Category Archives: logic

synapsebutton.jpg is a neuroscience carnival devoted to all areas of neuroscience, including neurobiology, psychology, psychiatry, and neural systems — healthy brains to perverse minds — neurotransmitters to theories of mind.

To kick off the final installment of The Synapse before the new year, Corpus Callosum gets a little Popperian on the falsification of hypotheses and the connection between antidepressants and suicide. In the same vein, the Neurocritic bites into an antidepressant study and outlines why some of the claims being made are hard to swallow.

Bearing in mind Corpus Callosum’s reiteration that ‘correlation does not imply causation’, we turn to Vaughan’s submission of an fMRI study related to psychopathy at Mind Hacks.  Non Causa Pro Causa has interesting implications for the old nature/nurture debate and makes neuroimaging studies all the more nuanced. For more on psychopathy, I’d recommend Inside the Mind of a Psychopath on CBC’s Quirks & Quarks.

On Autism, Dr. Deborah Serani, host of the previous Synapse, highlights a paper on genetic mutation and its link to the risk of Autism.

Musings on Neurology and Lenitives In Simplistic Art outlines his top 5 strategic areas for research in neuroscience. Is the NIH accepting grant proposals in blog format? While quite broad in scope, there are some sympathies on this end to neuroinformatics and making conversion between file formats easier or potentially adopting a more standard format (imaging people, I know you sympathize. Oh, to be back in the DICOM days). Hat tip on Neuroethics, look north.

On touching brains in a bad way, the Neurophilosopher elaborates on every neuroscientist’s perennial favourite:  Phineas Gage.  A lot seems to fall out of rod-shaped objects piercing one’s head, although tamping irons may not be that common these days.  What, you ask, might be?  Chopsticks of course!

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Could a young man like this (and his chopsticks) be a key contributor to stem cell research? Shelley at Retrospectacle says yes

On touching brains in a good way, Jake at Pure Pedantry looks at brain stimulation and the therapeutic value of brain stimulation for Parkinsonism.  For coverage of Deep Brain Stimulation (DBS), including a talk by a Parkinson’s patient, check out the Dana Centre’s webcast on DBS during the 2006 Brain Awareness Week at the Science Museum in London.

Transcranial direct current stimuliation (tDCS) is another good touch, albeit less invasive.  The Fibromyalgia Research Blog reviews a paper on tDCS as a treatment for fibromyalgia pain.

For a more magnetic touch, consider the Neurocritic’s post on repetative transcranial magnetic stimulation, or rTMS.

Alvaro at SharpBrains interviews Dr. Elkhonon Goldberg on brain fitness and cognitive training and looks at what successful traders and students have in common. I concur on the point of bloated textbooks here in North America. That said, if you’d really like to know what Penfield or Newton thought, read them! Don’t just read a synopsis in a textbook! It’s unfortunate that there are not more programs like St. John’s Great Books program out there.

Outside of print, I Am A Scientist! caught up with Dr. Mary Harrington from Smith College at the Society for Neuroscience (SfN) conference in Atlanta this past October.  Listen to a discussion on the Faculty for Undergraduate Neuroscience live online, Sunday, December 10th at Noon (GMT -0600) on CKUW 95.9 FM.  Unable to listen?  The show will be archived on the show website.  In the meantime, lend your ears to another discussion at SfN, this time with Dr. Gladys Maestre from the University of Zulia in Maracaibo, Venezuela on neuroscience and developing countries.  Part 1 / Part 2 (MP3).

And heck, I’ll be hosting The Motel 6 later this morning (sigh, it’s late) live on CKUW 95.9 FM and ckuw.ca starting at 10AM (GMT -0600) on Sunday. Tune in!

Should you listen to the interview with Dr. Harrington, circadian rhythms will likely be on your mind. A Blog Around The Clock points to the refinement of questions in circadian rhythm research.

And, speaking of the molecular level, PZ Myers gives a near textbook explanation of the notch receptor.

While Sandy at The Mouse Trap makes his conjectures on the evolutionary trajectory of colour vision, Pete at Brain Hammer brings us back to philosophy and reminds us that a scientific theory, necessarily being falsifiable, is only as good as the predictive power it holds.

And it looks like that’s a wrap folks. Thanks for stopping by, see you in the new year, and in the words of the infamous Ivan Hrvatska, See you at party!

Weeee!

UPDATE
Synapse and Encephalon are consolidating! Regular and potential contributors to The Synapse are encouraged to submit posts here or by emailing encephalon.host at gmail.com. The next Encephalon will be held at Neurotopia on December 18th.

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I figured I’d repost this since Christmas is coming up. The link to amazon is at the bottom. ; )

‘An Essay on Metaphysics’ by Robin George Collingwood

IV

ON PRESUPPOSING

Whenever anybody states a thought in words, there are a great many more thoughts in his mind than are expressed in his statement. Among these there are some which stand in a peculiar relation to the thought he has stated: they are not merely its context, they are its presuppositions.

I write these words sitting on the deck of a ship. I lift my eyes and see a piece of string—a line I must call it at sea—stretched more or less horizontally above me. I find myself thinking ‘that is a clothes-line’, meaning that it was put there to hang washing on. When I decide that it was put there for that purpose I am presupposing that it was put there for some purpose. Only if that presupposition is made does the question arise, what purpose? If that presupposition were not made, if for example I had thought the line came here by accident, that question would not have arisen, and the situation in which I think ‘that is a clothes-line’ would not have occurred.

The priority affirmed in the word presupposition is logical priority. It is not a priority in time, whether that time belong to the history of the clothesline or to the history of my thoughts about it. When I say that its being for some purpose is a presupposition of its being for that purpose, that it first had a kind of general or indeterminate purposiveness, and that then, when it was rigged as a clothes-line, it exchanged this general or indeterminate purposiveness for a particular or determinate one by beginning to serve the purpose of hanging up washing to dry. I am not now asking whether anything like this really happened or not when the line was put up; I am only referring to when I used the word ‘presupposition’

Nor did I mean that my thoughts about the clothesline moved from ‘that line is meant for something’ to ‘that line is meant to hang washing on’. They might have moved in that way, and if I had been thinking about the line in an orderly or scientific manner I should have seen to it that they did move in that way; but as a matter of fact they did not. The thought ‘that is a clothes-line’ came plump into my mind, so far as I am aware, all at once and unheralded. Only by a kind of analysis, when I reflect upon it, do I come to see that this was a presupposition I was making, however little I was aware of it at the time.

