kind of stimulation would explain anger at further bouts of quantitative easing by the Federal Reserve? Is philosophical indifference to science, merely indifference to science of a certain kind? But enough for now.

Wednesday, November 03, 2010

Why light passes through glass

The Longeway book arrived very quickly (2 days) and is a credit to Amazon . Compare this with Waterstone's, who had no copy in any of their London shops, and who said that ordering may take weeks or months, or with the university libraries in London (only UCL library had a copy, but this horribly-designed and uncomfortable building is to be visited only as a last resort).

There is much to say about the book. The introduction is long and as interesting as the reviews suggest. One example, illustrating Longeway's attention to detail, is the way he notices the interesting passage by Aristotle at 88a11. This is in some ways more interesting than the later and better known passage about the lunar eclipse beginning at 89b26. In the case of the eclipse it is theoretically possible for us directly to observe to cause of the eclipse (namely, as he says at 90a24, if we were living on the moon). In the case the transparency of glass, by contrast, it is theoretically impossible for us to observe directly the passage of light through the 'pores' in glass. The passage is also interesting for the insight that some ancient Greek scientists thought that the transparency of glass could be explained through some atomic or molecular theory.

On why glass actually is transparent, see this elementary explanation. It is intended for children, although I didn't follow it that well. It says the reason is that the molecules in liquids are disorganised and random, and so light can pass through them. It cannot pass through solids, because the arrangement of molecules is ordered (I didn't follow this reasoning). Light passes through all liquids, glass is a liquid, therefore light can pass through glass (I did follow this, however).

Note we can express the second reasoning in both Aristotelian propter quid and quia forms, as follows.

Propter quid
Light passes through liquids
Glass is a liquid
Therefore, light passes through glass

Light only passes through liquids
Light passes through glass
Therefore glass is a liquid

My earlier observations apply here as well. Both syllogisms are essentially trivial and hardly count as 'reasoning' at all. The real reasoning involves how we arrive at the (superficially implausible) premiss that glass is a liquid.

Outsourcing the truth

The posts here are mostly about philosophy. Sometimes they are about Wikipedia. Sometimes, happily, they are about both. I was amused by Guardianista Seth Finkelstein's comment here.
Ah, you have put your finger on one of the dirty little secrets of Wikipedia -
it is in fact not possible to do what it claims to do, which is outsource the
problem of Truth
. Relying on "reliable sources" ultimately begs the question,
since no simple rule will work for determining what is "reliable". People often
mistake a very superficial and rather US-centric idea of news-not-opinion as all
that's necessary. In reality, the topic is far more complex. It's necessary to
know something about a subject in first place in order to have a sense of what's
reliable (failures in grappling with this quasi-paradox explain much Wikipedia
tail-chasing on specific controversial issues). Anyway, what I can tell you for
The Guardian was all my columns were read in detail by the relevant editor for
factual claims, and I was expected to substantiate any significant statements of
fact which were arguable (this is a matter of judgment, of course).
Controversial claims about living people received special legal scrutiny. The editorial code is online. I can't speak about what the New York
Times does, I've never written anything for them. -- Seth
(talk) 22:46, 17 October 2010 (UTC)
Quite right. It's the same as the problem of hiring an expert on a subject. How do you know that the person actually is an expert, when you are not an expert? In reality there are all sorts of mechanisms which generally (not always) get round the problem in practical ways. The usual method is to rely on the property that experts are usually good at recognising other experts. Hence professional bodies, accreditation schemes and all that kind of old-fashioned thing. Wikipedia always officially eschewed this, although an unofficial system of a similar kind operated in practice.

Such schemes are far from perfect, and can often lead to a sort of freemasonry. Nor do they prevent practitioners of pseudo-scientific nonsense from getting together according to their own internally-recognised standards of expertise and accreditation (I won't mention any of these, in case I am prosecuted for libel). But I can't think of anything better.

Tuesday, November 02, 2010

A priori and propter quid

In chapter 17 of Book III part 2 of Summa Logicae, Ockham gives a neat explanation of the terms propter quid and quia that shows how they are close, or even equivalent to the terms a priori and a posteriori respectively. I discussed this earlier. The translation is mine. (Sadly, I failed to get John Longeway's translation from our local Waterstone's, or indeed any Waterstones in the country, and had to resort to Amazon).

Separately, I am working on a translation of Buridans Questions on the Posterior Analytics. The translation of 'scire' is tricky, as both Ockham and Buridan use it with 'notare'. Both mean a sort of knowing. As they use it (and define it) 'scire' means a sort of reasoned knowing, the thing you get from understanding a demonstration, or 'syllogism that produces knowing'. Thus scientia, from which we get the English word 'science'. The modern and the medieval Latin meaning are closely connected. Understanding how they are different is a difficult matter that needs teasing out.

Propter quod oportet scire quod quaedam est demonstratio cuius praemissae sunt simpliciter priores conclusione, et illa vocatur demonstratio a priori sive propter quid.On account of this we must know [scire] that one sort of demonstration whose premisses are absolutely prior to the conclusion, and this is called demonstration a priori or propter quid.
Quaedam est demonstratio cuius praemissae non sunt simpliciter priores conclusione, sunt tamen notiores sic syllogizanti, per quas devenit sic syllogizans in notitiam conclusionis, et talis demonstratio vocatur demonstratio quia sive a posteriori.Another sort is demonstration whose premisses are not absolutely prior to the conclusion, and which are nevertheless better known to the syllogiser in this way, through which the syllogiser thus arrives at knowledge of the conclusion. And such demonstration is called demonstration quia or a posteriori.

Monday, November 01, 2010

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

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

"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.