Wednesday, 4 June 2008

The Localised Falsification Diagnosis of Meaning

Logical Positivism is dead. With its demise the world lost a wonderful tool for dealing with nonsense: the Logical Positivists insistence on a Universal, Verification Criterion of Meaning ('UVCM').This post examines the, much criticised, UVCM. It discovers that there is a lot to be said for a Universal, Verification, Criterion of Meaning that is stripped of 'universal' 'verification' and 'criterion' and puts forward a replacement Localised, Falsification Diagnosis of Meaning.

0 Introduction

Logical Positivism, as has been known for over forty years is dead. This is a matter of regret. It was a matter of regret to Karl Popper, who claimed responsibility, but expressed his admiration for the movements ‘rational attitude’[1]. It was naturally a matter of regret to its foremost Anglophone proponent, A. J. Ayer. When reflecting on the movement after its demise he thought the ‘the most important of (its) defects was that nearly all of it was false’. Never-the-less Ayer still felt he wanted to say that ‘it was true in spirit – the attitude was right’[2].

That ‘truth in spirit’ and the right (rational) attitude was manifest in Logical Positivism’s attacks on meaningless nonsense. The Logical Positivists’ main tool in these attacks was the institution of a universal, verification, criterion of meaning (‘UVCM’):

The meaning of a statement is its method of verification

For all statements the mode of verification was held to elucidate the meaning and, where no verification method could be presented by an opponent, was held to be conclusive evidence that the opponent was talking gibberish. So central was the criterion as to, almost, become synonymous with Logical Positivism itself. UVCM was there at the start of the movement and it was difficulties with the theory that precipitated its death.

Ayer blamed considerable difficulties in formulating a viable version of UVCM[3]. In my opinion the cause of these difficulties can be laid at the door of three flaws in the basic conception. UVCM was pressed into service beyond its capabilities. Logical Positivism was concerned to delineate ‘science’ from ‘metaphysics’. This seems a reasonable enough aim until you bring into the equation the Logical Positivists’ attitude to science and metaphysics. Under the Logical Positivist banner ‘science’ was all that was intellectually good and ‘metaphysics’ was all that was intellectually bad. The proposed use of UVCM was not just to sharpen and give content to the meaning of ‘meaning’ but to do so in such a way as to enforce a dichotomy and come down firmly on the ‘correct’ side of that dichotomy. Secondly, it was to enforce that dichotomy over all intellectual activity. Finally it was to use ‘verification’ to do that: for all their admiration of Hume the Logical Positivists did not incorporate his full inductive scepticism into their philosophy.

Whilst the UVCM is often traced back to Charles S. Peirce’s pragmatism I trace it back to a reformulation of ‘Leibniz’s Law’. This Straw Man methodology enables the best case possible to be made for what is good in UVCM whilst highlighting the negative effects of universal application, emphasis on verification and use as a criterion. There was a lot of nonsense about when Logical Positivism came to be, there is a lot of nonsense about now. The motive behind UVCM is still with us, even though UVCM is untenable. I propose an alternative, a Localised Falsification Diagnosis of Meaning and argue that; stripped of ‘universal’ ‘verification’ and ‘criterion’ a Universal Verification Criterion of Meaning is just what we need!

1 ‘Leibniz’s Law’ and meaning

My reformulation of ‘Leibniz’s law’ asserts the identity of A and B where A and B share all predicates.

A is identical to B if and only if every property of A is also a property of B and vice versa.

Which is unproblematic, simply the assertion that if something is the same then everything about it is the same. If we want to cast the principle in a pragmatic way, which I do, it can be:

A is identical to B if and only if everything that can be said of A can be said of B and vice versa

(One thing in particular that can be said of either A or B is that it is A). The principle is still an unproblematic exposition of what ‘being the same’ is. If problems are needed the principle can be split in two:

Indiscernibility of Identicals: If A and B are identical then no difference can be discerned

Identity of Indiscernibles: If no difference can be discerned between A and B then A and B are identical.

