Realism, Anti-realism, and Evidence-transcendent Statements

This piece deals with the nature of truth-valued statements which have semantic contents which are said to be “evidence-transcendent”. In less technical terms, the nature of unobservability and observability-in-principle are tackled within an anti-realist versus realist context.

The classic cases are covered: including the doubling in size of the universe, Bertrand Russell's flying teapot, Michael Dummett's organisms in Andromeda, past and future events, electrons, other minds and what it is to be bald.

Within these contexts, we'll also try to clarify what it is to understand statements which have evidence-transcendent content.

Realist Truth

The realist position on truth can appear strange, at least prima facie. Take this statement:

“In 607 AD there were precisely one million people with ginger hair in Europe.”

According to the realist, that's either true or false. He may also say that it's determinately true or false (i.e., it's truth is fixed in time).

Similarly for this statement:

“Is is true [false] that Theresa May, at this precise moment, is dreaming about flowers.”

If Theresa May isn't asleep, it's false. That would be easy – in principle – to determine. Though what about if she is asleep at this precise moment? Is it still determinedly true or false that she's dreaming about flowers?

Despite that, it may well be the case that although one takes a realist position on this, one needn't take a similarly realist position on all other domains of discourse. (This is often said of anti-realism, not realism.)  More specifically, statements about Bertrand Russell's flying teapot or Dummett's organisms in Andromeda (both covered later) may well be determinately true. Nonetheless, is it automatically the case that a realist should also have exactly the same position, for example, on statements about the future? Perhaps a realist believes that statements about the future throw up problems which aren't encountered in these other domains.

Understanding Statements

Following on from that, an anti-realist can ask a realist two questions:

i) If you understand the statement “It is true [or false] that that the universe sprang into existence just five minutes ago, replete with traces of a long complex past” [worded by Bob Hale], then how do you understand that sentence?

ii) What gives you the warrant to say that it's either true or that it's false?

The realist may now reply:

What do you mean by the word 'understand' [as in “understand that sentence”]?

A standard picture is that in order to understand p, one needs to understand both p's truth-conditions and then somehow decide whether or not those truth-conditions obtain. So, in the case of the statement about the universe doubling in size, how would the truth-conditions for the universe being the same size differ from the truth-conditions of a universe which has doubled in size? (I'm assuming here that the philosophical puzzle of a doubled universe works. As it is, there are arguments against it.) Secondly, how would someone be warranted (or justified) in saying that the universe has or hasn't doubled in size?

The argument is that if the realist can't answer these questions, then his position is untenable. That is, he doesn't know what he's talking about. Or, less judgementally, he doesn't understand what he's talking about. That means that we have no means of understanding what a realist position on truth (at least as regards the doubled-universe scenario) amounts to.

The Doubled Universe

Since we've just mentioned the doubled-universe scenario, Bob Hale talks in terms of what he calls “chronically e-transcendent statements” [1999]. (The 'e' is short for 'evidence'.) He cites the doubled-universe case:

“Everything in the universe has doubled in size.”

As well as:

“The entire universe sprang into existence just five minutes ago, replete with traces of a long and complex past.”

(These statements have been much discussed in philosophy; though not always in the context of the realism vs. anti-realism debate.)

If the universe had doubled in size (so the argument goes), then there'd be no way of telling that it had actually done so. Thus we couldn't say that it has or that it hasn't doubled in size. Nonetheless, isn't it the case that it either has or it hasn't doubled in size? And if that's the case according to the realist, the statement is indeed determinately true or determinately false.

Unobservable Electrons

There are many problems for the anti-realist position too; especially if anti-realism is closely tied to acts of verification (or to verificationism).

Take the many unobservable phenomena of science (specifically of physics). Can it be said that statements about, say, electrons are similar in kind to statements about our doubled universe or flying teapots in distant galaxies? Certain anti-realists would say that even though electrons aren't observable, we're nonetheless led to posit their existence because of the evidence supplied by phenomena which are indeed observable. Thus, although electrons are too small to be observed, we're led to them by observable phenomena - plus, of course, lots of theory. (Couldn't the realist argue that he's led to his statements about determinate truth about the unobservable-in-principle by what is actually observable?)

