William Lane Craig on the Finitude of the Past

Today I commented on a blog which referred to the thought experiment of Hilbert’s Hotel and suggested that it showed that the idea of an actual infinity is incoherent. I put my two cents worth in, saying that there does not appear to be anything incoherent about Hilbert’s Hotel, it’s just weird because infinity is weird.

Anyway, William Lane Craig also argues from the apparent absurdity (not inconsistency, mind) of Hilbert’s Hotel to the absurdity of an infinite past. This is by way of support for one premise of his Kalam Cosmological Argument: that the universe began to exist. It occurs to me that, even if Craig is right about there being no actual infinite sets of things, that does not necessarily help him, considering his actualist presentism.

Craig seeks to solve the problem posed to presentists by extra-present facts by adapting something like Plantinga’s actualist solution to the problem of grounding modal truths. [Craig, W. L. (1998). McTaggart’s Paradox and the Problem of Temporal Intrinsics. Analysis 58: 122-7 at n. 4.] Plantinga has it that modal truths are truths at possible worlds and that possible worlds are abstract entities. Such worlds have been called ersatz or proxy worlds for the manner in which they stand in for ways that the universe could be – where ‘the universe’ is the set of all concrete and abstract things.

Craig defines the present world as the world that obtains. Of course, this is not enough to explain past and future facts, because it fails to distinguish the actual past and future from an infinite array of merely possible pasts and futures that have not obtained and will not obtain. Craig’s modification to worlds actualism, to make it fit for the purpose of explaining past and future facts, is to allow that there are tensed worlds that are actual at some time t. If t is yet to elapse then some of such tensed worlds will obtain and, thus, truths about the future are grounded by reference to these worlds. If t has already elapsed then some of such tensed worlds did obtain and, thus, truths about the past are grounded by reference to these world.

So, on Craig’s own view, an infinite past would not be actual simpliciter in that the worlds that make it true that there is an infinite past would not obtain. Rather, they would did-obtain. Neither a finite or infinite past is actual, they merely were actual. Further, if we suppose that the past is infinite then there is still no time at which there is an actual infinite procession of times. At every time it would be the case that there were an infinite series of times, i.e. such a series did-obtain.

It seems, therefore, that arguments against actual infinite sets are beside the point if we grant Craig his actualist presentism.

The Existent and the Real

At the very beginning of ‘On the Plurality of Worlds’, David Lewis says that the ‘real’ in ‘modal realism’ should be taken as an existence claim. Something is real iff it exists. A noneist need not reject this conflation of the real and the existent, instead simply claim claiming that some things are unreal. However, I am a noneist who prefers to say that existence and reality can come apart.

Noneists eventually face the prospect of having to talk about at least some things that do not exist as though they do. Even Graham Priest, who claims that things can exist at non-existent worlds, has to admit that, if he also wants to say non-actual worlds do not exist then we often mistakenly speak of non-existent (non-actual) worlds as though they are the existing (actual) one. I tend to see this end point as reason to accept that we cannot be extensionalists about meaning to the bitter end. This does not strictly follow from the above, but a uniform treatment of erroneous but meaningful claims is going to push in the direction of a non-extensionalist end point: a point where meaningful sentences/statements/propositions are not made meaningful by virtue of reference to anything included at any world.

I also don’t give the reasons to avoid thinking that this non-extenionalist end-point will provide a reason to become intensionalist all the way back to the actual world. I just want to state the basis of a distinction, here: the distinction between the real and the existent. Real things may or may not possess the property of existence, while there are no unreal things, just meaningful talk and thought as if there are unreal things. The distinction between existence and reality presupposes a mixed extensionalist and intensionalist theory of meaning, requiring both sets of worlds and structured propositions to give a full account of what meaning is. I give no such account here. I’ve just said enough to explain why I would say that ‘existence’ and ‘reality’ come apart.

