Reducing Hesperus

Does a reductivist or 'identity' theory have to be eliminativist? Perhaps not. The theory could simply be asserting an identity. Take an early scientific discovery: the heavenly body that appears in the morning (Phosphorus) is identical with the heavenly body that appears in the evening (Hesperus). Is the theory that Hesperus = Phosphorus a reductivist theory? Nothing has been eliminated. Hesperus has not been eliminated because Hesperus is identical with Phosphorus, and Phosphorus has not been eliminated. By equal reasoning, Phosphorus has not been eliminated. So nothing has been eliminated. But is the theory reductivist? It seems to be lacking the asymmetry that we expect of a properly reductivist theory. It seems reasonable to assert that mental states are really brain states. But if this were merely an identity statement like Hesperus = Phosphorus, it would be just as reasonable to assert that brain states are 'really' mental states. Which seems odd.

On artefactual identity

Following some severe strictures by Brightly on my earlier posts I offer reformulations of the 'aporetic set' of propositions, as follows.

A. If an artefact X1 has a replacement component, and X contained the replaced component, and the other components of X1 have been components of X since the replacement, and if the arrangement of components is the same in X1 as in X, then X1 = X.
B. If the components of Y are now the components of X, similarly arranged, then X=Y
C. If Fx and x=y, then Fy
D. If it is not the case that components of X = the components of Y, then it is not the case that X = Y.
E. Artifacts exist.

The only notion that may need elucidation is 'plural identity'. I propose the following definition: the x's = the y's if every one of the x's = some y, and every one of the y's = some x, which uses singular identity. Note I have made a significant change to C. That is because substitutivity is more fundamental than transitivity, and because (I think) we can derive transitivity. For let x = y, and y = z. The identity x = y allows us to substitute 'x' for 'y' in 'y = z'. Then x = z, which is transitivity.

We can then prove inconsistency as follows.

1. Suppose there are an X1 and an X such that A is true. Then X1 = X.
2. Suppose next that there is an X2 such that A is true regarding X2 and X1. Then X2 = X1, and from C above, X2 = X.
3. Repeat this process, ensuring that each replaced component is always one of the original components (and not a replacement component). Then, repeating this n times for the n original components, we have Xn such that Xn = X. Note that while all of the components of Xn are components of X (because of the identity, and because of C above), it is nonetheless true that at one time none of the components of Xn was a component of X. Indeed, it is true (again because of C above) that none of the components of X was at one time a component of X.
4. Take all the original components of Xn/X and reassemble them so that they are arranged exactly as they were when they were part of Xn/X, to make Y. Then (from B above) X = Y.
5. But from D above, since the components of Xn/X are currently different from those of Y, it is not the case that X = Y.
6. Thus X = Y and not X=Y. Contradiction.

Is Hume an eliminativist about objects?

Hume's philosophy is more radical than we imagine. He did not hold, as Locke held, a representative theory of perception such that our sense impressions are fleeting and perishable, but are representative of objects which are relatively permanent and durable. He held that, when we analyse and examine the world carefully, we find that the things we call tables, chairs and houses really cease to exist when we are not perceiving them. For such things are really identical with our perceptions or sense impressions. He says* "it is impossible for us distinctly to conceive, objects to be in their nature any thing but exactly the same with perceptions". But "it is a gross illusion to suppose, that our resembling perceptions are numerically the same; and it is this illusion, which leads us into the opinion, that these perceptions are uninterrupted, and are still existent, even when they are not present to the senses. " Only philosophical analysis can penetrate and expose this illusion. Even that analysis can fail. The illusion is so strong that as soon as philosophers have discovered it - namely discovered, like Locke and the seventeenth century philosophers of perception, that our sense-impressions are fleeting and impermanent - that they immediately invent a new set of impressions that have the required permanence. Thus the representative theory at once refutes and re-establishes the illusion.