The idea that an electron is posited due to phenomena we can observe (along with theory) is parallel - or additional - to the idea of something's being observable-in-principle.

It could be said that something as tiny as the electron could be observable in principle; except for the large problem that it's deemed to be a “theoretical entity” anyway. That is, besides mathematical structure (as well as theory), there would be nothing to observe even if we could observe it. On the other hand, we can say that a distant something in our solar system could be observed in principle. That may mean that this something isn't a theoretical entity at all. Well, in a sense, it is a kind of theoretical entity in that it hasn't actually been observed. Though being, say, a teapot, it could be observed if we were able to travel to the distant place it inhabits. (Let's forget the science here!)

There's one clear problem for this observable/unobservable opposition. This is that there isn't always (or never) a clear dividing line between observation-statements and theoretical statements. That can be because observation-statements involve theory and theoretical statements involve (elements derivable from) observation. Still, whatever problems there are here, they're not as problematic as those statements about unprovable mathematical statements; and certainly not as problematic as our doubled-universe scenario.

Other Minds

A similar problem arises for anti-realism when it comes to other minds. We can't observe the goings-on in other people's minds. Nonetheless, like electrons, we're led to acknowledge other minds because of the things we can indeed observe. However, in this case we still need to accept that behaviour (including speech and writing) isn't conclusive evidence for other minds.

There are many problems thrown up by other minds. Behaviourism, for one, was/is one response to these philosophical problems. And that's why certain types of behaviourist relied exclusively on behaviour (whether physical or verbal behaviour) in their experiments and musings. That meant that other minds ceased being a problem for behaviourists because minds in effect didn't (really) exist. Or, at the least, behaviourists believed - at one time - that the mind wasn't a fit subject for science.

Is John Bald?

There's also the problem of statements which involve vague concepts or references to vague states-of-affairs (if there can be such a thing!). Take the well-known case of whether a certain person is bald.

To clarify with a statement: “John is bald.” This can certainly be said to have truth-conditions (which certain earlier examples didn't have). Nonetheless, in a certain sense, truth-conditions don't really help here. That is, we have access to John and to John's head. What we don't have access to is whether or not it's true or false that he's bald. (I'm taking it here that someone can be bald even if they have a few hairs left.) Since it's already been said that truth-conditions aren't the problem, then perhaps we do have a problem with the “vague predicate” that is “bald”.

Here we encounter problems covered by a sorties paradox. Can we ignore them for now? Perhaps we can. It can be said, for example, that we can make a stipulation as to what makes someone bald. (This is deemed to be problematic if taken as a sorties paradox.) We can say that anything less than 100 hairs constitutes baldness in a given male. Consequently it can be said that it's determinately true that John is bald or not bald (i.e., post-stipulation).

What if we accept the sorties paradox? Then we'd be unable to decide (care of truth-conditions or anything else) whether or not John is bald. Nonetheless, the realist, yet again, would argue that it's a determinate fact which makes it the case that either John is bald or John isn't bald. The problem is that if we accept the paradox, we can't know either way.

Michael Dummett, for one, had a problem with this realist conclusion.

In terms of the word “bald”, that would mean that our use of words like that would have “confer[red] on them meanings which determine precise applications for them that we ourselves do not know”. Basically, that would mean that the world tells us if John is bald or not. Or, at the least, the world (including John's head) determines the truth or falsity of the statement “John is bald”. In addition, the world determines the truth regardless of whether or not we can ever determine it to be true or false. Yet surely whether or not someone is bald is something to do with what we decide. The world has no opinion on this or on anything else.

Still, this sorties paradox has an impact on the nature/reality of baldness even if we accept a conventional stipulation about baldness. That is, the logical process which leads from having, say, 1000 hairs to having a single hair is still ultimately paradoxical. That is, step by step we can move from the statement “A man has a thousand hairs is not bald” to the statement “A man with three hairs is not bald” without a hiccup.

Another way of looking at this is to say that if the realist is correct, then any indeterminacy there is has to do with our vague predicates or vague statements, not the world itself (or with John's baldness).

The Teapots/Organisms of Andromeda

Michael Dummett offers us this statement:

“'There are living organisms on some planet in the Andromeda galaxy.'”