I guess that I am promoting a semantic account of realism, being my natural usage of the term. Mind-independence as an alternative criterion to existence is simply too hard to define in a principled way. Does this make my realism more prone to deflationism? The primitive concept in my realism is that of a ‘thing’. Talk and thought is of something real if its meaningfulness is dependent upon some thing other than the talk or thought. If you want to mess with my primitive, I guess we have nothing left to talk about.

Metametaphysics

I have just finished working my way through Chalmers, Manley & Wasserman (eds) ‘Metametaphysics’ (2009) Clarendon Press: Oxford and I am slightly disappointed.

Though, in his paper, Peter Van Inwagen makes the usual question-begging assertion that existence is synonymous with the existential quantifier (read unrestricted and unloaded particular quantifier), and Kit Fine passes over the idea of existence as a predicate on his way to declaring that a primitive reality operator is the correct device to use in order to assume a metaphysical tone of voice, there is no representative in the collection of the simple view that ontology is the taxonomy of the kinds of things that do and may exist, as contrasted with everything else that does not exist. Metaphysics, on the other-hand, might be seen as the taxonomy of the kinds of things that may either exist or not exist, i.e. the full range of all things that populate the possible worlds, as contrasted with impossibilia.

Many of the philosophers in the collection are well known to the Australian philosophical scene. One wonders if Graham Priest was or might have been approached to offer a noneistic perspective.

Some Thoughts on Realism About Absences and Holes

Martin(1) felt the need to theorise about absences in order to provide truth-makers for negative existential truths such as, ‘There are no arctic penguins.’ No aggregation of things, properties, relations and (positive) facts is sufficient alone to rule out that there are penguins in the arctic. It is the absence of penguins that clenches it. Yet, Martin claims that these absences are not entities. They are localised states of the world or universe.(2) Similarly, Kukso says that absences are features of the physical world, located in space and time.(3) Apart from the thought that one man’s localised state or feature of the universe is another man’s entity, there is a more focused concern about this non-entity position. We might consider Martin’s quite reasonable claim that absences are always absences of something – some entity or entities.(4) Kukso agrees with this claim.(5) If this claim is correct then we have a criterion of identity for absences: the identity of an absence will be determined by the identity of that of which it is an absence and its spatio-temporal location. A criterion of identity may not be a necessary condition for thing-hood, but surely it is a sufficient condition.

Martin and Kukso also take it as a virtue that their absences are located in space and time because such location is a mark of the concrete and the avoidance of abstracta has the odour of respectability for a metaphysics that sits comfortably with a naturalistic methodology. Yet, the claim that absences have a location may well confuse the properties of the absence with the properties of that of which it is an absence. If the absence of liquid in a cup does not have the property of liquidity, how can it be assumed that it has the relational property of being in the cup? A principled basis is required determined that some properties of an absent thing are shared with its absence, and no such principled basis is available to privilege as such shared properties relational location properties. There is no reason to prefer the view that the absence of Pierre is located in the café as against the view that some absence is the absence of the state of affairs Pierre-in-Café X. Martin and Kukso gratuitously privilege the sharing of relational location properties because that is what their methodology requires. It is not at all clear from intuitions of absences that this sharing is essential to them. Indeed, the opposite view will be given preference below. That is, the criterion of identity for absences is simply the identity of those things of which they are absences.

The Lewis’ initiated the recent discourse on holes within Anglophone philosophy with their article of that name.(6) The respective conclusions of Argle and Bargle – the personae between which a dialogue proceeds – are that holes are material hole-linings and that holes are irreducibly immaterial entities. Another materialistic approach is to take holes to be a region of space-time, bound by a hole-lining. To be precise, as holes can be moved and spatial regions cannot, holes are a 4-dimensional region of space-time that extends along the path of “motion” of its 3-dimensional time-slices. Things may move through space, but they do not move through space-time.(7) Taking up Bargle’s approach, Casati and Varzi(8) instead argue that holes are immaterial things that are ontologically dependent upon discontinuities in the surfaces of material things. To be precise, Casati and Varzi(9) argue that material things are made of space-time, but are not identical to space-time. That is, material things are made of qualified space-time: space-time at which certain properties are instantiated. By contrast, holes are made of (though, not identical to) unqualified regions of space-time. As material things are made of qualified space-time and holes are made of unqualified space-time, holes are immaterial things. However, this is not a view of holes as sui generis things and it may take up a merely terminological dispute as to whether holes are material or immaterial things. Sorensen(10) argues that holes are not immaterial things because materialism requires both atoms and void. That is, while holes are not constituted by matter, they are things at home in a materialist’s world. Yet, there is still the question as to whether or not holes taken as sui generis things can be eliminated or reduced to other kinds of thing for the sake of parsimony. All three of the above approaches reduce holes to space-time and/or matter in some way. Yet, each leaves out something in the nature of holes for the reduction.