The Indiscernibility of Identicals still gives us no problems. If it is the same there is no difference, if there is no difference then none can be discerned.

The identity of indiscernibles can be used with less confidence. That we are unable to make a distinction is far from a guarantee that no distinction is to be made. Fun is to be had imagining different objects, removing as much of what distinguishes them as possible, and trying to find what makes them different objects. Take three spheres alone in a nice symmetrical universe. If all qualities by which we could distinguish them, size, weight, colour etc. are removed we begin to need to create new ones. Unable to say ‘the small one’, ‘the heavy one’ or ‘the blue one’ we are reduced to talking about ‘this one’ and ‘that one’. We create the quality of ‘thisness’ or, as reification is always easier with Latin, ‘haecceity’.

‘Thisness’ and ‘haecceity’ are not qualities we are able to detect. Only if, in some way, we can rule that predicates not available to us ‘do not count’ as differentiating may we proceed from ‘it seems the same’ to ‘it is the same’. Whilst this seems horrendously ad hoc it is often a perfectly proper course to take. Consider the electronic encoding of a piece of music. Electronic encoding proceeds by converting the analogue soundwave into digital format. There are infinitely many points on the analogue wave but a limited number of digital bits into which to encode these points. Digital encoding thus ‘samples’ points at a certain frequency, the encoding program informing the user of the ‘bitrate’ measure of the sampling frequency. If I convert music from one format to another, say in order to listen to the music in my car, I can alter the sampling rate. The greater the sampling rate the more faithful the reproduction of the original recording. The smaller the sampling rate the less memory is needed, enabling more music to be stored in the car. As the sampling rate is increased a point is reached (call it ‘A’) where I am unable to distinguish the quality of the music whilst driving in the car. I should not increase the bitrate beyond A to A+1 as I will not increase my listening pleasure but will decrease the amount of music that can be stored. I can make the distinction between the two encodings. I cannot make that distinction by using only my ears in the car, from this limited body of evidence. For the purpose of ‘listening enjoyment’ A and A+1 are the same piece of music: using only ‘listening enjoyment’ as my guide I cannot distinguish between A and A+1.

We can say that something is unitary for a particular purpose if, and only if, differences cannot be discerned with the body of evidence brought into play by that purpose. This aligns with commonsense and, in much discourse, labels the ‘type’ of description:

For the purposes of describing the shape of the two figures shape-statements are used. With these statements no distinction can be made between (a) and (b). They are the same shape. For the purpose of describing the angle, angle-statements are used. With these a clear distinction can be made. Thus (a) and (b) are the same shape at different angles.

I shall call the varying bodies of evidence brought into play ‘magisteria’ following on from Stephen Gould’s[4] use of the term in arguing against a necessary conflict between science and religion. The separation of religious and scientific knowledge Gould advanced was argued from the differing purposes of science and religion:

‘science in the empirical constitution of the universe, and religion in the search for proper ethical values and the spiritual meaning of our lives.’[5]

For the purpose of discussing the empirical constitution of the universe we use empirical statements. For the purpose of discussing ethical values and the spiritual meaning of life we use ethical and spiritual statements. The body of empirical statements is the magisterium of science and distinctions we make using these statements are ‘scientific’ or ‘empirical’. The body of ethical and spiritual statements are the magisterium of religion and distinctions made using the magisterium of religion are ‘religious’, ‘spiritual’ or ‘ethical’.

Gould takes ‘the soul’ as an example and the Catholic teaching that, if humans evolved, at some point in that evolution God infused man with a soul. The soul has no empirical consequences, we cannot touch, see, smell, taste or hear the soul nor does the soul entail anything touchable, visible, odorous, noisy or tasty. Using the magisterium of science no distinction can be made between a human body before infusion (‘BS’) of the soul and after ‘AS’. For the purposes of science BS and AS are the same body. Using the religious magisterium there is a ready distinction to be made. We can say something like ‘BS and AS are the same body with different persons’.

