Graham Priest's Dialetheism: Quantum Mechanics and... Nothing (3)

i) Nothing Both is and is Not an Object

ii) Ontologically Dependent on Nothing

iii) Possible Worlds and Dialetheism

iv) Is Dialetheism About Reality?

iv) Quantum Mechanics

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One can stress the ontological nature of his dialetheism in that it has been claimed that isn't a formal logic. Instead, it's argued to be "a thesis about truth". Thus it's no surprise that Graham Priest ties it to nothing and therefore to ontology.

Nothing Both is and is Not an Object

Graham Priest hints at dialetheism in this passage:

“Nothing is not an object because you've taken away all objects to get it.”

Elsewhere, Priest says that nothing is an object. Thus nothing “both is and is not” an object. Hence the dialetheism.

So despite the work of Russell, Quine, Carnap, etc., Priest comes out with phrases such as

“we posit nothingness in advance as something that is such-and-such we posit it as a being a thing”.

No; we don't “posit” anything ontological when we use the word “nothing”. Some philosophers (very few) have done so; although “we”, generally, haven't.

Priest then offers us the contradiction.

The first horn of the contradiction is that “nothingness is not an object”. The second horn is that nothingness “is an object”. Dialetheists (or at least Priest) make sense of this by arguing that nothingness “depends like all objects on nothingness”. The argument is this:

i) All objects depend on nothingness.

ii) So if nothingness is an object,

iii) then it too must depend on nothingness.

iv) Therefore nothingness must depend on itself.

Priest poetically calls this “going from nothingness to nothingness”.

Then we get back to the other dialetheic horn – nothing is not an object. That is:

i) “Only objects depend on nothing/ness.”

ii) If nothing/ness is not an object,

iii) Then it doesn't depend on nothingness. (It doesn't depend on itself.)

Or in Priest's own words:

“[N]othing depends on itself. Though since it's not an object, it doesn't depend on itself.”

Here again we have a contradiction.

Or so the argument goes.

If Priest firstly accepts that “nothingness is an object”, then these contradictions are bound to follow. In other words, if we begin with the claim that nothingness is an object, then no wonder Priest can then say that

“nothing [] depends on itself; but since it's not an object, it doesn't depend on itself”.

Yes, that is indeed a statement of a contradiction. But do we have the reality of a contradiction?

(Readers will need to backtrack to the section on objects in order to see exactly why Priest believes that nothingness can be seen as an object.)

Here's some more dialetheism from Priest. He says:

“Since [nothing] is an object, it is something. But it is the absence of all things too; so nothing is nothing. It is no thing, no object. Here, Heidegger got it exactly right: What is the nothing?”

Then, in a note, Priest is more dialetheically explicit when he states the following:

“Nothing, then, is a most strange, contradictory, thing. It both is and is not an object; it both is and is not something.”

So Priest appears to be magicking dialetheisms (as it were) out of the air. Actually, he doesn't accept that all the contradictions he mentions (in various places) are real contradictions (i.e., he denies that logical “explosion” also applies to dialetheism).

For example, Priest rejects the posited contradiction found in Wittgenstein's Tractatus idea that the “form of the world” is ineffable. Why? Basically, because we can both speak about - and describe - it. On the other hand, Priest does seem to accept that “the ground of reality [] embodies another contradiction” because nothingness “both grounds itself and doesn't ground itself” and “it is and isn't an object”. There nothingness is “the contradictory ground of reality”.

Ontologically Dependent on Nothing

Priest then makes this massive claim:

“At the ground of reality you have nothing - this contradictory ground of nothingness. So at the ground of reality there is one enormous contradiction.”

Firstly, why is nothing a “ground”? Indeed what is it for “nothing to be the ground of reality”? And where, exactly, is the “contradiction”?

No wonder Priest then says that this “is good old-fashioned metaphysics”. (It is!) And it's no surprise, either, that Priest also ask: “What to make of the contradictory ground of reality?” And he concludes:

“I'm going to leave [that question] to theologians to make sense of that question.”

So why theologians and not philosophers?

Possible Worlds and Dialetheism

Priest uses possible-worlds speak to justify his dialetheism. Take this example:

“It might be thought that the fact that ¬(A ∧ ¬A) holds at a world entails that one or other A and ¬A fails; but this does not necessarily follow.”

Is Priest saying that ¬(A ∧ ¬A) holds at the actual world (i.e., our world); though not “necessarily” at all possible worlds? Or does Priest believe that only at other possible worlds A ∧ ¬A holds? In any case, the dialetheic position is that A ∧ ¬A is not necessarily false.