First, Casati and Varzi(11) make an important point as to the nature of holes in that, in addition to having hosts (those things in which they are holes), holes can have guests, i.e. the things that partially or completely fill. Holes can be filled without ceasing to be a hole. In term of Casati and Varzi’s theory, holes taken as “immaterial” things are made of either qualified or unqualified space-time. Miller(12) notes that this inclusive account, holding that holes can occupy the same spatial region as material things, is not the only available interpretation of the filling of a hole. One might, instead, hold to an exclusive account wherein a hole cannot occupy the same spatial region as material things and, so, a filled hole ceases to be a hole. Miller(13) goes on to argue that the internal and external accounts are equally warranted for any given hole and this equivalence motivates her conventionalism about holes. That is, it is purely a matter of convention as to whether or not the contrast between the matter contained in or constituted by a given region of space-time is sufficiently diverse to be called a hole. Yet, there is a more realistic way to reconcile the distinction between internal and external accounts of holes and their fillability. We might hold that Casati and Varzi fail to distinguish between cases in which hosts are in some way completed or restored by the filling of a hole and cases in which the host is not so completed or restored. In the former cases, there ceases to be a hole, while in the latter cases there is yet a hole in the host. These two kinds of cases may be distinguished as events of filling in a hole and filling up a hole respectively. While a filled in hole is also filled up, a filled up hole is not necessarily filled in. The difference lies with the material used to fill up a hole. Rather than to say that this difference is purely a matter of convention, a realistic approach is to say that holes are a kind of absence: holes are absences of the material of their hosts. If the material used to fill a hole is not of the kind and arrangement necessary to complete or restore the host then the host will still have a hole as the relevant material will still be absent. The hole has not been filled in; it has merely been filled up. It is this distinction between the possibilities of being filled in and being filled up, realistically construed, for which theories of holes that seek to reduce them to matter and/or space-time cannot give an adequate account.

For a simple example of the contrast between filling in and filling up, we may note that Sorensen(14) considers that shadows are holes in light. As such, shadows can have guests or fillers, just as all holes do. All manner of things can be in shadow, including light that “pollutes” the shadow. Light pollution is a light filler of the wrong kind to fill in the shadow because it contrasts with the light of the hole-lining that bounds the shadow. Sorensen allows that the filler of a shadow can completely fill the shadow, so that a shadow can be full of blue light where the bounding light is white. The difference between filling up and filling becomes clear when contemplating the filling of a shadow with the same colour and intensity of that of the hole-lining. The shadow disappears. Another example is a round hole of a metre in diameter cut into a brick wall. In order to fill in the hole in the wall, we might consider that it must be filled with a sufficiently similar arrangement of bricks and mortar to that which constitutes the existing wall. Yet another example is a sphere with a cavity at its surface. To fill in this hole would seem to require similar material to that which constitutes the sphere, sufficient in volume and shaped to remove any discontinuity from the surface of the sphere.