Here lies the difference between the desultory and casual thinking of our unscientific consciousness and the orderly and systematic thinking we call science. In unscientific thinking our thoughts are coagulated into knots and tangles; we fish up a thought out of our minds like an anchor foul of its own cable, hanging upside-down and draped in seaweed with shellfish sticking to it, and dump the whole thing on deck quite pleased with ourselves for having got it up at all. Thinking scientifically means disentangling all this mess, and reducing a knot of thoughts in which everything sticks together anyhow to a system or series of thoughts in which thinking the thoughts is at the same time thinking the connexions between them.

Logicians have paid a great deal of attention to some kinds of connexion between thoughts, but to other kinds not so much. The theory of presupposition they have tended to neglect; and this is perhaps why the theory of metaphysics, which depends on it, has been allowed to remain in an unsatisfactory condition. I will try to state so much of this theory as seems necessary for my present purpose. For the sake of reference later on, I will sate it in a formal manner, in numbered propositions, with definitions of such terms as are used in sense they do not bear in ordinary English usage, or of terms whose meaning in ordinary usage depends on the propositions I am expounding. In expounding these propositions I shall not be trying to convince the reader of anything, but only to remind him of what he already knows perfectly well.

Prop. 1. Every statement that anybody ever makes is made in answer to a question.

When I speak of statements I do not mean only statements made out loud to somebody else; I include statements made by somebody to himself in the course of solitary thinking. Similarly when I speak of questions I do not mean only questions asked him by somebody else; I include questions asked him by himself.

The reader’s familiarity with the truth expressed in this proposition is proportional to his familiarity with the experience of thinking scientifically. In proportion as a man is thinking scientifically when he makes a statement, he knows that his statement is the answer to a question and knows what that question is. In proportion as he is thinking unscientifically he does not know these things. In our least scientific moments we hardly know what the thoughts we fish up out of our minds are answers to questions at all, let alone what questions these are. It is only by analyzing the thought which I expressed by saying ‘this is a clothes-line’ that I realize it to have been an answer to the question ‘what is that thing for?’ and come to see that I must have been asking myself that question although at the time I did not know I was asking it.

Note. A question is logically prior to its own answer. When thinking is scientifically ordered, this logical priority is accompanied by a temporal priority: one formulates the question first, and only when it is formulated begins trying to answer it. This is a special kind of temporal priority, in which the event or activity that is prior does not stop when that which is posterior begins. The act of asking the question begins and takes a definite shape as the asking of a determinate question before the act of answering it begins; but it continues for the whole duration of this latter. Unless the person who answered a question were still going on asking it while he formulated the answer, he would have ‘lost interest in the subject’, and the ‘answer’ would not have been an answer at all. It would have been a meaningless form of words. By being answered a question does not cease to be a question. It only ceases to be an unanswered question.

Def. 1. Let that which is stated (i.e. that which can be true or false) be called a proposition, and let stating it be called propounding it.

Note. This is an arbitrary use of the words. In English usage a question or supposition is, equally with a statement, said to be ‘propounded’, and the word ‘proposition’ is not exclusively used for that which is stated. I adopt it here, warning the reader that it is jargon, because it is customary among logicians.

Prop. 2. Every question involves a presupposition.

It may be doubted whether any question that was ever asked involved one presupposition and no more. Ordinarily a question involves large numbers of them. But a distinction should be made between what a question involves directly and what it involves indirectly. Directly or immediately, any given question involves one presupposition and only one, namely that form which it directly and immediately ‘arises’ (see Def. 2). This immediate presupposition, however, has in turn other presuppositions, which are thus indirectly presupposed by the original question.

Unless this immediate presupposition were made, the question to which it is logically immediately prior could not be logically asked. Verbally, no doubt, it might be asked. There is no verbal impossibility in the way of asking a man whom you suppose to be an indulgent husband whether he has stopped beating his wife. But there is a logical impossibility; for that question arises from the presupposition that he has been in the habit of beating her. If he is not supposed to have been in that habit, the question whether he has stopped ‘does not arise’.

Def. 2. To say that a question ‘does not arise’ is the ordinary English way of saying that it involves a presupposition which is not in fact being made.

A question that ‘does not arise’ is thus a nonsense question: not intrinsically nonsensical, but nonsensical in relation to its context, and specifically to its presuppositions. A person who asks another a question which ‘does not arise’ is talking nonsense and inviting the other to talk nonsense in the same vein.

As one can ask questions without knowing it, and a fortiori without knowing what questions one is asking, so one can make presuppositions without knowing it, and a fortiori without know what presuppositions one is making. When I ask ‘What is that thing for?’ I need not be aware that I am presupposing that it is ‘for’ something. It is only in proportion as I am thinking scientifically that I take trouble to make myself aware of this. For example, when I am trying to decipher a worn and damaged inscription I know very well that before I begin answering the question ‘What does that mark mean?’ I must first assure myself that the mark is not accidental but is part of the inscription; that is to say, I must first answer the question ‘Does it mean anything?’ An affirmative answer, i.e. the statement ‘That mark means something’, causes the question to arise, ‘What does it mean?’

Def. 3. The fact that something causes a certain question to arise I call the ‘logical efficacy’ of that thing.

The question ‘What does that mark mean?’ would equally have been caused to arise if I had not stated but only ‘assumed’ or ‘supposed for the sake of argument’ that it means something; and this is what, like any other epigraphist, I do when I find myself unable to give a definite answer to the question whether a certain mark is part of the inscription or not. The logical efficacy of the supposition that the mark means something is identical with the logical efficacy of the proposition that it means something.

Def. 4. To assume is to suppose by an act of free choice.

A person who ‘makes an assumption’ is making a supposition about which he is aware that he might, if he chose, make not that but another. All assumptions are suppositions, but all suppositions are not assumptions; for some are made altogether unawares, and others, thought the persons who make them may be conscious of making them, are made without any consciousness of the possibility, if it is a possibility, that others might have been made instead. When correctly used, the word ‘assumption’ is always used with this implication of free choice, as when it is said ‘let us assume x = 10’. Sometimes it is in correctly used of malice prepense, by way of an insult; as when a man says to another with whom he is arguing, ‘you are assuming that no one will work except for payment’, where the point is that no one but a fool would make that assumption, though it is a supposition that might easily be made unawares. Similarly a man who wishes to be insulting may ask ‘What do you mean by treading on my toe?’ knowing perfectly well that the treader meant nothing by it, because he did not do it on purpose.

Prop. 3. The logical efficacy of a supposition does not depend upon the truth of what is supposed, or even on its being thought true, but only on its being supposed.

The point has already been made clear in discussing the previous proposition. It is a matter of common knowledge in the conduct of scientific thinking; where it is possible and often profitable to argue from suppositions which we know to be false, or which we believe to be false, or concerning which we have neither knowledge nor belief as to whether they are false or true. These doubts or negations in no way affect the validity of the argument.