If we ask a question such as ‘what is meant by ‘the soul’?’ the answer will consist of outlining what the concept entails. Whilst the elucidation is unlikely to be complete whatever magisteria are used the magisterium of religion will be necessary and the magisterium of science will be useless. Let us consider an actual ‘body A’ and the proposition P that ‘body A has a soul’. If we are presented with ‘body A’ there are two possibilities, it is identical to either of two ideal bodies:

1. A body with a soul
2. A body without a soul

If body A is identical to 1 then P is true. If body A is identical to 2 then P is false. However as we have seen, for science, body 1 and body 2 are identical. Body A is thus identical to both and either true and false at the same time or, on this particular question, falls silent. ‘The soul’ entails nothing in the scientific magisterium. Where nothing is entailed there is no claim to relate to the facts and so there is neither the possibility of truth nor of falsity: for science ‘the soul’ is meaningless.

Magisteria abound, corresponding to the sets we either can or do make of propositions. We may, and do, distinguish separate non-overlapping magisteria; as Gould did with ‘science’ and ‘religion’. We also break magisteria into proper sub-sets (‘biology’, ‘physics’, ‘chemistry’), ill-defined sets (such as Wittgenstein’s analysis of the ‘family’ of games) and overlapping sets. We argue that one magisterium can be subsumed in another. Quine’s claim that arithmetic reduces to set theory amounts to the claim that all the distinctions that can be made by the magisterium of arithmetic can be made by the magisterium of set theory. The same phenomena may be meaningful for one magisterium, meaningless for another. The magisterium of science is unable to distinguish a dead Schrödinger’s cat from a live Schrödinger’s cat; the magisterium of the cat can readily make the distinction. We may, and do, also take diverse magisteria to create a new, broader, magisterium: taking the magisteria of ‘melody’, ‘rhythm’ and ‘dynamics’ enables us to talk cogently about ‘music’.

Some statements patently fail to have meaning no matter which magisteria are use. The magisterium of ‘literature’ or of ‘story telling’ makes sense of George Orwell’s ‘1984’:

‘It was a bright cold day in April, and the clocks were striking thirteen. Winston Smith, his chin nuzzled into his breast in an effort to escape the vile wind, slipped quickly through the glass doors of Victory Mansions, though not quickly enough to prevent a swirl of gritty dust from entering along with him.’[6]

But rather fails to make sense of Lewis Carroll’s ‘Jaberwocky’:

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.[7]

A new magisterium could be constructed, such as Tolkien’s invention of ‘elvish’, but it seems beside the point: the poem is supposed to be (mostly) nonsense[8].

2 Universality

This raises the question as to whether we can bring together all important magisteria into one group which excludes irrelevant magisteria, a ‘Universal Magisteria’. That which was outside the all embracing over-magisteria would be confidently classified as meaningless. If it did have meaning we would be happy to ignore that meaning. We might never know what borogoves were, other than being mimsy, but we would be no worse off for that.

It is not too much of a distortion to re-cast much of Kant’s critical project in these terms, as an attempt to categorise the discriminating limits of the magisterium ‘reason’. At least we can replicate his argument for the empirical reality of space and time by using the language of magisteria:

The ‘empirical’ magisterium necessarily describes the world in terms of space and time. As a result this magisterium cannot distinguish between:

A­-with-a-non-time-non-space-property and

The non-time-non-space-property is meaningless for empirical discourse. An object consisting entirely of non-time-non-space-properties is indistinguishable, in empirical discourse, from:

1. Nothing
2. Everything
3. Anything

Thus it does not, for empirical discourse, have any meaning. Each and every of property of any object distinguishable using the empirical magisteria necessitates either time or space. Thus, for empirical discourse, time and space are constant requirements: time and space are empirically real.