It should be apparent from these few examples above that normativity has been snuck into the distinction between filling in and merely filling up. It seems that the distinction rests on ways that a host ought to be in some idealisation. Light and brick walls ought to be uniform and continuous. Spheres ought to be completely round. This normativity is not to be confused with the telos or proper function of a thing because the proper function of a thing might require that a thing have holes in it. An obvious example is the proper function (if there is such a proper function) of organs such as the heart or ear. A heart may have the proper function of pumping blood and, yet, there is a sense in which the heart’s irregular shape and the presence of holes makes it a less than perfect solid. The idealisation of certain uniform shapes and constitutions therefore goes beyond – though it may include – the idealisation of function. Indeed, idealisations may pull in different directions, just as an ideal solid would make a less than ideal heart. Having clarified that the relevant normativity is idealisation, broadly construed, the question becomes one as to whether or not holes may be fully explained by idealisations of certain material forms.

The idealisation of certain material forms is not sufficient to explain the distinction between filling in and filling up a hole because the addition of missing parts is not all there is to attaining an ideal form. For example, an otherwise perfect sphere could have a protrusion in exactly the same shape as the cavity in the previous example of a sphere, save for its inversion at the surface of the sphere – a horn, say. So, idealisation need not involve the filling of a hole, or the filling of any vacancy, for that matter. It may simply require the filing down of a protrusion, i.e. it may require an absence to be instated. Thus, holes cannot be reduced to a relation between actual and ideal things as such a relation is not sufficient to distinguish between holes (deficits) and protrusions (overabundances). Our ability to identify a relation between a host, a hole and an idealisation of the kind or kinds of thing the host is does not explain the hole but presumes that absences such as holes are in or about the host. Such a ternary relation privileges one amongst among an infinite number of absences, the infinite array of things that are also absent from the spatial region of the hole, to make one absence the absence that is the hole. In the case of holes and other absences, the choice between realistic and conventional accounts of the normativity of idealisation is a choice between the privileging of one absence among many by means of some objective relation between the things in which there is a hole and the relevant absence, or by means of the inter-subjective practices of a community. It is not the same choice as that between treating holes and absences as real things or as merely conventional posits. It might be thought that the example of organs such as a heart is sufficient to challenge the objectivity of idealisations. The ideal form of a heart can pull in opposite directions in being more like a pump or more like an ideal solid. Not only such conflicting idealisations but, vagueness as to what is and what is not ideal for a given thing, seem to favour conventionalism as to idea forms. However, these are not reasons for a stance on whether or not absences should be regarded realistically, but whether or not absences (which may in any case be regarded realistically) should be privileged in the idealisation of a hole-host by objective or conventional relations.

 If idealisation as it relates to determining the material required to fill in a hole is but the privileging of one amongst an infinite number of relevant absences then the next question arising is what the usual relation is supposed to be between those infinite number of absences, whether privileged or not, and the hole-host. Miller(15) also motivates her conventionalism about holes by means of an equivalence of warrant for opposing views as to whether holes are negative parts of their hosts, as proposed by Hoffman and Richards(16), or parts of a larger immaterial thing made of the space-time region that surrounds and partly coincides with the hole-host, as proposed by Casati and Varzi.(17) However, there is a third view of the relation between holes (privileged or otherwise) and hole-hosts that Miller does not consider. In the discussion above of the view of Martin and Kukso that absences are spatially located, it was suggested that this was to confuse properties of an absence with properties of that of which it is an absence. It is suggested that both the view of Hoffman and Richards and that of Casati and Varzi are founded on a similar error. A hole is not a part of its host, or a part of something made of a larger region of space-time; a hole is the absence of something as part of the hole-host. That is, a hole is the absence of the state of affairs of some specific thing being part of the hole-host. The “ontological” dependence of holes on their hosts turns out to be nothing beyond the same ‘of’ relation that holds between any absence and that of which it is an absence.

