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.

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.

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.

[2] Ibid p. 265

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

Initial thought for a noneistic theory of holes: -

Of existing things with non-existent parts, holes are the parts that do not exist. For example, a donut cannot exist without being partially composed by a non-existent volume of fried bread in the middle.

I haven’t posted here for a while. So here are my thoughts on worlds.

It is supposed, in agreement with Priest, that all but the actual world do not exist (in the noneist sense of the negation of the predicate “exists”). However, it is denied that any non-relational properties of things vary across worlds. The Indiscernibility of Identicals is a concern – at least, for existing things. As the Indiscernibility of Identicals is strictly applied: (a) something that possesses existence at some possible world does not fail to possess existence at any other world – it exists at every world that includes it; and (b) something that does not possess existence at some possible world does not possess existence at any other world – it does not exists at every world that includes it. Thus, there cannot be something that exists at one world, but that does not exist at another world. Parsimony also dispenses with the thought that there may be alien existents that are denizens of non-actual worlds. Yet, while only the actual world exists, and only things that exist at the actual world exist at non-actual worlds, this does not mean that only the actual world is a possible world. Possibility is indifferent to existence. The actual world includes both existing and non-existent things and the actual world is the exemplary possible world.

There are both possible and impossible worlds, remembering that we do not bloat our ontology with more than one world of any kind because all but the actual world do not exist. It is felt that there should be a stronger differentiation between possible and impossible worlds than there is between worlds with different grades of possibility. For this reason, there is still the need to give a role to abstracta or the mind of God or the actual world itself of representing all of the possible worlds. Abstracta such as structured universals are preferred because universals may also serve to individuate natural properties where one’s concepts are too flexible to make such demarcations in any authoritative way.

Whatever the representations may be that ground possibility, the significant point is that they ground possibility relative to a world. That is, there are other worlds with abstracta or some such that represent a different set of worlds as its possible worlds. In this way, impossible worlds may exhibit different logical laws by whatever means that logical laws can be mapped across all possible worlds construed as widely as possible. It can be seen then that the possibility of existence is not grounded by the existence of mere possibilia. That cannot be right because most mere possibilia do not exist. Rather, the possibility of existence is grounded by possibility relative to the world that exists, i.e. relative to the actual world.

There is also transworld identity in Lewis’ sense of an overlap of worlds.[1] First, it need not be asserted that things possess different intrinsic properties at different worlds if the Indiscernibility of Identicals is a concern (and it is). While it may be possible that an actual person with five fingers might have possessed six fingers, such a possibility can be paraphrased as quantification over worlds in which the remainder of the person apart from the varying finger parts is included at some other possible worlds in which it partially composes a different whole person with a different number of fingers. Second, spatio-temporal and/or mereological relations need not explain the unity of a world as Lewis would have it. Instead, there are primitive relations of inclusion that characterise that unity, given that worlds are not just closed regions of space and time but sui generis things. Worlds include various things and are not included at other worlds. This must be so because spatio-temporal and/or mereological relations cannot explain the unity of a world if some things do not exist at a world, because some things that do not exist do not stand in any spatio-temporal and/or mereological relations. Some abstracta may even be things that do exist at the actual world, that do not stand in such relations.

There are variable domains of things across different worlds, whether possible or impossible. This is so because all non-existents do not exist at the actual world. The actual world includes all non-existents of any given characterisation because there are no constraints on that which the actual world may include – no reason that any given non-existent is not there – given the fundamental respect in which non-existents do not matter. Indeed, the actual world is the only possible world that includes impossibilia, because the distinction between existing and non-existent things allows a principled basis to call it a possible world – possible as to its existing domain – though it does include impossibilia in its non-existent domain. There is not such principled distinction for non-actual (non-existent) worlds and, thus, they are impossible worlds if they include any impossibilia. Now, if all non-actual worlds are non-existent things then there can be such worlds of any characterisation at all. Hence, they have variable domains.

How can the actual world include non-actual worlds when worlds are not included at any other world? The answer: in a converse manner to that in which an infinity of men occupied Quine’s doorway, even though the spatial region including Quine’s doorway excluded all other spatial regions that include non-existent men. That is, worlds are not included at other worlds, but other worlds include them, anyway, because the totalising properties of worlds are inconsequential. It is this non-reciprocal inclusion that holds logical space together. If one does not exist then all entailments from one’s properties to the possession by other things of any given other property fail. So, one cannot help but be included at the actual world if one does not exist.

[1] Lewis, D., ‘On the Plurality of Worlds’ pp. 198-209

Oh, my goodness!

I just realised how completely obvious it is that Ockham’s Razor favours presentism.

How many more things (and kinds of things, like dinosaurs) is the four-dimensionalist committed to there being than the presentist? Everything in the past and everything in the future, that’s how many.

Even the growing block theorist is committed to all that stuff in the past.

The odd thing is, I commented on someone else’s post concerning this argument a few months ago, and I didn’t realise how good this point was at the time.

Assumptions:

1. Internalism about mental content is right (i.e. representation is an internal relation).

2. The Characterisation Principle applies to all simple and complex predicates except existence (i.e. we are able to stand in the representation relation with an instance of any characterisation we care to formulate so long as existence is not included in the characterisation).