Priest offers us the following symbolisation of his position:

¬A is true at w iff is A false at w.

¬A is false at w iff A is true at w.

So what about Priest's A ∧ ¬A?

According to Priest, “it is possible for A to be both true and false at a world”. That is, of course, the dialetheic position. Yet does this position require possible-worlds theory when Priest (elsewhere) has said that it's also applicable at our world – the actual world?

Not surprisingly, Priest concedes that

“it is natural to ask whether there really are possible worlds at which something may be both true and false”.

He also believes that this is a “fair question”. Nonetheless, Priest also argues that

“the best reasons for thinking this to be possible are also reasons for thinking it to be actual”.

That seems to follow from the earlier possible-worlds logic. We can now argue the following:

i) If it's possible for A ∧ ¬A to be true at at least one possible world,

ii) then it's also likely to be - or possibly - true at our actual world.

Is Dialetheism About Reality?

In order to tackle Priest's later dialetheic views on quantum mechanics (see the next section), let's firstly take the words of Bryson Brown as an introduction.

Bryson Brown (in his paper 'On Paraconsistency') stresses “the world”, rather than words. That is, he's stresses ontology, not semantics.

More specifically, Bryson stresses the importance of inconsistency for dialetheism. He also says that dialetheists are “radical paraconsistentists”. He writes:

“[Dialetheists] hold that the world is inconsistent, and aim at a general logic that goes beyond all the consistency constraints of classical logic.”

Deriving the notion of an inconsistent world (or a world which contains contradictions) from our psychological and/or epistemological limitations (as well as from accepted notions in the philosophy of science and mathematics) is problematic. In other words, the epistemological position that we have inconsistent (or even contradictory) positions/systems can't also be applied to the world itself.

Another way to put this is in terms of set-theoretic paradoxes, as also mentioned by Bryson Brown.

Brown says that “the dialetheists take paradoxes such as the liar and the paradoxes of naïve set theory at face value”. That is, it may be the case that dialetheists choose - for logical and/or philosophical reasons - to accept paradoxes even though they also believe that, ultimately, they aren't true of the actual world. Then again, Brown continues by saying that dialetheists “view these paradoxes as proofs that certain inconsistencies are true”. Thus:

These inconsistencies are true of what?

True only of the paradoxes (in themselves, as it were)?

Or true of the world itself?

Again, this stress on the world may betray a naïve, crude and, perhaps, an old-fashioned view of logic. Nonetheless, Priest himself does mention “reality” on a few occasions. When discussing the virtue of simplicity, for example, he asks the following question:

“If there is some reason for supposing that reality is, quite generally, very consistent – say some sort of transcendental argument – then inconsistency is clearly a negative criterion. If not, then perhaps not.”

This again concerns reality. As it is, it's difficult to see how the world can be either inconsistent or consistent. This position is similar – or parallel – to Baruch Spinoza's philosophical point that the world can only, well, be. (Graham Priest is a Buddhist.) Thus:

“I would warn you that I do not attribute to nature either beauty or deformity, order or confusion. Only in relation to our imagination can things be called beautiful or ugly, well-ordered or confused.”

What we say about the world (whether in science, philosophy, mathematics, logic or everyday life) may well be consistent or inconsistent. However, the world itself can neither be consistent nor inconsistent. Thus, it seems to follow, that inconsistency is neither a “negative criterion” nor a positive criterion.

Quantum Mechanics

Priest says that

“those who worked on early quantum mechanical models of the atom regarded the [Neils] Bohr theory [as] certainly inconsistent”.

Priest then tells us:

“[Y]et its empirical predictions were spectacularly successful.”

Priest appears to be hinting at the following:

i) We had an inconsistent physical theory about the world (or about the atom).

ii) That theory led to “empirical predictions [which] were spectacularly successful”.

iii) Therefore it is possible that the world itself is inconsistent. (Or more strongly: The world is inconsistent.)

It must be stressed here that the meaning of the word “inconsistent” is very different to the meaning of the word “contradictory” (or “paradoxical”). Something can indeed be inconsistent because it contains contradictions. Though can't something be inconsistent without also containing (logical) contradictions?

Here's a passage from Priest on an aspect of quantum mechanics that he sees as being relevant to dialetheism:

“Unobservable realms, particularly the micro-realm, behave in a very strange way, events at one place instantaneously affecting events at others in remote locations.”