Notes

 1. Martin, C. B., ‘How it is: Entities, Absences and Voids’ (1996) 74/1 Australasian Journal of Philosophy pp. 57-65

 2. Ibid. p. 58

 3. Kukso, B., ‘The Reality of Absences’ (2006) 84/1 Australasian Journal of Philosophy pp. 21-37 at pp. 22, 29

 4. Martin, C. B., ‘How it is’ p. 64

 5. Kukso, B., ‘The Reality of Absences’ pp. 29-30

6. Lewis, D. & S., ‘Holes’ (1970) 48/2 Australasian Journal of Philosophy pp. 206-12

7. Fowler, G., Spencer, J. & Wake, A., ‘Holes as Regions of Spacetime’ (2007) 90/3 The Monist pp. 372-8 — Miller, K., ‘Immaterial beings’ (2007) 90/3 The Monist pp. 349-371 at p. 355

8. Casati, R. and Varzi, A. C., ‘Holes and Other Superficialities’ (1994) MIT Press: Cambridge, Mass; London pp. 13, 18-9

9. Ibid. pp. 32-6

10. Sorensen, R., ‘Seeing Dark Things’ (2008) Oxford University Press: Oxford; New York etc. p. 190

11. Casati, R. and Varzi, A. C., ‘Holes’ pp. 56-7

12. Miller, K., ‘Immaterial beings’ p. 358

13. Ibid. p. 365-7

14. Sorensen, R., ‘Seeing Dark Things’ pp. 188-90

15. Miller, K., ‘Immaterial beings’ pp. 364-5

16. Hoffman, D. D., and Richards, W. A., ‘Parts of Recognition’ (1984) 18 Cognition pp. 65-96 at 85

17. Casati, R. and Varzi, A. C., ‘Holes’ pp. 56-7

A Very Short Modern History of the Non-Existent

Brentano described the problematic, quasi-relational nature of mental representation, or intentionality, for modern (post-Cartesian) philosophy in Psychology from an Empirical Standpoint. Intentionality appeared to consist of a relation between a mind and an intentional object, yet such intentional objects include things that do not, and even cannot, exist. This put the status of intentionality as a relation into question. Hence, it is a quasi- relation. Brentano stated that the intentional object was in-existent – which is not to say that it did not exist, per se. Rather, considering Brentano’s reputation as a scholar of Aristotle, the in-existence of the intentional object in the mind likely relates to the Aristotelian model of representation in De Anima. That is, the form of the intentional object is borne by the mind as it would be borne by inanimate matter.

Meinong, a student of Brentano, took more seriously the sense in which intentionality is a relation between mind and intentional object. He proposed that some things do not exist but merely subsist. Further, that some things neither exist nor subsist, but are simply non- existents objects. Intentionality is, thus, a perfectly normal relation to non-existent things that could possess monadic and polyadic properties just as existing things do.

While taking a linguistic turn in his philosophy, Russell initially accepted Meinong’s approach to reference without existing referents. However, Russell eventually rejected the Meinongian approach and, in his On Denoting, expressed his famous theory of complex descriptions to analyse away such empty reference in favour of predicate attributions to only existing things. Quine later adopted a version of this approach of employing contextual definitions with his claim that names of non-existent things could be paraphrased as a unique predication of a bound variable.

The descriptivist solution became the accepted wisdom until Kripke, inter alia, put the adequacy of a descriptivist account of most proper names into question with his modal concept of semantic rigidity. In Naming and Necessity, Kripke gave examples of folk intuitions of proper names as rigid designators (having the same referent in all possible worlds in which they refer), whereas descriptions turned out to be flaccid designators (having different referents in different possible worlds). Instead, Kripke proposed a causal- historical theory of naming. Yet, the original problem reared its head again: reference to non-existent things. Kripke could only account for such reference by denying that reference to non-natural referents is truly meaningful at all. Then again, this offended against some of the very folk intuitions about ordinary language that he had relied upon to attack the descriptivist theory.

More recently Sylvan (formerly Routley) and Priest have resurrected a purified version of the Meinongian solution called noneism, arguing that the property of existence is not trivially equivalent to existential quantification and, so, we can quantify over non-existent things. Parsons and Zalta are other neo-Meinongians of note… Yet, this approach is still plagued by the need for an ad hoc distinction between nuclear and non-nuclear (characterising and non-characterising) properties, or the exemplification v. encoding of properties. Otherwise, because existence is a property, things conceived of as existing must exist. Priest tries to solve this problem by proposing that things need only have their characterisations at worlds that are the way we imagine the actual world to be. However, Priest still wants to say that only the actual world exists. It is then whole worlds that do not exist, though worlds other than the actual world may be characterised as existing. Thus, existence still seems to be a non-characterising property of worlds.