Okay, I will now argue that, given these two assumptions (which I hold and I believe can be independently motivated) property dualism follows.

Let’s say I represent some other person and let’s say the other person is Peter Forrest. Peter actually exists, so the representation relation holds between two existents in this case. I am an internalist, so I say that there are intrinsic properties of my mind or brain that determine my mind or brain as representing Peter Forrest and not someone else, like David Armstrong or even David Lewis (presently a non-existent person).

If it were the case that mental representation properties metaphysically supervene over physical properties of, say, brain states then it is in principle possible to identify the brain states over which such representational properties supervene. The trouble is, such a distribution of physical properties can only be just complex enough to determine representational properties finely enough to individuate the represented object Peter Forrest, i.e. to ground the representation relation as holding between my brain and Peter Forrest and no other. However complex my physical brain states turn out to be, Peter Forrest’s brain states will be of an equivalent order of complexity. So, a representation of Peter constituted by my physical brain pushes the structure of my brain to the limit as to what it may determine that I represent.

Okay, so now imagine that Peter Forrest and David Armstrong merge to become one person. They are still two distinct people, but they are the same. Yeah, this is impossible. Yet, it does not seem any less plausible that we may represent such an contradictory future fusion of Peter and David (call it Petvid Forrstrong) than it is to represent a circular square. Sure, there are no actual circular squares, but we can represent such impossibilia – particularly if you buy the Characterisation Principle.

So, now I am representing something that is more complex than Peter Forrest, i.e. the contradictory fusion Petvid Forrstrong. Yet, the possibility of my brain being complex enough to represent the person of Peter Forrest on an internalist basis already pushed the structural complexity of my brain’s physical properties to their limits as a sufficient supervenience base to determine the representational properties that would ground such a representation. Now, that I am representing Petvid Forrstrong – an entity at least twice as complex as Peter Forrest – I could not possibly have a brain structure sufficiently complex to constitute the supervenience base of the representation of such an impossibilium.

Hence, my representational properties must be instantiated independently of my physical properties (though they may nomologically supervene over them).

Hence, property dualism. QED.

In his 1990 Article in Mind ‘Noneism or Allism?’, David Lewis argued against the thesis of Richard Sylvan in ‘Exploring Meinong’s Jungle and Beyond’ that the existential quantifier is unnecessarily, existentially loaded in most modern ontology and logic. Sylvan’s noneism is a neo-Meinongian view of the existential quantifier (or the ‘particular quantifier’) to the effect that it should not be defined so as to be synonymous with the property of existence. Instead, ‘exists’ is a respectable but primitive property. Thus, one often encounters a loaded particular quantifier that is sneakily restricted to entities with the property of existence, and then there is the unrestricted particular quantifier that is restricted in no respect and ranges over both existing and non-existent things. This distinction means that statements like, ‘Some men are giants and do not exist,’ are true.

Lewis argues that, whatever Sylvan’s existence predicate is supposed to be, it is not ‘existence’ in the way that everyone else (philosophers) use the term, which is as a redundant, second-order predicate synonymous with the particular quantifier: Quine’s dictum, ‘To be is to be the value of a bound variable.’ Lewis says that Sylvan is just an Allist. That is, someone who believes that every characterisable thing exists. Sylvan just happens to also attribute to some of these things an undefined property he calls ‘existence’… whatever that might be, who cares? However, contra Lewis, the role of this primitive 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 sense, only existing things “matter”. Things that do not exist are not constrained by logical laws (as to the propositions that are true of them), and may be multiplied ad infinitum, because they do not matter in this fundamental sense. The property of existence and its complement constitute two sides of a fundamental division of the truly unrestricted domain of quantification because the non-existent side is entirely unprincipled, overpopulated and irrelevant while the existent side is lawful, relatively sparse and where it’s at. Any embarrassing rubbish one needs to quantify over, one can render non-existent in one’s theory with relief.

So, existence taken as a property is not vacuous, but a reduction to property form of the irrelevance and harmlessness of some things that theorists of the Quinean persuasion hope to achieve by excluding such pointless things from the unrestricted domain. Yet, the Quinean approach lacks an adequate account of reference to such pointless things, leading to problems in providing an adequate and non-ad hoc theory of semantics generally.

In ‘Necessary Existents’, Williamson put forward an argument to the effect that any arbitrary thing x exists necessarily.

(1) Necessarily, if x does not exist then the proposition that x does not exist is true.

(2) Necessarily, if the proposition that x does not exist is true then the proposition that x does not exist exists.

(3) Necessarily, if the proposition that x does not exist exists then x exists.

(4) Necessarily, if x does not exist then x exists.

(5) Necessarily, x exists.

The reason given for (3): if x did not exist, there would be nothing for the proposition to state the nonexistence of.

After my theory of representation was demolished at AAP 2009, I am once again prepared to say that the dodgy premise is (3). Some things do not exist.

Bill Lycan admitted at a paper given by Graham Priest at AAP 2007 that he did not have any good reason to say that nothing does not exist. In the comment time for his paper at AAP 2009 Bill went so far as to suggest that it may be a Moorean truth that some things do not exist.

I therefore think that I am in good company as I resume the mantle of noneism.