That statement, according to Dummett's realist, is “determinately true or false” [1982].

In response, the anti-realist adds an extra dimension to this case in terms of the aforementioned idea of observability-in-principle. Dummett expresses the anti-realist's (as well as, I suppose, the realist's) position in this way:

“'If we were to travel to the Andromeda galaxy and inspect all the planets in it, we should observe at least one on which there were living organisms.'”

Basically, because the science and the practicalities are so far-fetched in this case, we can't do anything else but forget them. In other words, we need to give the anti-realist the scientific benefit of the doubt. The problem here, though, is that if we give the anti-realist the benefit of the doubt about this currently unobservable situation (which is nonetheless supposedly observable-in-principle), then we can - or must – do the same in the countless other cases of unobservable phenomena in science (particularly in physics). Having said all that, these provisos may not be to the point here.

In any case, if the aforementioned organisms are observable-in-principle, then perhaps they can't be (fully) theoretical entities. Or, less strongly, if the Andromeda organisms are theoretical entities at the present moment, then they needn't remain theoretical entities simply because they can be observed in principle. (Though, again, perhaps the atomic and subatomic world may one day be observed; though not if the entities concerned are simply “theoretical posits” and/or mathematical structures.)

Statements About the Future

Dummett also brings up another example of something that's unobservable-in-principle: a future event. How can we deal with truth-valued statements about future events?

My prima facie position is twofold. 

i) Such statements are neither true nor false. ii) If such statements are neither true nor false, then they serve little purpose.

The realist believes that statements about future events are determinately true or false. According to Dummett, the realist believes that 

“there is [ ] a definite future course of events which renders every statement in the future tense determinedly either true or false” [1982].

I find realism towards statements about the future even more difficult to accept than realist claims about other domains. I would agree with Dummett when he says that the only way that a future-tensed statement can be true or false at this moment in time would “only [be] in virtue of something that lies in the present”. This is surely Dummett hinting at some form of determinism in that what is the case at this moment in time will have a determinate causal affect on what will be the case in the future. (Try to forget arguments against determinism here; as well as references to quantum mechanics, backwards causation, action-at-a-distance, etc.)

Let's take that deterministic position to be the case. That is, a future-tensed statement is true or false at the present moment in time because of what is the case at the present moment in time. That's the case even though the event referred to is in the future. That's fair enough; though it's clear that the realist would have no way of knowing whether or not it's true or false at the present moment. Nonetheless, we've already seen that the realist happily and willingly accepts his position of epistemic deficiency.

Instead of using the word “determinism”, Dummett talks about “physical necessity” instead.

Dummett picks up on an interesting consequence of what was said in the previous paragraph. What the realist must do, Dummett argues, is tell us what are the truths about the statement (or situation) at the present moment in time and how these truths bring about the truth of a statement about a future event. That means that only known truths at the present moment can contribute to truths about future events – at least within this context of “physical necessity” or determinism.

Dummett spots a double problem with the realist's position here. The realist can't determine the present-time truths which would bring about truths about the future. And, by definition, he can't determine - as a consequence of this - a statement about the future that's true at the present moment. That means that although the realist acknowledges his lack of a means to determine the truth of a statement about a future event, he hasn't even got a way of determining the present-time truths which will determine - or cause by virtue of physical necessity – the truth of statements about future events. Thus, in order to make sense of his realism, the least we should expect from the realist is the truths of statements about current situations which would cause - or determine - the truths of statements about future events. Without all that, realism towards statements about the future make little sense.

References

Dummett, Michael. (1982) 'Realism'.

Hale, Bob. (1999) 'Realism and its Oppositions'.

Paraconsistent Logic: Inconsistency, Explosion and Relevance

(1) Do paraconsistentists really accept the conjunction P & ¬P? (2) Does that conjunction really “generate every theorem in the language”?

The following essay will question the paraconsistent acceptance of inconsistencies. It will also question the related acceptance of logical explosion and logical triviality (which paraconsistent logicians also reject) by classical logicians.