[...] it is liable to the same difficulties; and is over-and-above loaded with this absurdity, that it at once denies and establishes the vulgar supposition. Philosophers deny our resembling perceptions to be identically the same, and uninterrupted; and yet have so great a propensity to believe them such, that they arbitrarily invent a new set of perceptions, to which they attribute these qualities.

Does this make Hume an eliminativist, or a reductionist? I have argued elsewhere that the distinction is arbitrary, and I shall argue that this applies to Hume's position also. If we define 'material object' as something which is mind-independent and permanent, then it is clear Hume is denying the existence of any such things. The only objects we are aware of, he says, are these fleeting and perishable sense-impressions, which have no continued and uninterrupted existence. So he is an eliminativist regarding material objects defined in this way. But as I have argued, we don't have adopt this definition. If we define 'material object' as something identical with our sense-impression, then uninterrupted existence turns into a mere accidental feature of objects. An accidental feature that, as Hume argues, may not apply to any object at all, just as 'carried by the ether' does not apply to light, as people once thought.

In summary: whether Hume is an eliminativist or reductionist about the term 'material object' depends entirely on how you choose to define the term. There are the observable phenomena - the sense impressions - and there is whatever unobservable X explains or underlies these phenomena. And that X can have any features you like. There are no 'essential features' of things that are essentially unobservable.

* A Treatise of Human Nature, Book I. 4. ii - "Of scepticism with regard to the senses". This section is essential reading for any understanding of Hume. People often don't read it because it occurs towards the end of the first book, and because there is a lot of focus on the causation stuff in Part III. Part IV, particularly sections 2-4, are by far the most interesting and enjoyable and indeed strange parts of the work.

Radical versus conservative ontology

Before I move on to discuss the other assumptions that generate the conclusion that there are no artefacts, I realise there is something else to discuss. This is the distinction between what Steven Savitt calls 'ontologically conservative' or 'retentive' theory change, or reductionism, and 'ontologically radical' or 'eliminitavist' theory change, or eliminativism. This is explained well here. Ontological conservatism is when we revise our view of the entities posited by the original theory, without eliminating them. For example, our conception of light was transformed by the discovery that it is electro-magnetic radiation, and older explanations of it had to be rejected as incorrect or incomplete or misleading. But this discovery did not lead to abandoning the existence of light. Ontological eliminativism is when we drop completely the view that certain entities exist. For example, there is nothing in modern psychology that justifies the existence of malevolent spirits or demons. So we dropped demons altogether from our modern scientific ontology.

This is closely connected with what I discussed here about Inwagen's paraphrase argument. If his paraphrase of a story about ships is intended merely to change our view about ships (e.g. that they are not identical with their component parts, and that there is something singular over and above the parts corresponding to the grammatically singular 'a ship') then the paraphrase is ontologically conservative. It still affirms the existence of ships, just as the electro-magnetic theory affirms the existence of light, but it changes our view of what ships are, just as the electro-magnetic story changes our view about light. By contrast, if the paraphrase really 'loses ships', then it is ontologically radical. It challenges our common-sense ontology in a way that modern psychology challenged demons.

It is also connected with the 'aporetic' set of propositions I discussed earlier. (I have modified proposition B to meet an objections made by earlier comments).

A. An artifact remains numerically the same if one of its components is replaced, without replacing the others.
B. If the components of X, are now the components of Y, arranged in the same way, then X=Y
C. Identity is transitive (if X=Y and Y=Z, then X=Z)
D. If artifact a and artifact b have numerically different components at the same time, a and b are numerically different.
E. Artifacts exist.

If the four propositions A-D are true, artefacts do not exist, which is the ontogically radical position. Otherwise, one of more of these four propositions is false. This would revise our view about the fundamental properties of artefacts, which is ontologically conservative. This is by way of background. I will return to the original plan tomorrow, when I will discuss whether modifying our account of numerical identity could resolve the logical inconsistency between the five propositions above.