The point is no less familiar in the conduct of practical affairs than it is in the conduct of scientific thinking. A man (or at any rate an intelligent man) does not regard himself as insulted if some one who has paid him a sum of money asks him for a receipt, or if the family of a lady whom he is about to marry proposes that a marriage settlement should be drawn up. He knows that the request or proposal is based on the assumption that he is capable, or will one day become capable, of acting dishonourably; but though he knows people assume this he does not necessarily think they believe it. He finds no difficulty in his distinguishing between their supposing him a rascal and their believing him one, and he does not regard the former as evidence of the latter.

Prop. 4. A presupposition is either relative or absolute.

In this context the word ‘presupposition’ refers not to the act of presupposing but to that which is presupposed.

Def. 5. By a relative presupposition I mean one which stands relatively to one question as its presupposition and relatively to another question as its answer.

Thus, if I do a piece of surveying in the course of which I take some hundreds of measurements with my old 66-foot tape, every time I ask any question in the form ‘What is the distance between these two points?’ I presuppose that the answer as given by a reading on my tape will be the right answer: that is, I presuppose that my tape is within a certain percentage of the length which it professes to be. But this is only a relative presupposition. A tape by a reputable maker is not likely to have been made grossly inaccurate in the first instance; but it is quite likely to have stretched during years of service in all weathers; and a sensible man will check it from time to time against something not liable to that accident, for example a surveyor’s chain. The accuracy of the tape, which while I am using it is a presupposition of the questions I ask, is one of the two possible answers, the affirmative answer, to the question I ask while I am thus checking it.

A man may use a measuring-tape without its ever occurring to him that the question of its accuracy might be raised. In that case his assumption of its accuracy remains unquestioned, and one might suppose that this fact removed it from the sphere of relative presuppositions as above defined. But this would be a mistake. That a certain conclusion follows from certain premises is not disproved by the fact that some one who states the premises fails to see that the conclusion follows. Similarly, that certain presuppositions are questionable is not disproved by the fact that some one who makes them fails to see that they are questionable. The business of logical inquiries, like that on which we are now engaged, is to study high-grade or scientific thinking: their conclusions are not impaired by the fact that low-grade or unscientific thinking also exists.

To question a presupposition is to demand that is should be ‘verified’; that is, to demand that a question should be asked to which the affirmative answer would be that presupposition itself, now in the form of a proposition. To verify the presupposition that my measuring-tape is accurate is to ask a question admitting of the alternative answers ‘the tape is accurate’, ‘the tape is not accurate’. Hence to speak of verifying a presupposition involves supposing that it is a relative presupposition.

Def. 6. An absolute presupposition is one which stands, relatively to all questions to which it is related, as a presupposition, never as an answer.

Thus if you were talking to a pathologist about a certain disease and asked him ‘What is the cause of the event E which you say sometimes happens in this disease?’ he will reply ‘The cause of E is C’; and if he were in a communicative mood he might go on to say ‘That was established by So-and-so, in a piece of research that is now regarded as classical.’ You might go on to ask: ‘I suppose before So-and-so fount out what the cause of E was, he was quite sure it had a cause?’ The answer would be ‘Quite sure, of course.’ If you now say ‘Why?’ he will probably answer ‘Because everything that happens has a cause.’ If you are importunate enough to ask ‘But how do you know that everything that happens has a cause?’ he will probably blow up right in your face, because you have put your finger on one of his absolute presuppositions, and people are apt to be ticklish in their absolute presuppositions. But if he keeps his temper and gives you a civil and candid answer, it will be to the following effect. ‘That is a thing we take for granted in my job. We don’t question it. We don’t try to verify it. It isn’t a thing anybody has discovered, like microbes or the circulation of the blood. It is a thing we just take for granted.’

He is telling you that it is an absolute presupposition of the science he pursues; and I have made him a pathologist because this absolute presupposition about all events having causes, which a hundred years ago was made in every branch of natural science, has now ceased to be made in some branches, but medicine is one of those in which it is still made.

Absolute presuppositions are not verifiable. This does not mean that we should like to verify them but are not able to; it means that the idea of verification is an idea which does not apply to them, because, as I have already said, to speak of verifying a presupposition involves supposing that it is a relative presupposition. If anybody says ‘Then they can’t be of much use in science’, the answer is that their use in science is their logical efficacy, and that the logical efficacy of a supposition does not depend on its being verifiable, because it does not depend on its being true: it depends only its being supposed (prop. 3).

Prop. 5. Absolute presuppositions are not propositions.

This is because they are never answers to questions (def. 6); whereas a proposition (def. 1) is that which is stated, and whatever is stated (prop. 1) is stated in answer to a question. The point I am trying to make clear goes beyond what I have just been saying, viz. that the logical efficacy of an absolute presupposition is independent of its being true: it is that the distinction between truth and falsehood does not apply to absolute presuppositions at all, that distinction being (see def. 1) peculiar to propositions.

Putting the same point differently: absolute presuppositions are never (see def. 1) propounded. I do not mean that they sometimes go unpropounded, like the so-called ‘propositions’ of the fashionable modern logic, which are called propositions even when nobody in fact propounds them, and would on that account be more accurately called ‘proponibles’; I mean that they are never propounded at all. To be propounded is not their business; their business is to be presupposed. The scientist’s business is not to propound them but only to presuppose them. The metaphysician’s business, as we shall see, is not to propound them but to propound the proposition that this or that one of them is presupposed.

Hence any question involving the presupposition that an absolute presupposition is a proposition, such as the questions ‘Is it true?’ ‘What evidence is there for it?’ “How can it be demonstrated?’ ‘What right have we to presuppose it if it can’t?’, is a nonsense question.

Hence, too, it is nonsense to say, as some modern logicians do say, that supposing is one of various ‘attitudes’ which we can take up towards a proposition, where a proposition means something which can be either true or false. This is merely a device for imposing on unwary readers the dogma, of which more will be said hereafter, that all presuppositions are relative, or that there are no absolute presuppositions.

More here and here.

 

I was on Richard Dawkins’ blog, lavishing in his clear-thinking oasis, when I came across a critique Sam Harris wrote of Pope Benedict XVI’s now infamous speech.  Partly to keep an open mind, partly to stroke my obsessive Amazon.ca package tracking fetish, I am eagerly awaiting Sam Harris’ ‘Letter to a Christian Nation’ to arrive at my flat.  However, after reading his article my expectations were somewhat deflated.  In what follows, the pope’s remarks are in bold, Harris’ in regular text, and italicized, moi.