The main theme of this piece (if sometimes implicit) is that both logical explosion and logical triviality result from taking logical statements, premises or propositions as being empty logical strings (or syntactic strings) — i.e., notations without semantic content. Indeed the position advanced here can be deemed to be (if loosely and in a limited sense) against logical formalism, in which logical strings are treated as being autonomous of — and independent from — semantics.

(The positions expressed above amount to the same argument I’ve previously provided for the purely logical renditions of the Liar Paradox and even for Gödel sentences — see here and here. It’s of course the case that all such logical strings are provided with what is called a “semantics”. Yet that is a semantics purely in the limited sense that these strings are somewhat arbitrarily classified as being “true”, “false”, as having an “extensional domain”, etc.)

So the following is an essay in the philosophy of logic (which will explain the dearth of logical notation). In other words, this essay is not a work in logic itself.

Introduction

As the American philosopher C.I. Lewis once claimed (as quoted by Bryson Brown) that no one “really accepts contradictions”. From that it can be said that the prime motivation for paraconsistency (as can sometimes be gleaned from what various paraconsistent logicians themselves say — at least implicitly) is mainly epistemological. Sometimes it’s also inspired by theories, experiments and findings within quantum physics.

The following is also at one with the position of the American philosopher David Lewis (1942–2001) who argued (see here) that it’s impossible for a statement and its negation to be true at one and the same time. (Lewis believed in the “reality” of possible worlds. He also believed that in none of these possible worlds is the conjunction P &¬P true.) Having said that, all this depends on what exactly is said about the embracing of both P and ¬P; as well as on how that embracing is defended.

A related objection is that negation in paraconsistent logic isn’t (really) negation: it’s merely, according to B.H. Slater, a “subcontrary-forming operator”. Indeed the dialetheic philosopher Graham Priest (1948-) explicitly states that paraconsistent negation isn’t Boolean negation. Thus Priest also uses the (epistemic and psychological) word “denial” when referring to negation.

Thus if the acceptance of inconsistencies is largely an epistemological move (as shall be argued), then that move isn’t really (or isn’t actually) an acceptance of both P and its negation (i.e., at one and the same time) at all.

The Acceptance of P∧ ¬P

The American philosopher Bryson Brown says that

“a defender of [C.I.] Lewis’s position might argue that we never really accept inconsistent premises”.

Yet Brown immediately follows that statement with a defence of inconsistency which doesn’t seem to work.

Brown continues:

“After all, we are finite thinkers who do not always see the consequences of everything we accept.”

Perhaps C.I. Lewis’s reply to those words might have been that we don’t “accept inconsistent premises” that we know — or that we think we know — to be inconsistent. Of course it’s the case that having finite minds is a limit on what we can know. Nonetheless, we still don’t accept the conjunction P ∧ ¬P. (It needn’t always be entirely a case of symbolic autonyms.) Paraconsistent logicians don’t accept the statement “1 = 0” either; and virtually no one would accept the conjunctive statement “John is dead and John is alive”.

As for not seeing the consequences of our premises.

No, we don’t see all the consequences of all the premises we accept. However, we do know the consequences of some of the premises we accept. So the finiteness of human minds doesn’t stop us accepting certain premises — or even entire arguments — either. Still, Brown may only be talking about inconsistent premises which reasoners simply aren’t sure about. In such cases, then, the limitations of our minds is salient: we can’t know all the consequences of all the premises we accept. In addition, we can’t know if the all the premises and conclusions we accept are mutually consistent.

Similarly, do we (or do quantum physicists, scientists, theorists, paraconsistentists, etc.), as Bryson suggests, accept inconsistent premises for (to use Brown’s word) “pragmatic” reasons? Would C.I. Lewis (again) have also said that even in this case “we never really accept inconsistent premises”?

Brown goes on to say that

“[i]nference is a highly pragmatic process involving both logical considerations and practical constraints of salience”.

This talk of a “pragmatic process” and “salience” is surely bound to make us less likely to accept inconsistent premises, rather than the opposite.

Take salience.

Not only will inconsistent premises throw up problems of salience (or relevance): such problems will also (partly) determine our choice between two contradictory — or simply rival — premises. What’s more, further talk of (to use Brown’s words) “how best to respond to our observations and to the consequences of what we have already accepted” will, again, make it less likely that we would accept inconsistent premises, not more likely.