More on 'Replacement Identity'

Not everyone is sure about replacement identity, the assumption that when a component of some artefact (or at least a very small component such as a brick) is replaced, the artefact remains the same. Some of these arguments are qualified by the assumption that the components are 'simple'. But what components are simple? An artefact like a bike is made from artefacts such as mudguards, wheels, brakes and so on. These artefacts (a brake e.g.) are built from other artefactual components such as rubber blocks, steel wingnuts, plastic cables and so on. An artefact such as a plastic cable is made of molecules. A molecule is not an artefact, of course, but it is complex, being made of atoms. An atom is made of sub-atomic particles and so on.

It seems entirely implausible that when a small sliver of material, or molecule or sub-atomic particle is shaved off the bike, the bike is no longer identical with the bike that existed before. So some qualified version of Replacement Identity must be true. But then the Transitivity of Identity kicks in. If the bike is the same bike after a tiny part has been removed and then replaced, then it is the same bike. And still the same bike after another part has been shaved off and replaced. And so on until the whole bike has been completely replaced. The enemies of (A) must bite the bullet. Either it is false, even for sub-atomic changes in composition. That seems implausible. Otherwise Replacement Identity + Transitivity gets us to the paradoxical conclusion. More on Transitivity later, as I promised.

Bikes, now and then

In discussing temporal identity, there is a strong temptation to use expressions like 'the bike then' or 'the bike as it was yesterday' or 'the bike as it was at that spatio-temporal moment' - see the comments to my previous post. As though 'the bike then' refers to some different object than 'the bike now' or 'the bike today'.

These expressions don't make any sense to me. Surely 'then' and 'now' or 'yesterday' and 'today' are just adverbs modifying the verb, rather than an adjective modifying a referring phrase or description. Consider

This bike, which was repaired yesterday, has a new mudguard today.

The sentence contains just one subject: 'this bike'. It is modified by two predicates. The first - 'was repaired yesterday' - tells us something that happened at some previous moment to the bike. The second - 'has a new mudguard' - tells us something that is true of it today, now. It makes no sense to divide the subject into something that is or was 'the bike yesterday', and another, different thing, that is 'the bike today'. Both 'was repaired' - which is a predicate in the past tense - and 'has a new mudguard' - which is in the present tense - qualify this single bike. Or 'this bike now', if you really want.

If there really is an object such as 'this bike then', it is an object to which the predicate 'is now being repaired' applies. For it was true to say of the bike, then, 'this bike is being repaired'. By contrast, the past tense predicate 'was being repaired' applies to 'the bike now'. But as I say, modifying a subject expression by means of an adverb doesn't make sense.

The medieval writers keenly appreciated this. A noun or referring phrase has no tense attached to it. Its semantics does not include time. The sense of time is what a verb brings in. Hence past, present and future tenses, and hence qualifying adverbs like 'now' and 'then'.

Identity in replacement

I will express the 'Ship of Theseus' argument using an 'aporetic' set of propositions. An aporetic set of propositions is where each proposition seems to express an obvious truth, but all of them together are logically inconsistent. As follows.

A. An artifact remains numerically the same if one of its components is replaced, and the rest remain the same.
B. An artifact is numerically the same if all of its components are numerically the same.
C. Identity is transitive (if A=B and B=C, then A=C)
D. If artifact a and artifact b have numerically different components at the same time, a and b are numerically different.
E. Artifacts exist.

It is fairly easy to show they can't all be true*. Therefore one of them is false. In particular, if we accept A-D, we have to drop E. There can be no objects that conform to our intuitive idea of an artifact, which is the implied conclusion of the Ship of Theseus story.

In this post and three later posts, I will examine the four assumptions A-D to examine if the proposition-set is really aporetic (usually what appears to be an aporetic set dissolves upon enquiry, when we find that one or more of the propositions are not obvious or self-evident at all).