Abitrary-p-entailing properties

Ideally, to avoid ad hoc-ness, a noneist would be able to hold that at least one thing satisfies any given characterisation. One problem with such a claim is that the property of existence could be included in a characterisation, which would mean that anything so characterised must truly have the property of existence. This problem of characterisations including the property of existence is set to one side for this post. A related problem is to be dealt with here involves characterisations with arbitrary-p-entailing properties: properties such as ‘being such that p’ for any arbitrary p. Our ability to endlessly multiply such properties appears to entail trivialism.

Priest’s solution to this problem in Towards Non-Being allows that there is always something that satisfies these characterisations, but requires that they are often located at some non-actual world. To accommodate the satisfaction of truly perverse characterisations, these non-actual worlds include impossible worlds and worlds not closed under entailment. Such worlds do not bloat Priest’s ontology because non-actual worlds do not exist. For an alternative approach, consider a thing that exists at the actual world a and an impossibilium i such that i is characterised as being both identical and not identical to a, and by any other properties we care to list. To avoid the ultimate outcome of all actually existing things being contradictory in any arbitrary respect, Priest would have to locate i in some impossible world lacking certain entailments between relevant propositions or other truth bearers (bracketing Priest’s dialetheism). Yet, since Priest would make impossible worlds respectable by claiming that they do not exist, and he locates i at impossible worlds, the proposed solution is to cut out the impossible worlds middle man and allow that such things as i can be found as non-existent things at the actual world. The problem is then resolved by denying entailments from characterisations. Thus, the entailment of (2) or (3) by (1) is to be denied if i does not exist.

(1) i = (ex)((x = a) & -(x = a))

(2) (i = a) & -(i = a)

(3) (3x)(3y)((x = y) & -(x = y))

[Take ex as the epsilon operator and 3x as the particular quantifier]

What is the principled basis to deny these entailments?

The property of existence is clearly understood because things that do not exist (lack the property of existence) are not counted in one’s ontology. In a fundamental and absolute sense, only existing things “matter”. What is meant by the terms ‘fundamental’ and ‘absolute’ here is brought out by a contrasting example. Let us say that the sun will become a red giant in 1 billion years and, at that time, the Earth will surely be destroyed. We might well conclude that such an event does not matter because everyone alive today, their recognisable descendants and, in all probability, the human species will have long before shuffled off this mortal coil. The irrelevance of the contemplated event is not fundamental because an explanation can be given for it, i.e. the event is too remote in time to have any adverse consequences for those who contemplate it now. It is not absolute because it is relative to the interests of those contemplating the event that its irrelevance is assessed, i.e. our desire to continue living. If one had a religious concern for the planet Earth itself, believing it to be an imperative for the planet to endure in support of life for all time, then that different interest might make the predicted destruction of the Earth something that matters, notwithstanding the temporal remoteness of the predicted event. Unlike this contrasting example, if something does not exist then it is fundamentally irrelevant, in that no further explanation is required as to why it does not matter. Further, if something does not exist then it is irrelevant absolutely and regardless of one’s interest. It would not matter to any ideal but interested thinker who comprehended what it means to exist.

Now, as i does not exist, its characterisation is irrelevant to the characterisation of any other thing. As the entailment of (3) or (2) by (1) would entail an impossible characterisation of something other than i, that entailment fails. The reason that identity with a characterisation is privileged as a way of attributing properties to non-existent things is because, unlike such attribution by means of general or singular propositions with distinct constants and variables, is that the former allows for the asymmetrical attribution of n+1-place properties. It is possible to express this asymmetry in the present case by introducing something like asymmetrical identity, such that (i := a) and -(a := i). However, such asymmetrical identity may then be used to produce further characterisations that defeat such a way of asymmetrically attributing relational properties to i such as (4).