An unfortunate side-effect of Kant’s philosophy, as pursued by those who came immediately after him, was a rekindling of hope in transcendental metaphysics. These later philosophies made much use of magisteria that lay wholly outside any experiential statements and ended up describing a world which we simply did not live in. And so we come to Peirce and his plea for usefulness:

‘Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.’ [9]

The plea is to ignore anything that does not fit into a magisteria of practicality, to identify the ‘Universal Magisteria’ with statements of practical effects.

There is a degree of ambiguity in the use of the word ‘conceivably’. This would appear to authorise the use of conditional magisteria: the practical effects that would have occurred if. Peirce is not clear on this, sometimes allowing a conditional; at other times claiming it is irrelevant. Peirce is happy to call a thing heavy where if it were to be dropped it would fall and yet questions whether a diamond whose hardness is ever actually put to the test can be called ‘hard’. We can, with justice, dispute the asserted irrelevance of conditionals. Let us suppose, with Peirce ‘that a diamond could be crystallized in the midst of a cushion of soft cotton, and should remain there until it was finally burned up.’ Whilst we can never actually retrieve the diamond and perform a scratch test we can, quite clearly, understand what it would mean. Indeed the meaning of the example depends upon these very imaginative capabilities.

We can also dispute the completeness of the ‘practical’ magisterium, even if expanded by the authorisation of conditionals. The time of the never-existent Winston Smith’s entry into the never-existent Victory Mansions has no practical effects. We can, never-the-less distinguish the, true, statement ‘Winston Smith entered Victory Mansions at 1 p.m.’ from the, false, statement ‘Winston Smith entered Victory Mansions at 2 p.m.’. Now this may well be parasitic on concepts learned in practical discourse; such as people, Mansion flats and times of the day; but the distinction can still be made.

Ignoring, for the moment, Peirce’s specific views on which magisteria are acceptable his basic view of meaning is sound. We use magisteria to distinguish, if we cannot distinguish between hard and soft the statement ‘x is hard’ fails to entail anything, cannot be said to be either true or false and, thus, fails to have meaning. If there is no magisteria to make a distinction, such as between mimsy and non-mismsy borogroves, the concept fails to have meaning. The totality of practical effects of an object is our whole conception of the object for practical purposes.

On the choice of magisteria, Peirce’s view might be sound if suitably rephrased. Just as the magisteria used in deciding a bitrate to encode music for the car depends on what I am interested in (sound quality and storage capacity) the ‘Universal Magisterium’, to be Universal, will depend on the totality of our interests. Peirce is, in effect, stating ‘I am not interested in anything other than practicality’. However I am interested in things other than ‘practicality’, and I rather suspect Peirce was interested in things other than practicality. Instituting a distinctive border, especially between ‘all things good’ and ‘all things bad’, rather depends on an accurate drawing of the boundary. Drawn too broadly, ‘everything I am interested in and nothing I am not’, it fails to serve as a guide. Drawn narrowly enough to act as a guide it risks ruling out matters of genuine interest (‘what happens to Winston at the end of the book?’). I shall refer to this as the Universality Problem.

The Universality Problem was repeated as Logical Positivism developed the UVCM. Some removed conditionals entirely, the propositions would have to be actually verified, some allowed a vast range of conditionals: that we should be able to give some indication of how a proposition might be verified. All however limited the magisteria to empirical evidence, preferably statements about phenomena.

The limit to this magisterium failed. The Logical Positivists may have been only ultimately interested in phenomena but talk of phenomena is underpinned by talk of other things. Talk of phenomena necessitates talk of things held to produce those phenomena and things have non-phenomenal characteristics. Talk of things usually leads to talk of the stuff from which they are constituted. As we are interested in propositions about phenomena we are, at least subsidiarily, interested in propositions about the things and stuff that let us formulate and test those propositions, the ethics that inform us what to do with them and the art that lets us express them.