I will begin with the assumption that an artefact remains the same, when one of its components is replaced. My son recently wrecked the mudguard of my bike so badly that it fell off and is still lying in the front garden. I plan to take the bike to the repair shop to fit a new mudguard. Will the bike plus new mudguard be numerically identical with the bike as it was with the old mudguard (this is precisely what Peter van Inwagen appears to deny)? The question appears to involve deep metaphysical concepts like temporality and numerical identity, which makes it tempting to challenge it (on the grounds that deep metaphysical assumptions involve doubt and uncertainty from their very nature). But the question is actually quite mundane. Suppose, after getting the bike repaired, I say

(*) This bike had its mudguard replaced at the repair shop yesterday.

Is that true? Surely, on the assumption that I did take this bike to the repair shop, and that the crappy and bent mudguard was replaced with a shiny new one, what I say is unquestionably true. Yet it involves both 'metaphysical' assumptions. It involves identity through the very structure of the proposition. Identity: this bike = the bike that was taken to the repair shop. Temporality: the present reference to 'this bike', and the past 'had' of 'had its mudguard replaced'. Without the 'metaphysical' assumptions embedded in the proposition, we could not make the most simple, mundane and matter-of-fact statements about our ordinary everyday life. Such as replacing mudguards on bikes.

Note also (see my previous post) that we cannot re-tell this story by means of expressions like 'bikewise arrangement of parts'. For it is false to say that this bikewise arrangement of parts (which includes the new mudguard) is the arrangement of parts taken to the repair shop (which included the old mudguard).

I conclude that the principle of identity under replacement - which involves merely the assumption that we can refer to an artefact that exists now (this bike) by means of a past tense statement (the artefact that was taken to the repair shop) - is unquestionably true. Tomorrow (or whenever I can be bothered to write it): the transitivity of identity.

* Roughly as follows. If artifacts exist, suppose that some artifact X exists. Then suppose we replace one of its component to give artifact X1. Then (from A above), X=X1. Then replace one another component in X1 to give X2, as in the Ship of Theseus story. From A above, X1 = X2. And from C above, X = X2. Repeat this process for all the n original components to give Xn. Then X = Xn, by the previous argument.Now take the n replaced components, and assemble appopriately to make artifact Y. From B above, X = Y. From transitivity, X=Y and X = Xn so X = Y. Xn and Y are co-existing, i.e. exist at the same time. But Xn and Y have different components (since Y is made from the original components of X, and Xn is made from entirely new and different components). Thus, from D above, Xn /= Y. Since X = Xn, X /=Y. Contradiction: X=Y and X /= Y.

Reduction by re-telling

A reductionist argument might go as follows. If you can take any story that ostensibly involves the existence of X's, and re-tell it without mentioning X's and without 'losing something' in the re-telling, then conclude that there aren't any X's. It's a bad argument. Either the re-telling means the same, but avoids mentioning X's by name. In which case we haven't avoided mentioning X's at all. It's as though we translated a story about ships into German, thus avoiding use of the English 'ship' by using the German word 'Schiff'. We have avoided the English 'ship', but we haven't avoided mentioning ships. Or the re-telling really doesn't mention X's at all, in which case the requirement that we aren't 'losing something' (ships, e.g.) is violated. You can't fail to mention X's in a re-telling without failing to mention something that was in the original story, and so the argument is obviously not valid.

Yet this is precisely what Peter Inwagen's argument against the existence of ships appears to do, when he re-tells the story of the Ship of Theseus.