In other words, P may have observational consequences radically at odds with the observational consequences of ¬P. So why would we accept both — even provisionally?…

… Unless, that is, accepting both P and ¬P is simply an (epistemic) way of hedging one’s bets! So is that really all that (philosophical) paraconsistency amounts to?

Logical Explosion

The American philosopher Dale Jacquette (1953–2016) put the paraconsistent position when he said that

“logical inconsistencies need not explosively entail any and every proposition”.

What’s more, “contradictions can be tolerated without trivialising all inferences”. Here we have the twin problems (for paraconsistent logic) of logical explosion and logical triviality.

[Ex contradictione sequitur quodlibet = (one of a few translations) “from contradiction, anything follows”.]

To be honest, I never really understood the logical rule (as Brown puts it) that

“if someone grants you (or anyone) [inconsistent] premises, they should be prepared to grant you anything at all (how could they object to B, having already accepted A and ¬A?)” .

How does this work? What is the logic — or the philosophy — behind it?

In other words, how does anything follow from an inconsistent pair of premises (or propositions) being (taken to be) true, let alone everything?

An inconsistent pair of premises (when taken together) surely can’t have any consequences — at least not any obvious ones. (You can derive, it can be supposed, logical strings such as ¬¬A ∧ ¬A and similar trivialities.) In terms of truth conditions (if we take our symbols — or logical arguments — to have semantic interpretations and even truth conditions), how could we derive anything from the premises “John is a murderer” and “John is not a murderer” if both are taken to be true? We can, of course, treat both premises only as-if-they-were-true — but surely that’s not paraconsistency.

In terms of the technical logic of explosion.

Let’s take explosion step by step so it can be shown where the problems are.

One symbolisation can begin in the following way:

i) If P and its negation ¬P are both [assumed to be] true,

ii) then P is [assumed to be] true.

So far, so good (at least in part).

If the conjunction P ∧ ¬P is (assumed to be) true, then of course P (on its own) must also be true. Here, the inference itself is classical; even though the original conjunction P ∧ ¬P isn’t.

Following on from that, we have the following:

iii) From i) and ii) above, it follows that at least one other (arbitrary) claim (symbolised A) is true.

This is where the first problem (apart from the conjunction of contradictories) is found. It can be said that some proposition or other must be the consequence of P; though how can — or why — is that consequence (A) arbitrary? An arbitrary A doesn’t follow from P. Or, more correctly, some A may well follow; though not any arbitrary A. (This is regardless of whether or not A, like P, is actually true.)

So perhaps all this isn’t actually about consequence.

“Consequent” A, instead, may just sit (or be consistent) with P without being a consequence of — or following from — P. Thus if A isn’t a consequence of P (or it doesn’t follow from P), then the only factor of similarity it must have with P is that both are (taken to be) true. However, if that’s the case, then why put A together with P at all? Why not say that P is arbitrary too? If there’s no propositional parameter between P and A, and if A doesn’t actually follow as a consequence of P, then why state (or mention) A at all?

Then comes the next bit of the argument for explosion. Thus:

iv) If we know that either P or A is true, and also that P is not true (or ¬P), then we can conclude that A (which can have any — or no — content) is true.

This is where the inconsistent conjunction is found again. Here there’s a (part) repeat of i) and ii) above. That is, P is both true and also not true; and again we conclude A. In other words, A follows the conjunction P∧ ¬P. This can also be seen as A following P and also A following ¬P (i.e. separately).

Again, why an arbitrary A? Instead of any A following from an inconsistent conjunction, why not say that A can’t’ follow from an inconsistent conjunction? Yet (as is now clear), the broad gist is that because we have both P and ¬P together, then it’s necessarily (or automatically) the case that any arbitrary A must follow from such an inconsistent conjunction.

We now encounter logical triviality; which is very similar to logical explosion.

Logical Triviality

Basic translation: For every p (i.e., for every proposition or statement), every p is true.

Instead of dealing with any (arbitrary) proposition (or theorem within a system/theory) following from an inconsistent conjunction, we now have every proposition (or theorem) doing so. It goes as follows:

If a theory contains a single inconsistency, then it must be trivial. That is, it must have every sentence as a theorem.