(4) i = (ex)((a := x) & -(a := x))

This solution of simply denying entailments from characterisations of non-existent things can be adapted to render inconsequential any allegedly arbitrary-p-entailing property. That is, any given property of ‘being such that p’ can be possessed by a non-existent thing without entailing that p. The lack of entailments from characterisations of non-existent things also extends to the curtailment of logical explosion arising from propositions concerning non-existents with contradictory characterisations. Just as (1) fails to entail (2) or (3), it also fails to entail (5).

(5) A & -A

Indeed, for any property F, something that is an F and a non-F either possesses F or does not possess F, but not both. Whichever is the case is a contingent matter. So, a non-square square is either square or non-square, but not both. It may well be that contradictory characterisations of existing things entail the truth of every proposition. However, granting that propositions are made true by reference to either existing or non-existent things that satisfy their predicates, such logical explosion is simply not entailed by contradictory propositions concerning non-existent things. Again, non-existents of any characterisation make no difference to the properties of anything else, or even themselves. Insofar as the characterisation of a non-existent thing entails that anything possesses properties other than those attributed to the non-existent thing by the characterisation – in accordance with logical laws applicable as between propositions concerning existing things – those entailments fail. To be fundamentally irrelevant is to be fundamentally inconsequential – both causally and logically.

Second Thought on Holes

My first thought on holes was that they are non-existent parts.

My second thought is that holes are a more specific kind of non-existent thing, i.e. absences. Absences are not just something that does not exist, as even existing things may be absent. Further, all absences are absences “of” something.

It would be nice, therefore, to stick a more recognisable relation in place of the general ”of” relation, and for this to shed light on the properties of holes, .e.g. the circumstances in which they are filled up and/or filled in.

I’m very much inclined to invoke the relation of lacking here. Thus, absences lack the things of which they are an absence and holes lack something (or a general range of things) that is the complement of the missing part of the hole host. Such a complement would be constrained to have something like the same material as the hole host, or at least the material of a part that one would normally expect to be present in the place where the hole actually is.

Remember, in accordance with noneism, I claim to get my non-existent metaphysical entities (such as absences) for free.

Blue Eyes Puzzle

I have not had anything to post for a while, so here is something trivial to keep things ticking over.

 

If refer to this puzzle here:

 

http://xkcd.com/blue_eyes.html

 

…and the answer here:

 

http://xkcd.com/solution.html

 

In short, I do not think that this is a purely deductive solution to the puzzle.

 

The solution only works if everyone on the island is thinking about blue eyes.

 

The guru sets the agenda for this to occur, yet there is nothing deductive about this framing of the question as to whether one has blue eyes, rather than the more open question as to what colour eyes one has.

 

Indeed, the problem that architects of AI systems encounter (originally predicated by Hubert Dreyfus) is the framing problem: i.e. the inability of purely, syntactically driven systems to focus on relevant matters out of a sea of information.

 

What is required to properly set the agenda and solve problems by achieving equilibrium in cooperative scenarios is a strong Principle of Charity. Charity is what has been assumed in the solution to this Blue Eyes problem, which makes the solution a non-sequitur. Yet, it will seem like a perfectly correct solution to many, as we do read situations charitably and with the right framing for relevance in mind.

Kripke’s Puzzle

I offered an error theory of informative identity here.