“The intention here is not one of retrenchment or negative criticism, but of broadening our concept of reason and its application. While we rejoice in the new possibilities open to humanity, we also see the dangers arising from these possibilities and we must ask ourselves how we can overcome them. We will succeed in doing so only if reason and faith come together in a new way, if we overcome the self-imposed limitation of reason to the empirically verifiable, and if we once more disclose its vast horizon….”

The pope suggests that reason should be broadened to include the empirically unverifiable. And is there any question these new “vast horizons” will include the plump dogmas of the Catholic Church? Here, the pope gets the spirit of science exactly wrong. Science does not limit itself merely to what is currently verifiable. But it is interested in questions that are potentially verifiable (or, rather, falsifiable). And it does mean to exclude the gratuitously stupid.

Pope Benedict XVI does call for reason to include the empirically unverifiable.  Yes.  Any careful examination of our reason should arrive at such a conclusion.  If only empirically verifiable statements are open to reason, we will have amputated mathematics from our body of knowledge.

Analytic statements are not verifiable.  Synthetic statements are.

Sam is right in acknowledging that the scientific method not only tests what is verifiable or falsifiable right now, but is open to what may become falsifiable if the right questions are asked.  Pope Benedict XVI, however, has not gotten the spirit of science ‘exactly wrong’, he has put his finger on a dogma, on a ‘self-imposed limitation’ that does not deny questions ripe for testing, nor questions waiting to bloom.  The pope has noted that some questions cannot be addressed by the scientific method. 

“Only thus do we become capable of that genuine dialogue of cultures and religions so urgently needed today….”

It is ironic that a man who has just disparaged Islam as “evil” and “inhuman” before 250,000 onlookers and the world press is now talking about a “genuine dialogue of cultures.” How much genuine dialogue can he hope for? The Koran says that anybody who believes that Jesus was divine—as all real Catholics must—will spend eternity in hell (Koran 5:71-75; 19:30-38). This appears to be a deal-breaker. The pope knows this. The Muslim world knows that he knows it. And he knows that the Muslim world knows that he knows it. This is not a good basis for interfaith dialogue.

Nor is the mischaracterization of the Abrahamic religions as nothing more than a conglomerate of fundamentalists a good basis for interfaith dialogue. 

“In the Western world it is widely held that only positivistic reason and the forms of philosophy based on it are universally valid. Yet the world’s profoundly religious cultures see this exclusion of the divine from the universality of reason as an attack on their most profound convictions. A reason which is deaf to the divine and which relegates religion into the realm of subcultures is incapable of entering into the dialogue of cultures….”

Astrologers don’t like “their most profound convictions” attacked either. Neither do people who believe that space aliens have traversed the galaxy only to molest ranchers and their cattle.

…Astrologers and alien enthusiasts clearly being equivalent to those who are theists…

Happily, these groups do not take to the streets and start killing people when their irrational beliefs are challenged. I suspect that the pope would be the first to admit that there are millions of people on this Earth who harbor “most profound convictions” that are neither profound nor compatible with real dialogue.

…One might even say that was a major point of his speech…

Indeed, one doesn’t even need to read between the lines of his speech to glean that he would place the entire Muslim world beyond the “universality of reason.”

Actually, yeah Sam.  You would.  You’d have to take the view that a quote is equivalent to an endorsement, take the quote out of context, and chastise a man who has written voluminously on this subject matter. 

He is surely right to be alarmed by Islam—particularly by its doctrines of martyrdom and jihad. He is right to find the treatment of Muslim women throughout the world abhorrent (if, indeed, he does find it abhorrent). He is right to be concerned that any Muslim who converts to Christianity (or to atheism) has put his life in jeopardy, as conversion away from the faith is punishable by death. These profundities are worthy objects of our derision. No apologies necessary, Your Holiness.

Weird.  Thanks for the vote of confidence though.

We might, however, note in passing that one of the pope’s “most profound convictions” is that contraception is a sin. His agents continue to preach this diabolical dogma in the developing world, and even in sub-Saharan Africa, where over 3 million people die from AIDS each year. This is unconscionable and irredeemably stupid. It is also a point on which the Church has not shown much of an intelligent capacity for dialogue. Despite their inclination to breed themselves into a state of world domination, Muslims tend to be far more reasonable on the subject of family planning. They do not consider the use of temporary forms of birth control to be a sin.

Perhaps opening up dialogue with the modern age will be cause for revision of theological arguments for or against issues such as contraception.  Why don’t we return to the point where the pope starts his conclusion, the point that Sam left out:

And so I come to my conclusion. This attempt, painted with broad strokes, at a critique of modern reason from within has nothing to do with putting the clock back to the time before the Enlightenment and rejecting the insights of the modern age. The positive aspects of modernity are to be acknowledged unreservedly: we are all grateful for the marvelous possibilities that it has opened up for mankind and for the progress in humanity that has been granted to us. The scientific ethos, moreover, is the will to be obedient to the truth, and, as such, it embodies an attitude which reflects one of the basic tenets of Christianity. The intention here is not one of retrenchment or negative criticism, but of broadening our concept of reason and its application.

“Modern scientific reason quite simply has to accept the rational structure of matter and the correspondence between our spirit and the prevailing rational structures of nature as a given, on which its methodology has to be based. Yet the question why this has to be so is a real question, and one which has to be remanded by the natural sciences to other modes and planes of thought—to philosophy and theology….”

This may have been where Sullivan found the Holy Father to be particularly “deep and complicated” and “profound.” Granted, questions of epistemology can make one sweat, and there are many interesting and even controversial things to be said about the foundations of our knowledge. The pope has not said anything interesting or controversial here, however. He has merely insinuated that placing the God of Abraham at the back of every natural process will somehow reduce the quotient of mystery in the cosmos. It won’t. Nearly a billion Hindus place three gods—Brahma (the Creator), Vishnu (the Preserver) and Shiva (the Destroyer)—in the space provided. Just how intellectually illuminating should we find that?

Sam.  Buddy.  He has said something incredibly interesting and very controversial to your materialist argument.  That’s why you paid very little attention to the backlash from the Muslim community and are focussing so much attention on the arguments in his speech.  It’s OK to fess up.  C’mon.  I’ll buy you a coke.

“The West has long been endangered by this aversion to the questions which underlie its rationality, and can only suffer great harm thereby. The courage to engage the whole breadth of reason, and not the denial of its grandeur—this is the program with which a theology grounded in Biblical faith enters into the debates of our time. “Not to act reasonably, not to act with logos, is contrary to the nature of God”, said Manuel II, according to his Christian understanding of God, in response to his Persian interlocutor….”