There are two problems here, both related to the points already made about logical explosion.

Why does an inconsistency have “every sentence as a theorem”? Sure, if this is indeed the case, then one can see the triviality of the situation. Nonetheless, how does the conjunction P ∧ ¬P generate every sentence as a theorem? Indeed, how does P ∧ ¬P generate even a single sentence? Surely the conjunction P ∧ ¬P generates nothing!

This isn’t to say that inconsistencies aren’t a problem for theories. Of course they are. However, arguing that the conjunction P ∧ ¬P itself generates every sentence as a theorem is another thing entirely…

… Or is it?

At the beginning of the last paragraph it was stated that I’ve rarely seen a defence of logical explosion — only bald statements of it. However, Bryson Brown does present C.I. Lewis’s “proof” of logical triviality (the bedfellow of explosion). Nonetheless, before that Brown does argue that “this defence [of Triv] is just a rhetorical dodge”. And, indeed, that’s how it can be seen. That is, it seems that the logical rule that “from any inconsistent premise set, every sentence of the language follows” is indeed rhetorical in nature. This logical rule is “rhetorical” because it simply can’t be taken literally. That is, it can’t literally be the case that the conjunction P & ¬P can generate every sentence of the language.

So perhaps the proof (or rule) actually amounts to stating (or even shouting) the following:

If a person accepts (or doesn’t even note) an inconsistency (such as the conjunction P & ¬P), then he or she may as well accept any statement!

In terms of the logical notion of the unsatisfiable nature of such premise sets, things seem to be much more acceptable. This is Brown’s formulation of that situation:

“A set Γ is inconsistent iff its closure under deduction includes both α and ¬α for some sentence α; it is unsatisfiable if there is no admissible valuation that satisfies all member of Γ.”

Unlike Triv, this seems perfectly acceptable. Of course there’s “no admissible valuation” of α & ¬α!… At least not in my own (non-formal and philosophical) book.

Logical Relevance

If relevance logic is a type of paraconsistent logic (see Graham Priest here), then that may well be relevant to some — or many — of the points raised above about explosion and triviality.

The main point is that if relevance is a logical stance, then nothing explodes from accepting both P and ¬P. That’s because it’s not the case than an arbitrary A can follow from a conjunctive inconsistency. Nor does it follow that if both P and ¬P are part of a theory (which, for example, arguably occurs in some formulations of quantum mechanics — see my ‘Is Graham Priest’s Dialetheism a Logic of Quantum Mechanics?’), then they trivially bring about every sentence as a theorem.

On the other hand, if we accept the relevance of relevance, then the very acceptance of a conjunctive contradiction (or inconsistency) may also be problematic. If both P and ¬P are accepted, it’s hard to see relevant derivations (or consequences) which follow from contradictory propositions. Of course we can accept that P (on its own) has relevant derivations and(!) that ¬P (on its own) has relevant derivations. But does the actual conjunction P & ¬P have relevant — or any — derivations?

For example, what follows from the propositions “The earth is in the solar system” and “It is not the case that the earth is in the solar system”? Taken individually, of course, much follows from both P and ¬P. But what is the case when P and ¬P are taken together as being jointly true (i.e., as a conjunctive truth)?

In symbols, the semantic heart of the argument above can be expressed in the following way:

If

A → B

is a theorem, then

A and B must share a non-logical constant (sometimes called a propositional parameter).

On the other hand, that (if indirectly) means (if jumping to propositions rather than the symbols A and B) that

If we have the following:

i) (P ∧ ¬P) → Q, Y, Z…

then we must have this consequent too:

ii) then Q, Y, Z…

Yet i) and ii) can’t be a argument in relevance logic.

******************************

Note

(1) To show how radically non-relevant the principle of explosion is, let’s deal with an everyday statement rather than with — possibly misleading — symbolic letters. Thus:

i) Jesus H. Corbett is dead.

ii) Jesus H. Corbett is not dead.

iii) Therefore Geezer Butler is a Brummie.

This isn’t the classical-logic point that two true premises necessarily engender a true conclusion regardless of the propositional parameters of the premises and conclusion. In the classical case, then, all the premises can be genuinely true, along with the conclusion, even if they share no semantic content.