Priest gives another example of quantum happenings. This example is one of radioactive decay. He writes:

“[S]uppose that a radioactive atom instantaneously and spontaneously decays. At the instant of decay, is the atom integral or is it not?”

Now for the traditional logic of this situation. Priest continues:

“In both of these cases, and others like them, the law of excluded middle tells us that it is one or the other.”

Couldn't the atom be neither integral nor non-integral when it instantaneously and spontaneously decays? (Priest talks of either/or and “one or the other”; not neither/nor.) Or, alternatively, at time t, x may not be an atom at all!

So what of Priest's own (logical) conclusion when it comes to atomic decay? He claims that the aforementioned atom “at the point of decay is both integral and non-integral”. This isn't allowed – Priest says - if the law of excluded middle has its way. After all, the law of excluded middle tells us that the the atom must either be integral or nonintegral; not “both integral and non-integral”.

Note:

1) Some of the quoted words and passages from Graham Priest in the above are taken from the 'Everything and Nothing' seminar – a Robert Curtius Lecture of Excellence at Bonn University - which Priest gave. I relied on both the transcript and the video itself. However, I've edited a lot of what Priest says in that seminar to make it more comprehensible. For example, I removed many of the uses of the word “so”, added full stops, commas and suchlike. Hopefully, the philosophical content is kept intact. None of this applicable to the words and passages I quote which come from Priest's papers.


*) See my ‘Graham Priest — and Martin Heidegger! — on Nothing (1)’ and my 'Graham Priest & Martin Heidegger Take Language on Holiday: the Nothing (2)'.

Graham Priest & Martin Heidegger Take Language on Holiday: the Nothing (2)

i) Introduction

ii) Graham Priest on Nothing as an Object

iii) Quantifying Nothing

iv) Russell & Quine

Rhetorically speaking, can mere words bring objects into existence?

As we've seen, Martin Heidegger was perplexed by the fact that we can refer to nothing. He asked, “What about this nothing?” Heidegger also asked:

“The nothing – what else can it be for science but an outrage and a phantasm?”

Heidegger contended that “[s]cience wants to know nothing of the nothing”.

According to Heidegger (who was critical of science for many other reasons too), science's main sin is that it “tries to express its proper essence it calls upon the nothing for help”. (Note the words “the nothing”.) That is, science refer to (the) nothing (or at least scientists use the word “nothing”), yet it “rejects” nothing. (One wonders why Heidegger singled out science in this respect. After all, all of us use the word “nothing” and refer to nothing.) More specifically:

i) Do we “posit [nothing's] being” when we refer to nothing?

ii) Or do we simply use the word “nothing” because it's useful in certain - even many - contexts?

What did Heidegger think? This:

“With regard to the nothing, question and answer alike are absurd.”

Graham Priest on Nothing as an Object

Graham Priest too appears to believe (if only when viewed critically) that language creates objects. Actually, he doesn't actually make that rhetorical claim. (The words are mine.) Instead, his actual words can result in this interpretation.

In Priest's own words:

“An object is anything you can refer to with a noun phrase, think about quantify over.”

Thus, this is a liberal (or pluralist) position on objects in that Priest concludes that

“so there are many objects, like Marcus, like Bond, like the City University of New York, like the Sun and so on all these things you can think about you can refer to”.

Indeed, this is a positively Meinongian conclusion. (That is, apart from the fact that Alexius Meinong never stressed – and possibly even ignored – language.) However, as Bertrand Russell, Ludwig Wittgenstein, Rudolf Carnap and many others have put it (in their various ways), Priest and Heidegger might well have been “misled by language”.

Quantifying Nothing

We must add here that apart from language, Priest also emphasises quantification. However, this amounts to a very similar thing – quantification too brings objects into existence. (The miraculous powers of the “backward E” – as Hilary Putnam put it.)

Priest refers to quantifying over both everything and nothing. However, he has a position on quantification that's at odds with the common one. Usually, it's thought that all acts of quantification have a specific domain in mind. Priest, on the other hand, believes that “it's okay to use a quantifier with the widest possible scope”. That is, it's fine to quantify over literally everything. (Like Russell's universal set?)

Priest offers us a variation on the theme discussed in the history of philosophy (see later) by arguing for the following:

i) If we “quantify over” any given x,

ii) then x must be an “object” of some kind.