Please read that first sentence again. I hope it doesn’t seem peevish to point out that the West faces several dangers even greater than those posed by an incomplete epistemology. The West is endangered, primarily, by the religious fragmentation of the human community, by religious impediments to clear thinking, and by the religious willingness of millions to sacrifice the real possibility of happiness in this world for a fantasy of a world to come. In short, misguided reason that not only includes the aforementioned examples, but the dangers of extreme relativism as well, perhaps initiated by an incomplete epistemology? 

We are living in a world where untold millions of grown men and women can rationalize the violent sacrifice of their own children by recourse to fairy tales.

See above.

We are living in world where millions of Muslims believe that there is nothing better than to be killed in defense of Islam. We are living in a world in which millions of American Christians hope to soon be raptured into the sky by Jesus so that they can safely enjoy the holy genocide that will inaugurate the end of human history. We are living in a world in which a silly old priest, by merely giving voice to his religious inanities, could conceivably start a war with 1.4 billion Muslims who take their own inanities in deadly earnest. These are real dangers. And they are not dangers for which more “Biblical faith” is a remedy.

So, from what I gather, Sam agrees with calling violence violence, and that rational discourse may be a means to suppress if not end violence, but disagrees that such rational discourse should be taken up by a Christian.  What a sad state of affairs the world would be in for if a believer of Islam, Christianity, Judaism, could not question.  Luckily that’s not fully the case.

On why Newton’s theory did not derive from observation.

I was back home this afternoon. I let this churn in my brain for a while, then passed on the churning to my sister. After a lot of pacing we figured out how difficult this is when you don’t recognize what’s being said and how obvious it seems after a lot of pacing.

(Chapter 8)

// My third point—the contention that it is logically impossible to derive Newton’s theory from observations—follows immediately from Hume’s critique of the validity of inductive inferences, was pointed out by Kant. Hume’s decisive point may be put as follows:

Take a class consisting of any number of true observation-statements and designate it by the letter K. The statements in the class K will describe actual observations, i.e. past observations: thus we designate by the letter K any class whatsoever of true statements about observations actually made in the past. Since we have assumed that K consists only of true statements, all statements in the class K must also be consistent statements, and, furthermore, all statements belonging to the class K must be compatible with one another. Now take a further observation-statement which we shall designate by the letter B. We assume that B describes some future, logically possible, observation; for example, that B tells us that there will be an eclipse of the sun tomorrow. Since eclipses of the sun have already been observed, we can be certain that a statement B, asserting that there will be an eclipse of the sun tomorrow, is a statement which, on purely logical grounds, is possible; that is to say, our B is self-consistent. Now Hume shows the following: if B is a self-consistent observation-statement about a possible future event, and K any class of true observation-statements about past events, then B can always be conjoined with K without contradiction; or, in other words, if we add a statement B about a possible future event to statements in K we can never arrive at a logical contradiction. Hume’s finding can also be formulated as follows: no logically possible future observation can ever contradict the class of past observations.

Let us now add to Hume’s simple finding a theorem of pure logic, namely: whenever a statement B can be conjoined without contradiction to a class of statements K, then it can also be conjoined without contradiction to any class of statements that consists of statements of K together with any statement that can be derived from K.

And so we have proved our point: if Newton’s theory could be derived from a class K of true observation-statements, then no future observation B could possibly contradict Newton’s theory and the observations K.

Yet it is known, on the other hand, that from Newton’s theory and past observations we can logically derive a statement that tells us whether or not there will be an eclipse of the sun tomorrow. Now if this derived statement tells us that tomorrow there will be no eclipse of the sun, then our B is clearly incompatible with Newton’s theory and the class K. From this and our previous results it follows logically that it is impossible to assume that Newton’s theory can be derived from observations.

‘An Essay on Metaphysics’ by Robin George Collingwood

IV

ON PRESUPPOSING

Whenever anybody states a thought in words, there are a great many more thoughts in his mind than are expressed in his statement. Among these there are some which stand in a peculiar relation to the thought he has stated: they are not merely its context, they are its presuppositions.

I write these words sitting on the deck of a ship. I lift my eyes and see a piece of string—a line I must call it at sea—stretched more or less horizontally above me. I find myself thinking ‘that is a clothes-line’, meaning that it was put there to hang washing on. When I decide that it was put there for that purpose I am presupposing that it was put there for some purpose. Only if that presupposition is made does the question arise, what purpose? If that presupposition were not made, if for example I had thought the line came here by accident, that question would not have arisen, and the situation in which I think ‘that is a clothes-line’ would not have occurred.

The priority affirmed in the word presupposition is logical priority. It is not a priority in time, whether that time belong to the history of the clothesline or to the history of my thoughts about it. When I say that its being for some purpose is a presupposition of its being for that purpose, that it first had a kind of general or indeterminate purposiveness, and that then, when it was rigged as a clothes-line, it exchanged this general or indeterminate purposiveness for a particular or determinate one by beginning to serve the purpose of hanging up washing to dry. I am not now asking whether anything like this really happened or not when the line was put up; I am only referring to when I used the word ‘presupposition’

Nor did I mean that my thoughts about the clothesline moved from ‘that line is meant for something’ to ‘that line is meant to hang washing on’. They might have moved in that way, and if I had been thinking about the line in an orderly or scientific manner I should have seen to it that they did move in that way; but as a matter of fact they did not. The thought ‘that is a clothes-line’ came plump into my mind, so far as I am aware, all at once and unheralded. Only by a kind of analysis, when I reflect upon it, do I come to see that this was a presupposition I was making, however little I was aware of it at the time.

Here lies the difference between the desultory and casual thinking of our unscientific consciousness and the orderly and systematic thinking we call science. In unscientific thinking our thoughts are coagulated into knots and tangles; we fish up a thought out of our minds like an anchor foul of its own cable, hanging upside-down and draped in seaweed with shellfish sticking to it, and dump the whole thing on deck quite pleased with ourselves for having got it up at all. Thinking scientifically means disentangling all this mess, and reducing a knot of thoughts in which everything sticks together anyhow to a system or series of thoughts in which thinking the thoughts is at the same time thinking the connexions between them.

Logicians have paid a great deal of attention to some kinds of connexion between thoughts, but to other kinds not so much. The theory of presupposition they have tended to neglect; and this is perhaps why the theory of metaphysics, which depends on it, has been allowed to remain in an unsatisfactory condition. I will try to state so much of this theory as seems necessary for my present purpose. For the sake of reference later on, I will sate it in a formal manner, in numbered propositions, with definitions of such terms as are used in sense they do not bear in ordinary English usage, or of terms whose meaning in ordinary usage depends on the propositions I am expounding. In expounding these propositions I shall not be trying to convince the reader of anything, but only to remind him of what he already knows perfectly well.

Prop. 1. Every statement that anybody ever makes is made in answer to a question.