Now take logical triviality.

In this case, the premises above are supposed to generate all statements (or theorems) precisely because i) and ii) are mutually contradictory. This means that the propositional parameters of these premises are irrelevant: only their truth values matter. Not only that: we have now “proved” that Geezer Butler is a Brummie from the premises “Jesus H. Corbett is dead” and “Jesus H. Corbett is not dead”.

[I can be found on Twitter here.]

Is Graham Priest's Dialetheism a Logic of Quantum Mechanics?

Graham Priest tells us that in certain quantum-mechanical experiments “the law of excluded middle tells us that [an atom, particle, etc.] is one or the other”. He also claims that quantum mechanics (or at least its interpretations) suggests otherwise.

It’s tempting to think that the nature of quantum mechanics is the primary reason why the philosopher and logician Graham Priest (1948-) defends, accepts and uses dialetheic logic (or dialetheism generally).¹ Indeed, he mentions quantum mechanics (QM) a few times in various papers and in interviews.

It can now be asked if his views have any impact on the “classical world” or macro-reality (or, at the least, the world as it’s perceived and/or experienced). Perhaps, if dialetheic logic (DL) is truly dependent on the findings of quantum mechanics, it can also be asked if dialetheism is applicable to the “classical world” at all. Of course I may be barking up the wrong tree here. That is, why assume that this macro-world/micro-world opposition has any relevance to dialetheic logic?²

In any case, what has Priest got to say about what he calls “[u]nobservable realms”? (A term which needn’t only refer to the quantum world; but also to historical events, events beyond our galaxy, numbers/abstract objects, etc.) Take this passage from Priest:

“[I]t would sometimes (in the well-known two-slit experiment) appear to be the case that particles behave in contradictory fashion, going through two distinct slits simultaneously.”

Dialetheic logic would be an ideal logic to describe (or capture) such a phenomenon. Nonetheless, Priest’s clause “it would sometimes… appear” does seem to qualify things a little. In other words, since Albert Einstein, hasn’t the supposed “contradictory” (or “paradoxical”) nature of quantum phenomena — or states — been questioned by various physicists (including David Bohm, many-worlds theorists, etc.)?

More broadly, Priest says that “inconsistent theories may have physical importance too”. At first blush, the following can now be asked:

Does inconsistency necessarily have a connection with dialetheism?

And, if so, what’s the connection in particular instances?

What Priest continues to say may mean that not only is the statement above unconnected to dialetheism; it may not be connected to quantum mechanics either. Priest himself continues:

“An inconsistent theory, if the inconsistencies are quarantined, may yet have accurate empirical consequences in some domain. That is, its predictions in some observable realm may be highly accurate.”

Since Priest is talking about an “observable realm”, this mustn’t be about quantum mechanics. (Then again, some of the clues as to the reality of the quantum world are indeed observable.) Not only that: talk of the “accurate empirical consequences” of suspect, questionable and even false theories is something that’s widely accepted throughout the sciences and in the philosophy of science. Indeed Priest finishes off by saying that “one may take the theory, though false, to be a significant approximation to the truth”.³

Priest’s Examples From Quantum Mechanics

Here’s a passage from Priest on an aspect of quantum mechanics that’s relevant — or not! — 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.”

It’s difficult to see how this physical phenomenon has any direct relevance to dialetheism. Nothing contradictory (or paradoxical) is happening here; unlike the two-slit experiment. What’s does happen, however, does indeed go against common-sense views of causation and also against “classical” (or “local”) physics. Nonetheless, that doesn’t automatically entail contradiction or paradox.

Priest also gives the example 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 or “one or the other”; not neither/nor.) Or, alternatively, at that point it may not be an atom at all!

This appears to be a temporal problem which must surely incorporate definitions — or philosophical accounts — of the concepts [instantaneously] and [spontaneously].⁴ Nonetheless, if they define time instants that don’t exist (the period from t¹ to t² doesn’t exist), then Priest and others may have a point. However, can an atom — or anything else — “decay” (or do anything) in a “timespan” which doesn’t actually exist? How can decay — or anything else for that matter — occur if there’s no time in which it can occur?…

So what about Priest’s own conclusion when it comes to atomic decay?