According to Priest, we also refer to (or quantify over) everything – so that too must be an object. Yes, Priest says that “everything is an object”, just like nothing. (It's then that Priest gets all dialethic by saying that “it's not an object” too. But we'll leave that until later.) That is, Priest applies the same logic to everything as he does to nothing. The following words will make that clear:

“Everything is the mereological sum of every object [] If everything is the fusion of the sum of all objects, [then] what is nothingness? Nothingness is the sum of everything that isn't an object because everything is an object. [Nothingness is] the sum of no things. What you get when you fuse together no things is exactly nothingness.”

Philosophers too have referred to nothing, and hence it must be an object. Priest himself refers to Ludwig Wittgenstein and Nagarjuna. He says that these two thinkers

“tell[] you that something is ineffable; and then [they] explain why it's ineffable - thereby talking about”.

That is certainly the case with the Tractatus, in which Wittgenstein discusses the “form of the world”. We also had Kant's endless references to noumena; and that's even though he believed that nothing could be known about them. Then again, all this is also true of the round square or the brick with a sense of humour - which I've just referred to!

To repeat. Priest goes all linguistic (not all ontological – which doesn't mean there's an absolute distinction) when he says that “'nothing’, can also be a noun phrase”. Basically, that's because we can and do talk about it. Or, more specifically, Hegel and Heidegger talked about it a lot. That is, “[w]e may say that Hegel and Heidegger both wrote about nothing”.

Moreover, “nothing” is “not [always] a quantifier phrase”. That is, it's not all about counting or quantifying. It's also about a thing – an object.

One other way in which we can talk about nothing is to note that “[w]e can say that [Hegel and Heidegger] said different things about it”. In addition, Christianity talks about nothing in that the “Abrahamic God is supposed to have created the world” out of nothing.

We can see that Priest is fully committed to Plato's Beard in that human sayings bring things into existence.

So now let's do some history of philosophy.

Russell and Quine

Bertrand Russell - in his 1918 paper 'Existence and Description' - believed that in order for names to be names, they must name – or refer to - things which exist. Take this remarkable passage:

“The fact that you can discuss the proposition 'God exists' is a proof that 'God', as used in that proposition, is a description not a name. If 'God' were a name, no question as to existence could arise.”

That, clearly, is fairly similar to Parmenides's own position on the use of the word “nothing”. Russell's actual argument, however, is very different.

[Personally, I don't have much time for Russell's argument. It seems to have the character of a stipulation [That is, names must name existing things.]. It's primary purpose is logical and philosophical. Russell, at the time, was reacting to the “ontological slums” - as Quine put it - of Alexius Meinong. However, this semantic philosophy simply seems like a stipulation - or a normative position - designed to solve various philosophical problems.]

As for Quine, he had no problem with the naming of nonbeings or non-existents (though non-being and non-existence aren't the same thing). In his 1948 paper, 'On What There Is', he firstly dismisses Russell's position. Quine, however, puts Russell's position in the mouth of McX and uses the word “Pegasus” rather than the word “God”.

Quine wrote:

“He confused the alleged named object Pegasus with the meaning of the word 'Pegasus', therefore concluding that Pegasus must be in order that the word have meaning.”

Put simply, a name can have a “meaning” without it having to refer to something which exists (or even having to refer to something which has being). Quine unties meaning from reference, whereas Russell only thought in terms of reference (or, at the least, he strongly tied meaning to reference).

Parmenides made a similar mistake.

The ancient Greek philosopher didn't think that a name could have a meaning without the thing being named also existing or (having) being. However, we can speak of a something (an x) that doesn't exist because the naming of such an x doesn't entail or even imply its existence. However, and in homage to Meinong (as well as, perhaps, to the philosopher David Lewis), philosophers can now ask us the following question:

What kind of being does the named object (or thing) have?

If we return to Russell. His theory is an attempt to solve that problem by arguing that if a named x doesn't exist (or have being), then that name must be a “disguised description”. (In the case of the name “Pegasus”, the description would be “the fictional horse which has such and such characteristics”.)

Note:

1) Some of the quoted words and passages from Graham Priest in the above are taken from the 'Everything and Nothing' seminar – a Robert Curtius Lecture of Excellence at Bonn University - which Priest gave. I relied on both the transcript and the video itself. However, I've edited a lot of what Priest says in that seminar to make it more comprehensible. For example, I removed many of the uses of the word “so”, added full stops, commas and suchlike. Hopefully, the philosophical content is kept intact. None of this applicable to the words and passages I quote which come from Priest's papers and books. 

*) See my 'Graham Priest – and Martin Heidegger! – on Nothing (1)'.

To follow: 'Graham Priest, Martin Heidegger, Dialetheism and Nothing (3)'.