When I speak of statements I do not mean only statements made out loud to somebody else; I include statements made by somebody to himself in the course of solitary thinking. Similarly when I speak of questions I do not mean only questions asked him by somebody else; I include questions asked him by himself.

The reader’s familiarity with the truth expressed in this proposition is proportional to his familiarity with the experience of thinking scientifically. In proportion as a man is thinking scientifically when he makes a statement, he knows that his statement is the answer to a question and knows what that question is. In proportion as he is thinking unscientifically he does not know these things. In our least scientific moments we hardly know what the thoughts we fish up out of our minds are answers to questions at all, let alone what questions these are. It is only by analyzing the thought which I expressed by saying ‘this is a clothes-line’ that I realize it to have been an answer to the question ‘what is that thing for?’ and come to see that I must have been asking myself that question although at the time I did not know I was asking it.

Note. A question is logically prior to its own answer. When thinking is scientifically ordered, this logical priority is accompanied by a temporal priority: one formulates the question first, and only when it is formulated begins trying to answer it. This is a special kind of temporal priority, in which the event or activity that is prior does not stop when that which is posterior begins. The act of asking the question begins and takes a definite shape as the asking of a determinate question before the act of answering it begins; but it continues for the whole duration of this latter. Unless the person who answered a question were still going on asking it while he formulated the answer, he would have ‘lost interest in the subject’, and the ‘answer’ would not have been an answer at all. It would have been a meaningless form of words. By being answered a question does not cease to be a question. It only ceases to be an unanswered question.

Def. 1. Let that which is stated (i.e. that which can be true or false) be called a proposition, and let stating it be called propounding it.

Note. This is an arbitrary use of the words. In English usage a question or supposition is, equally with a statement, said to be ‘propounded’, and the word ‘proposition’ is not exclusively used for that which is stated. I adopt it here, warning the reader that it is jargon, because it is customary among logicians.

Prop. 2. Every question involves a presupposition.

It may be doubted whether any question that was ever asked involved one presupposition and no more. Ordinarily a question involves large numbers of them. But a distinction should be made between what a question involves directly and what it involves indirectly. Directly or immediately, any given question involves one presupposition and only one, namely that form which it directly and immediately ‘arises’ (see Def. 2). This immediate presupposition, however, has in turn other presuppositions, which are thus indirectly presupposed by the original question.

Unless this immediate presupposition were made, the question to which it is logically immediately prior could not be logically asked. Verbally, no doubt, it might be asked. There is no verbal impossibility in the way of asking a man whom you suppose to be an indulgent husband whether he has stopped beating his wife. But there is a logical impossibility; for that question arises from the presupposition that he has been in the habit of beating her. If he is not supposed to have been in that habit, the question whether he has stopped ‘does not arise’.

Def. 2. To say that a question ‘does not arise’ is the ordinary English way of saying that it involves a presupposition which is not in fact being made.

A question that ‘does not arise’ is thus a nonsense question: not intrinsically nonsensical, but nonsensical in relation to its context, and specifically to its presuppositions. A person who asks another a question which ‘does not arise’ is talking nonsense and inviting the other to talk nonsense in the same vein.

As one can ask questions without knowing it, and a fortiori without knowing what questions one is asking, so one can make presuppositions without knowing it, and a fortiori without know what presuppositions one is making. When I ask ‘What is that thing for?’ I need not be aware that I am presupposing that it is ‘for’ something. It is only in proportion as I am thinking scientifically that I take trouble to make myself aware of this. For example, when I am trying to decipher a worn and damaged inscription I know very well that before I begin answering the question ‘What does that mark mean?’ I must first assure myself that the mark is not accidental but is part of the inscription; that is to say, I must first answer the question ‘Does it mean anything?’ An affirmative answer, i.e. the statement ‘That mark means something’, causes the question to arise, ‘What does it mean?’

Def. 3. The fact that something causes a certain question to arise I call the ‘logical efficacy’ of that thing.

The question ‘What does that mark mean?’ would equally have been caused to arise if I had not stated but only ‘assumed’ or ‘supposed for the sake of argument’ that it means something; and this is what, like any other epigraphist, I do when I find myself unable to give a definite answer to the question whether a certain mark is part of the inscription or not. The logical efficacy of the supposition that the mark means something is identical with the logical efficacy of the proposition that it means something.

Def. 4. To assume is to suppose by an act of free choice.

A person who ‘makes an assumption’ is making a supposition about which he is aware that he might, if he chose, make not that but another. All assumptions are suppositions, but all suppositions are not assumptions; for some are made altogether unawares, and others, thought the persons who make them may be conscious of making them, are made without any consciousness of the possibility, if it is a possibility, that others might have been made instead. When correctly used, the word ‘assumption’ is always used with this implication of free choice, as when it is said ‘let us assume x = 10’. Sometimes it is in correctly used of malice prepense, by way of an insult; as when a man says to another with whom he is arguing, ‘you are assuming that no one will work except for payment’, where the point is that no one but a fool would make that assumption, though it is a supposition that might easily be made unawares. Similarly a man who wishes to be insulting may ask ‘What do you mean by treading on my toe?’ knowing perfectly well that the treader meant nothing by it, because he did not do it on purpose.

Prop. 3. The logical efficacy of a supposition does not depend upon the truth of what is supposed, or even on its being thought true, but only on its being supposed.

The point has already been made clear in discussing the previous proposition. It is a matter of common knowledge in the conduct of scientific thinking; where it is possible and often profitable to argue from suppositions which we know to be false, or which we believe to be false, or concerning which we have neither knowledge nor belief as to whether they are false or true. These doubts or negations in no way affect the validity of the argument.

The point is no less familiar in the conduct of practical affairs than it is in the conduct of scientific thinking. A man (or at any rate an intelligent man) does not regard himself as insulted if some one who has paid him a sum of money asks him for a receipt, or if the family of a lady whom he is about to marry proposes that a marriage settlement should be drawn up. He knows that the request or proposal is based on the assumption that he is capable, or will one day become capable, of acting dishonourably; but though he knows people assume this he does not necessarily think they believe it. He finds no difficulty in his distinguishing between their supposing him a rascal and their believing him one, and he does not regard the former as evidence of the latter.

Prop. 4. A presupposition is either relative or absolute.

In this context the word ‘presupposition’ refers not to the act of presupposing but to that which is presupposed.

Def. 5. By a relative presupposition I mean one which stands relatively to one question as its presupposition and relatively to another question as its answer.