 This error theory also takes care of Kripke’s puzzle concerning beliefs about the same thing as learnt of in entirely different contexts, or simply under the misunderstanding that it is two different things, possessing contradictory properties. Kripke gives examples of Pierre and Peter. Pierre believes that ‘Londres is pretty’, expressed in French, before travelling to London to live. Pierre does not realise that Londres is London. Perhaps he learnt of Londres from rudimentary map. After living in London, Pierre concludes that ‘London is not pretty’. As Londres and London refer to the same city, Pierre believes that London is both pretty and not pretty. Yet, Pierre does not appear at all conflicted by these separate beliefs.[1] The puzzle does not require translation in its formulation, though. In the case of Peter, he hears both that ‘Paderewski is a famous pianist’ and ‘Paderewski is a statesman’. Due, perhaps, to a prejudice against the musical talents of statesmen, Peter takes ‘Paderewski’ to be the name of two persons: one a pianist and another a statesman. Peter then believes that, ‘Paderewski is musically talented’ and that ‘Paderewski is not musically talented’, though ‘Paderewski’ actually refers to the same man. So, Peter appears to believe that Paderewski both is and is not musically talented, again without feeling at all conflicted by these beliefs.[2] The error theory of informative identity resolves these difficulties by noting that at least one of the cities or men represented by Pierre and Peter respectively does not exist, and is not the other city/man in any way. In relation to Frege’s puzzle, it was suggested that the only difference of properties between existing and non-existent referents in an apparently informative identity was that one exists and the other does not. However, this need not be the case, and the non-existent and existent things respectively can differ as to as many properties as one requires in order to make sense of the case. Pierre’s Londres is a pretty place… that does not exist. Peter’s Paderewski the Statesman is a poor pianist… who does not exist.

 It might be thought, though, that Kripke’s puzzle would become an issue again when Pierre or Peter finally learn that London is Londres and Paderewski is Paderewski the Statesman. On the proposed view, informative identity is the substitution of one thing for another at the nodal points of all inferential relations in which either thing being identified stood. This substitution is symmetrical, so that all of the properties attributed to each thing identified are then attributed to a single thing. Would it not then be the case that Pierre believes that London is both pretty and not pretty and Peter appears to believe that Paderewski both is and is not musically talented? It would, but at this point this causes no problem. As soon as the inferential relations of London and Londres or Paderewski and Paderewski the Statesman are combined, Pierre and Peter realise that they are in contradiction and they correct some of their beliefs about London and Paderewski, accordingly. The inferential relations are adjusted for coherence. This is exactly what one expects to see when a mind discovers the identity of thing(s) thought to be diverse. Pierre rejects the belief that Londres is pretty in favour of the view that Londres is not pretty. Peter rejects the belief that Paderewski the Statesman is not musically talented. The way that these reconciliations of inferential relations go will depend on a mind’s broader system of beliefs and inferential relations.

 

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[1] Kripke, S., ‘A Puzzle About Belief’ in Margalit, A. (ed.) ‘Meaning and Use’ (1976) D. Reidel Publishing Co.: Dordrecht pp. 255-7

[2] Ibid p. 265

Against Kant’s Argument that Existence is not a “Real” Property

It might seem obvious that we can imagine things that exist, but which do not really exist, and that we are not simply in error when we claim to use our imagination in this way. Kant (1) used this view to argue that existence is not a “real” property – i.e. existence is either not a characterising property or not a property at all. He reaches this famous conclusion about the so-called property of existence by first noting that existence adds nothing to the characterisation of a thing: one hundred thalers is not the least increased by acquiring existence. Rather than proving Kant’s point, this thought experiment could be taken to demonstrate that we are unable to even begin to do as Kant asks.

Kant is asking us to imagine one hundred existing thalers and then one hundred non-existent thalers, and then to compare the properties of the two. Kant is not merely asking us to go and examine one hundred thalers to compare them with an imagined one hundred thalers, as he acknowledges that the examinable one hundred thalers will improve one’s circumstances in a way that the imagined thalers will not. Kant means for us to imagine both existing thalers and non-existent thalers and to see that there is no difference between them. Of course, this finding will be of no surprise to those of us who think that the objects of imagination always lack existence unless they exist apart from the imagination. Kant saw no difference as there was none; he just said there was. We cannot imagine something as existing unless that thing does exist. All that we do in supposed cases of imagining existing things that do not “really” exist is to claim (erroneously) that we are imagining an existing thing.

Maybe you do think that we can imagine existing things that do not really exist. The important point about Kant’s argument is that he requires this as an assumption, and it is an assumption that may be rejected.

(1) Kant, I., ‘Critique of Pure Reason’ trans. Kemp Smith, N. (1961) Macmillan & Co: London, New York A598-602, B626-630