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (Peter van Inwagen, Material Beings (Cornell UP, 1990) 128-129)

Perhaps I have missed his point, but it appears to be that we can re-tell the story of the ship such that there is nothing in the standard version of the story that is not captured in the re-telling, and the re-telling does not mention ships, ergo there is no need for ships. If that is his argument, it involves the obvious fallacy I describe above. He begins "Once upon a time, there were certain planks that were arranged shipwise". What does that sentence mean? Does it mean the same as 'Once upon a time, there was a certain ship'? Does the expression 'shipwise arrangement of planks' mean the same as the word 'ship'? In which case the re-telling does mention ships, just as a German version of the standard story would mention ships (although by the word Schiff, of course). Or does it mean something different, something that is not a ship? In which case there is something in the standard version of the story (which begins with the assertion that there was a ship) that is not captured in the re-telling (which asserts only the existence shipwise arrangements of planks). Either way, the conclusion does not follow. Either the re-telling does assert the existence of ships, in which case it does not imply the non-existence of ships. Or it doesn't, in which case something has been lost in the re-telling, and the requirements of the argument are violated.

This casts some doubt on Vallicella's assertion here that Invagen "is a brilliant man". The argument does not strike me as brilliant at all. But perhaps I misunderstand it.

Argumentum pro homine

I just noticed something much more horrible.

Argumentum ad baculum

Argumentum ad baculum: literally 'argument to the stick' or as we say 'appeal to force'. Wikipedia gives an odd example in its article here, claiming it is not fallacious.

If you drive while drunk, you will be put in jail.
You want to avoid going to jail.
Therefore you should not drive while drunk.

Surely it is fallacious? If you want to avoid going to jail, then it probably follows that you want to avoid driving while drunk (assuming that you know the consequences of driving drunk, and that you are rational enough to not want anything that is a consequence of what you don't want). But it doesn't follow that you shouldn't drive when drunk. 'Should not' or 'ought not' expresses a moral conclusion. This does not follow from any psychological assumption such as wanting or desiring. Now, the following version of the argument is probably valid

If you drive while drunk, you will be put in jail.
You should not be put in jail
Therefore you should not drive while drunk.

But that is different, because the second premiss contains an explicit moral judgment. I say it is 'probably' valid, because it relies on the assumption that if B is a consequence of A, and if you should not do B, then you should not do A. Which could be questioned.

As for the rest of the article, it made no sense at all. Many things in Wikipedia are well done. What is it about philosophy and logic that Wikipedia finds so hard?

Impersonal assertion

A fundamental objection to my position on assertion (that assertion is a part of the semantics of a declarative sentence) is that assertion must be personal. That is, the subject of verbs like 'assert', 'state', 'say' and suchlike must be a person. Thus no sentence - which is an impersonal, inanimate linguistic item - can assert anything. Thus assertion cannot be part of the semantics of a sentence.

I shall argue against this in two ways.

1. Even if we concede that the subject of an assertion must be personal, it does not follow that we cannot analyse a sentence in such a way that a sign for assertion is made visible. I claim that we can analyse the sentence 'Tom runs' as

It is true / that Tom runs

which means the same, but which contains the sign 'it is true'. The other part is the that-clause 'that Tom runs', which signifies the content of the sentence. This is the same content referred to in sentences such as 'Alice believes that Tom runs', 'Carol hopes that Tom runs', 'Bob doubts that Tom runs' and so on. But no one who utters these sentences asserts that content. If I utter 'Alice believes that Tom runs', I have asserted that Alice believes something. But I have not asserted the thing that she believes: I have not asserted that Tom runs, only that Alice believes this. But when I utter 'It is true that Tom runs', I have asserted that Tom runs. Which suggests that 'it is true' is a sign indicating that I am asserting the content itself, rather than saying something about it (such that it is a belief, or a hope, of someone). The sign 'it is true' is a symbol which, suitably connected with a symbol for the content, signifies assertion.

2. In any case, we need the idea of impersonal assertion for statements whose author is unknown. For example "The next sentence in Genesis says the earth was without form and void, and darkness over it.

In summary. We can analyse a declarative sentence into another sentence which means the same, but which has two main parts: a sign for the content of the sentence and another sign which is used to indicate or signify that the speaker is personally asserting the content, rather than saying something about the content. It is not unreasonable to call this an assertion sign. And sometimes - when the author of the original sentence is unknown - it is equally reasonable to say that the sentence impersonally asserts its content.