Thus, if I do a piece of surveying in the course of which I take some hundreds of measurements with my old 66-foot tape, every time I ask any question in the form ‘What is the distance between these two points?’ I presuppose that the answer as given by a reading on my tape will be the right answer: that is, I presuppose that my tape is within a certain percentage of the length which it professes to be. But this is only a relative presupposition. A tape by a reputable maker is not likely to have been made grossly inaccurate in the first instance; but it is quite likely to have stretched during years of service in all weathers; and a sensible man will check it from time to time against something not liable to that accident, for example a surveyor’s chain. The accuracy of the tape, which while I am using it is a presupposition of the questions I ask, is one of the two possible answers, the affirmative answer, to the question I ask while I am thus checking it.

A man may use a measuring-tape without its ever occurring to him that the question of its accuracy might be raised. In that case his assumption of its accuracy remains unquestioned, and one might suppose that this fact removed it from the sphere of relative presuppositions as above defined. But this would be a mistake. That a certain conclusion follows from certain premises is not disproved by the fact that some one who states the premises fails to see that the conclusion follows. Similarly, that certain presuppositions are questionable is not disproved by the fact that some one who makes them fails to see that they are questionable. The business of logical inquiries, like that on which we are now engaged, is to study high-grade or scientific thinking: their conclusions are not impaired by the fact that low-grade or unscientific thinking also exists.

To question a presupposition is to demand that is should be ‘verified’; that is, to demand that a question should be asked to which the affirmative answer would be that presupposition itself, now in the form of a proposition. To verify the presupposition that my measuring-tape is accurate is to ask a question admitting of the alternative answers ‘the tape is accurate’, ‘the tape is not accurate’. Hence to speak of verifying a presupposition involves supposing that it is a relative presupposition.

Def. 6. An absolute presupposition is one which stands, relatively to all questions to which it is related, as a presupposition, never as an answer.

Thus if you were talking to a pathologist about a certain disease and asked him ‘What is the cause of the event E which you say sometimes happens in this disease?’ he will reply ‘The cause of E is C’; and if he were in a communicative mood he might go on to say ‘That was established by So-and-so, in a piece of research that is now regarded as classical.’ You might go on to ask: ‘I suppose before So-and-so fount out what the cause of E was, he was quite sure it had a cause?’ The answer would be ‘Quite sure, of course.’ If you now say ‘Why?’ he will probably answer ‘Because everything that happens has a cause.’ If you are importunate enough to ask ‘But how do you know that everything that happens has a cause?’ he will probably blow up right in your face, because you have put your finger on one of his absolute presuppositions, and people are apt to be ticklish in their absolute presuppositions. But if he keeps his temper and gives you a civil and candid answer, it will be to the following effect. ‘That is a thing we take for granted in my job. We don’t question it. We don’t try to verify it. It isn’t a thing anybody has discovered, like microbes or the circulation of the blood. It is a thing we just take for granted.’

He is telling you that it is an absolute presupposition of the science he pursues; and I have made him a pathologist because this absolute presupposition about all events having causes, which a hundred years ago was made in every branch of natural science, has now ceased to be made in some branches, but medicine is one of those in which it is still made.

Absolute presuppositions are not verifiable. This does not mean that we should like to verify them but are not able to; it means that the idea of verification is an idea which does not apply to them, because, as I have already said, to speak of verifying a presupposition involves supposing that it is a relative presupposition. If anybody says ‘Then they can’t be of much use in science’, the answer is that their use in science is their logical efficacy, and that the logical efficacy of a supposition does not depend on its being verifiable, because it does not depend on its being true: it depends only its being supposed (prop. 3).

Prop. 5. Absolute presuppositions are not propositions.

This is because they are never answers to questions (def. 6); whereas a proposition (def. 1) is that which is stated, and whatever is stated (prop. 1) is stated in answer to a question. The point I am trying to make clear goes beyond what I have just been saying, viz. that the logical efficacy of an absolute presupposition is independent of its being true: it is that the distinction between truth and falsehood does not apply to absolute presuppositions at all, that distinction being (see def. 1) peculiar to propositions.

Putting the same point differently: absolute presuppositions are never (see def. 1) propounded. I do not mean that they sometimes go unpropounded, like the so-called ‘propositions’ of the fashionable modern logic, which are called propositions even when nobody in fact propounds them, and would on that account be more accurately called ‘proponibles’; I mean that they are never propounded at all. To be propounded is not their business; their business is to be presupposed. The scientist’s business is not to propound them but only to presuppose them. The metaphysician’s business, as we shall see, is not to propound them but to propound the proposition that this or that one of them is presupposed.

Hence any question involving the presupposition that an absolute presupposition is a proposition, such as the questions ‘Is it true?’ ‘What evidence is there for it?’ “How can it be demonstrated?’ ‘What right have we to presuppose it if it can’t?’, is a nonsense question.

Hence, too, it is nonsense to say, as some modern logicians do say, that supposing is one of various ‘attitudes’ which we can take up towards a proposition, where a proposition means something which can be either true or false. This is merely a device for imposing on unwary readers the dogma, of which more will be said hereafter, that all presuppositions are relative, or that there are no absolute presuppositions.

More here and here.

Alfred Jules Ayer, of course.

// In 1922 he became the youngest scholarship student at Eton. Bright, bumptious and small for his age, he was handed over for five years to the care of a sadistic housemaster, ”Bloody Bill” Marsden, who disliked any sign of cockiness, cleverness or foreign origins in his charges. Ayer seldom spoke about his Eton schooling. No one encouraged him to read philosophy. It was a taste he discovered for himself, shortly before leaving with another scholarship to read classics at Christ Church College, Oxford. Here, he marked himself as suspect from the start by arriving at 18 already equipped with a mistress: a beautiful, cosmopolitan girl called Renée Lees, whose sophistication stood out like a Martian’s in an all-male college where women were still forbidden to dine in hall and most of the other boys had barely so much as spoken to a female contemporary. Christ Church was by far the grandest, most aristocratic and church-minded of all the Oxford colleges, with an even higher than usual proportion of homosexual dons. Ayer was half Jewish, a militant atheist and flamboyantly heterosexual.

More here, here, and here. And over here as well as juicey, gossipy letters talking about Freddy here.

What follows is an excerpt from chapter 11 of Karl Popper’s lucid and, as far as I’m concerned, inspiring book Conjectures and Refutations. Unfortunately I have only had the opportunity to read this chapter, but mark my words, by the end of this summer I’ll have the rest of Popper in my brain. The title of the chapter is ‘The Demarcation between Science and Metaphysics’ and the excerpt was gleaned from section 2, titled ‘My own view of the problem’.

// It was in 1919 that I first faced the problem of drawing a line of demarcation between those statements and systems of statements which could be properly described as belonging to empirical science, and others which might, perhaps, be described as ‘pseudo-scientific’ or (in certain contexts) as ‘metaphysical’, or which belonged, perhaps, to pure logic or to pure mathematics.