Logical Positivism thus led to constant failed attempts to describe non-empirical concepts in purely empirical terms. The emotivist theory of ethics is a case in point. Having outlawed ‘ethics’ per se as a result of UVCM the Logical Positivist is reduced to scratching around in the magisterium of empirical evidence for something that looks like an ethical injunction. The nearest that can be constructed in the empirical magisterium is something like ‘S says sticking needles into babies’ eyes is always wrong’. The emotive theory of ethics may, of course, be correct. There may be no ethical injunctions per se. It is, however, not a priori correct. It is certainly not the case that our non-emotive-theory statements are either identical to the emotive theory statements or are gibberish. By ‘sticking needles into babies’ eyes is always wrong’ we do not mean ‘S says that…’, we mean ‘sticking needles in babies eyes is always wrong whether S says so or not’.

Interestingly, this was Popper’s primary objection to the UVCM. Now Karl Popper is the last person anyone would expect to support a verification criterion. But some amongst the Logical Positivists were happy to accommodate Popper on this matter and ‘persuaded themselves that (Popper) would agree to substitute falsifiability for verifiability as a criterion of meaningfulness’[10]. They persuaded themselves incorrectly because Popper appreciated the Universality Problem. In their zeal to outlaw nonsense the Logical Positivists had inaccurately drawn their boundary. Too much of genuine interest was removed: the ‘positivists, in their anxiety to annihilate metaphysics, annihilate natural science along with it.’[11]

Never-the-less ‘S says sticking needles into babies eyes is always wrong’ is the totality of the meaning for empirical evidence. Speaking locally, as opposed to universally the arguments about meaning have considerable merit.

3 Verification

Being a good little falsificationist I would hold that verification was a mistake. But I do have an argument to give you that:

Outlining falsification outlines meaning.
Outlining meaning outlines falsification
Outlining verification does not necessarily outline meaning

We can agree, I hope, that a tautology does not mean anything for any particular magisterium. Now, suppose P entails Q, a proposition of magisterium-M. Q may be put forward as part of the meaning of P. Is P falsified by not-Q, does it have a ‘falsificatory mirror’? If ‘yes’ then a falsifying instance has been specified for P. If ‘no’ then a verifying instance only has been specified. However Q on its own is equally a verifying instance of any tautology T.

Failing to specify a falsifying instance for P means that no difference has been established between P and the, meaningless for magisterium-M, tautology T. Thus no meaning for P has been specified. On the other hand specifying not-Q as a falsifying instance on its own is sufficient to distinguish P from the tautology T. Not-Q is a verifying instance of the tautology T and a falsifying instance of the, meaningful, proposition P.

We can, thus, specify a conditional:

Conditional 1: if a situation has been specified where a proposition would be falsified then part of the meaning of that proposition has been specified.

We cannot specify the conditional:

Conditional 2: if a situation has been specified where a proposition would be partly verified then part of the meaning of that proposition has been specified.

A rule could be brought on that the complete verification method of P would have to be specified. This, naturally, would specify the complete meaning of P. A requirement of complete verification would be difficult to maintain consistently. As above we can place confidence in the principle of the indiscernibility of identicals. If P is falsifiable it can, clearly, be distinguished from a meaningless proposition and is, clearly, meaningful (conditional 1 holds). A full elucidation of what would verify P may not be possible even if some of the meaning were sat there staring everyone in the face.

We can go on and start with meaning. If a proposition has meaning for then it differs from a tautology. A tautology has nothing that will make it untrue. Thus P has meaning P has propositions in some magisterium that would make it false. We can specify another pair of conditionals:

Conditional 3: if a proposition has meaning there is a situation in which it would be false

Conditional 4: if a proposition has a situation in which it would be false then it has meaning

The two create the biconditional: if a proposition has meaning there is a situation in which it would be false and if a proposition has a situation in which it would be false then it has meaning. Alternatively, in less tortured prose:

The meaning of a proposition is what will falsify it.

4 Criterion

If the biconditional is split out this gets us back to much the same place we started, one consequence seeming beyond reproach:

If a proposition has no meaning no falsifying situation can be outlined

and a trickier situation:

If no falsifying situation can be outlined then the proposition has no meaning.