This is a problem which has agitated many philosophers since the time of Bacon, although I have never found an explicit formulation of it. The most widely accepted view was that science was characterized by its observational basis, or by its inductive method, while pseudo-sciences and metaphysics were characterized by their speculative method, or as Bacon said, by the fact that they operated with ‘mental anticipations’—something very similar to hypotheses.

This view I have never been able to accept. The modern theories of physics, especially Einstein’s theory (widely discussed in the year 1919), were highly speculative and abstract, and very far removed from what might be called their ‘observational basis’. All attempts to show that they were more or less directly ‘based on observations’ were unconvincing. The same was true even of Newton’s theory. Bacon had raised objections against the Copernican system on the ground that it ‘needlessly did violence to our senses’; and in general the best physical theories always resembled what Bacon had dismissed as ‘mental anticipations’.

On the other hand, many superstitious beliefs and many rule-of-thumb procedures (for planting, etc.) to be found in popular almanacs and dream books, have had much more to do with observations, and have no doubt often been based on something like induction. Astrologers, more especially, have always claimed that their ‘science’ was based upon a great wealth of inductive material. This claim is, perhaps, unfounded; but I have never heard of any attempt to discredit astrology by a critical investigation of its alleged inductive material. Nevertheless, astrology was rejected by modern science because it did not fit accepted theories and methods.

Thus there clearly was a need for a different criterion of demarcation; and I proposed (though years elapsed before I published this proposal) that the refutability or falsifiability of a theoretical system should be taken as the criterion of its demarcation. According to this view, which I still uphold, a system is to be considered as scientific only if it makes assertions which may clash with observations; and a system is, in fact, tested by attempts to produce such clashes, that is to say by attempts to refute it. Thus testability is the same as refutability, and can therefore likewise be taken as a criterion of demarcation.

This is a view of science which takes its critical approach to be its most important characteristic. Thus a scientist should look upon a theory from the point of view of whether it can be critically discussed: whether it exposes itself to criticism of all kinds; and—if it does—whether it is able to stand up to it. Newton’s theory, for example, predicted deviations from Kepler’s laws (due to the interactions of planets) which had not been observed at the time. It exposed itself thereby to attempted empirical refutations whose failure meant the success of the theory. Einstein’s theory was tested in a similar way. And indeed, all real tests are attempted refutations. Only if a theory successfully withstands the pressure of these attempted refutations can we claim that it is confirmed or corroborated by experience.

There are, moreover (as I found later), degrees of testability: some theories expose themselves to possible refutations more boldly than others. For example, a theory from which we can deduce precise numerical predictions about the splitting up of the spectral lines of light emitted by atoms in magnetic fields of varying strength will be more exposed to experimental refutation than one which merely predicts that a magnetic field influences the emission of light. A theory which is more precise and more easily refutable than another will also be the more interesting one. Since it is the more daring one, it will be the one which is less probable, But it is better testable, for we can make our tests more precise and more severe. And if it stands up to severe tests it will be better confirmed, or better attested, by these tests. Thus confirmability (or attestability or corroborability) must increase with testability.

This indicates that the criterion of demarcation cannot be an absolutely sharp one but will itself have degrees. There will be well-testable theories, hardly testable theories, and non-testable theories. Those which are non-testable are of no interest to empirical scientists. They may be described as metaphysical.

Here I must again stress a point which has often been misunderstood. Perhaps I can avoid these misunderstandings if I put my point now in this way. Take a square to represent the class of all statements of a language in which we intend to formulate a science; draw a broad horizontal line, dividing it into an upper and lower half; write ‘science’ and ‘testable’ into the upper half, and ‘metaphysics’ and ‘non-testable’ into the lower: then, I hope, you will realize that I do not propose to draw the line of demarcation in such a way that it coincides with the limits of a language, leaving science inside, and banning metaphysics by excluding it from the class of meaningful statements. On the contrary: beginning with my first publication on this subject, I stressed the fact that it would be inadequate to draw the line of demarcation between science and metaphysics so as to exclude metaphysics as nonsensical from a meaningful language.

I have indicated one of the reasons for this by saying that we must not try to draw the line too sharply. This becomes clear if we remember that most of our scientific theories originate in myths. The Copernican system, for example, was inspired by a Neo-Platonic worship of the light of the Sun who had to occupy the ‘centre’ because of his nobility. This indicates how myths may develop testable components. They may, in the course of discussion, become fruitful and important for science. In my Logic of Scientific Discovery I gave several examples of myths which have become most important for science, among them atomism and the corpuscular theory of light. It would hardly contribute to clarity if we were to say that these theories are nonsensical gibberish in one stage of their development, and then suddenly become good sense in another.

Another argument is the following. It may happen—and it turns out to be an important case—that a certain statement belongs to science since it is testable, while its negation turns out not to be testable, so that it must be placed below the line of demarcation. This is indeed the case with most important and most severely testable statements—the universal laws of science. I recommended, in my Logic of Scientific Discovery, that they should be expressed, for certain purposes, in a form like “There does not exist any perpetual motion machine’ (this is sometimes called ‘Planck’s formulation of the First Law of Thermodynamics’); that is to say, in the form of a negation of an existential statement. The corresponding existential statement—‘There exists a perpetual motion machine’—would belong, I suggested, together with ‘There exists a sea-serpent’ to those below the line of demarcation, as opposed to ‘There is a sea-serpent now on view in the British Museum’ which is well above the line since it can easily be tested. But we do not know how to test an isolated purely existential assertion.

I cannot in this place argue for the adequacy of the view that isolated purely existential statements should be classed as untestable and as falling outside the scientist’s range of interest. I only wish to make clear that if this view is accepted, then it would be strange to call metaphysical statements meaningless, or to exclude them from our language. For if we accept the negation of an existential statement as meaningful, then we must accept the existential statement itself also as meaningful.

I have been forced to stress this point because my position has repeatedly been described as a proposal to take falsifiability or refutability as the criterion of meaning (rather than demarcation), or as a proposal to exclude existential statements from our language, or perhaps from the language of science. Even Carnap, who discusses my position in considerable detail and reports it correctly, feels himself compelled to interpret it as a proposal to exclude metaphysical statements from some language or other.

But it is a fact that beginning with my first publication on this subject (‘Ein Kriterion des empirischen Charakters theoretischer Systeme’, Erkenntnis, 3, 1933, pp. 426 ff., now in The Logic of Scientific Discovery, pp. 312-14, see also Sections 4 and 10), I always dismissed the problem of meaninglessness as a pseudo-problem; and I was always opposed to the idea that it may be identified with the problem of demarcation. This is my view still.