This is very much like the bastardised Leibniz’s Law. Indeed the above principles can be re-written as principles of identity:

1*. If a proposition is identical in meaning to a tautology no falsifying situation can be outlined
2*. If no falsifying situation can be outlined then the proposition is identical in meaning to a tautology

Unfortunately the former, the one beyond reproach, did not really tie in with the aims of the Logical Positivists. Crudely put this was to shut the metaphysicians up once and for all. The Logical Positivists needed a criterion, an explicit hurdle which propositions would have to be seen to clear. This requires that the absence of falsifying situations in 2 and 2* be automatically available to us, unfortunately they are not.

The longing for a ‘criterion’ produces another problem: what actually counts as a falsification? We are now back to the ‘conditional magisteria’ mentioned in relation to Peirce and the problem of judging a proposition meaningless when there is meaning evident to all. Drawn as widely as possible any potentially falsifying scenario would reveal meaning. This would render the principle useless as a criterion. It is almost always possible to come up with some conditional in some magisteria, some ‘if’ that would get around the injunction. ‘But if Pegasus were to exist he would have a favourite food so it is not entirely meaningless to talk about whether he likes oats or not.’

All but ‘realistic’ falsifying pathways could be outlawed, but this brings up the same problems in drawing boundaries as search for a universal magisterium. And, of course, even a proposition that depends on ‘if Pegasus were to exist’ has some meaning. It is a particularly pointless meaning, but a meaning non-the-less.

We are left with the operation of 1 and 1* which will enable us to diagnose a meaning but not determine its absence.

5 Localised, Falsification Diagnosis of Meaning ‘LDFM’

I propose that we act locally, not universally; that we use falsification, not verification; that we remain aware that our diagnosis may not be a clear cut criterion. In short I propose a Localised, Falsification Diagnosis of Meaning.

Primarily I am concerned to put LFDM forward simply because I think that it is correct. I contend that if we have outlined all the circumstances in which a proposition can be falsified within a magisterium we have outlined, in full, its meaning in that magisterium. This would hold true whether or not LDFM advanced UVCM’s aim of exposing and combating nonsense. A localised falsification diagnosis of meaning would also be a useful analytical tool. Contextualists would find it useful in determining which context, magisterium, a proposition is held to apply to. “Does a proposition have objective meaning, or is it purely subjective?” is, again, a question about the magisteria to be applied in diagnosing its meaning. Alternatively we might find that, whilst a proposition has meaning the magisteria that give it meaning are not of real interest.

Again, this would hold true whether or not LDFM advanced UVCM’s aim of exposing and combating nonsense.

Happily LFDM does give us back some of the nonsense combating properties of UVCM. Both UVCM and Popper’s, related, criterion of demarcation were an attempt to fight against arrant nonsense. Popper’s acted against pseudo-science, UVCM against any and all nonsense. UVCM failed, universally. Popper’s criterion succeeded, and continues to succeed, but only for science. LFDM can be seen as a generalisation of Popper’s criterion of demarcation:

'In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality.’[12]

LFDM expands the magisteria to which it can be applied:

'In so far as a statement of magisteria X speaks about X, it must be falsifiable by other propositions about X; and in so far as it is not falsifiable by other propositions about X, it does not speak about X.’

LFDM separates X from pseudo-X by looking at the falsifying effect of other propositions within magisterium-X. That being the case it separates science from pseudo-science in the same way as Popper’s criterion does: scientific propositions are capable of falsification by scientific propositions. It separates history from pseudo-history: historical propositions are capable of falsification by other historical propositions. Pseudo-ethical propositions are those which cannot be falsified by other ethical propositions, pseudo-sexual-political propositions lack sexual-political falsifiers, and so on.

And so to the fight against nonsense. Take the, now notorious, question of Luce Irigaray:

‘Is E=Mc2 a sexed equation?’[13]

We are perfectly entitled to ask ‘what the **** is a ‘sexed equation’’? Interestingly this appears to be a question about the meaning of a (rhetorical) question about meaning. Is the meaning of ‘E=MC2 expoundable in anyway in terms of sex? Does the equation have meaning within the sex magisterium? A falsificationory diagnosis of part of the scientific meaning might be something along the lines of:

If you perform a calculation on the basis of E=MC2 you will not get an incorrect answer

or, perhaps,

If you ever find yourself in a position to measure the energy content of some matter you will not find it other than C2 times however much matter you have

So, for the magisterium of science, we can happily establish meaning. What about the magisteria of sex or sexual politics? It is difficult to see how it could possibly mean anything in either magisteria. Irigaray offers the, confirming, proposition that the equation ‘privileges the speed of light over other speeds vitally necessary to us’. Would ‘Is E=Mc2 a sexed equation?’ be falsified by it not privileging the speed of light? I suspect not, I suspect that this is some vaguely conforming proposition put forward without a falsificationary mirror. It is Q where not-Q also confirms.

Under LFDM the passage cannot be demonstrated to be meaningless tripe. As above, we cannot conclude from the inability to describe a falsificationary pathway that a proposition has no meaning. However, if a person writing or speaking cannot give us a falsificationary pathway then we can conclude that they do not know what they mean by what they say or write. Irigaray is quite happy to expound without any intentional meaning on her part. That empty intended meaning can be neither true nor false. Irigaray thus expounds it without regard to its truth: Frankfurt’s paradigm definition of bullshit[14].

Above I mentioned the possibility of throwing in some falsifying instance. Here the magisterium concept comes into its own. What would falsify the proposition R: ‘sticking needles in babies’ eyes is always wrong’? The proposition not-R ‘sticking needles in babies’ eyes is permissible if you really feel like it’ would do it. Not-R forms part of the ethical magisteria and so, as it is falsified by an ethical statement, R has ethical meaning. The proposition U: ‘S says that sticking needles in babies’ eyes is always wrong’ would not be falsified by not-R. U would be falsified by proposition not-U: ‘S says that sticking needles in babies’ eyes is permissible if you really feel like it’. Not-U is a proposition about S, a descriptive statement about S. U has descriptive meaning, not ethical meaning. What could Irigaray posit as a falsifying instance? What magisterium would be needed to frame that falsifying instance and what type of statement would that make ‘E=MC2 is a sexed equation’? I leave an answer to the reader, my suggestion being too unkind.

[1] Popper, Karl. Unended Quest: an intellectual autobiography. Fontana. Glasgow. 1976. pages 88-89
[2] In conversation with Bryan Magee. Magee, Bryan. Men of Ideas. British Broadcasting Corporation. London. 1978. Page 131
[3] Ibid. page 131
[4] Gould, Stephen Jay. ‘Nonoverlapping Magisteria,’ Natural History 106 (March 1997) Pages 16-22.
[5] Ibid.
[6] Orwell, George. 1984. Penguin Books, London 2004 p. 3
[7] Carroll, Lewis. Through the Looking-Glass. Project Gutenberg.
[8] It is not complete nonsense, as Alice points out ‘SOMEBODY killed SOMETHING:
that's clear, at any rate’.
[9] Peirce, Charles S. ‘How To Oake Our Ideas Clear’ in Buchler, James. Philosophical Writings of Peirce. Dover. New York. 1955. Page 31.
[10] Popper, Karl. Unended Quest : An Intellectual Autobiography. Fontana. 1976 p. 87
[11] Ibid p 36
[12] Popper, Karl. The Logic of Scientific Discovery. Hutchinson. London. 1986. page 314.
[13] Irigaray, Luce. ‘Sujet de la science, sujet sexué?’ in Sens et place des connaissances dans la société. Centre National de Recherche Scientifique. Paris. 1987. page 95 quoted in Sokal, Alan and Bricmont, Jean. Fashionable Nonsense. Picador. New York. 1998. page 109
[14] Frankfurt, Harry G. On Bullshit. Princeton University Press. Princeton and Oxford. 2005