Priest 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 is globally accurate or true. The law of excluded middle tells us that the said atom must either be integral or non-integral; not “both integral and non-integral”.

Again, none of this (basically) philosophy of science — on Priest’s part — is solely applicable to quantum mechanics or dialetheism. The word “solely” was just used because Priest does indeed give another example from QM. He states that

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

And “yet its empirical predictions were spectacularly successful”.

Needless to say, it must be stressed here that the word “inconsistent” is very different to the word “contradictory” (or “paradoxical”). Something can indeed be inconsistent because contradictory. However, can’t something also be inconsistent without being (logically) contradictory?

Abstract objects were mentioned in brackets earlier and Priest himself “move[s] away from the empirical realms” to “the realm of sets”.

Dialethic Logic and the Paradoxes of Set Theory

Priest claims that this realm “appears to be inconsistent” too.

Here again Priest uses the word “appears”. There are indeed paradoxes in set theory. However, haven’t logicians and mathematicians — like quantum physicists — attempted to rectify those inconsistencies or paradoxes? True, unsolved, these inconsistencies or paradoxes (again like QM) are perfect specimens to be dealt with — and captured by — dialethic logic. Nonetheless, it can be said that what’s captured isn’t a world (or reality) of any kind: it’s simply an unsolved paradox or inconsistency. In addition, just as it was asked earlier about how dialethic logic could be applied to the empirical world, so it can now be asked what the connection is between the paradoxes of set theory and the empirical world. That is, it can be argued that set theory needn’t have a necessary connection to such a world. (This will depend on a whole host of factors; such as what one’s take is on the reality — or existence — of numbers, sets, the members of sets, etc.)

If one believes in abstract objects such as sets, then they must exist in an abstract world. Thus dialethic logic, in this case at least, may be applicable to a world — an abstract world. (These vaguely Platonist announcements about sets and abstract objects will, of course, be rejected by certain philosophers, logicians and mathematicians.) ⁵

Conclusion

If dialetheic logic is all about quantum mechanics, then why not call it a logic of quantum mechanics? This means that if dialetheic logic is (as it were) justified by the nature of quantum reality, then it must also depend on that reality.

That said, there’s a tradition in the philosophy of logic which states that logic doesn’t depend on anything — least of all on the nature of the (or a) world. (Ludwig Wittgenstein, at one point, stated this position; and the early Bertrand Russell took the contrary view.) If that were the case, then it may also be the case that dialetheic logic isn’t dependent on the nature of quantum mechanics. It just so happens that QM sometimes — or many times — behaves in a way which can be captured by dialetheic logic. Yet that doesn’t also mean that dialethic logic is dependent on QM. And it doesn’t mean that dialethic logic is derived — in any way — from QM either.

In any case, Priest does clarify his position by arguing that

“the micro-realm is so different from the macro-realm that there is no reason to suppose that what holds of the second will hold of the first”.

True. However and again, is dialetheism independent of quantum mechanics? What’s more, is dialethism applicable to the “classical world”?

As already hinted at, perhaps Priest would reply:

What does it mean to ask if dialethic logic is applicable to the classical world?

Indeed need logic be applicable to the (or even a) world at all?

*****************************

Notes

(1) This case parallels — at least to some extent — ontic structural realism, which (it can be argued) is similarly motivated by the reality of quantum mechanics. Or to put that another way: what relevance does much of the ontic-structural-realist position have to the macro/classical world? (See here for my discussion of this subject.)

(2) Graham Priest is also inspired by Buddhist logic (or simply by Buddhist thought — see here). So, conceivably, this piece may just as justifiably have been entitled ‘Is Graham Priest’s Dialetheism a Logic of Buddhism?’.

(3) This chimes in with Karl Popper’s verisimilitude in which scientific theories have quantifiable truth-to-falsity contents.

(4) Perhaps, as hinted at earlier, what’s needed is some good old-fashioned conceptual analysis of the words “integral”, “non-integral”, “decay”, “spontaneously” and “instantaneously”. Not, of course, the kind of conceptual analysis which historically disappeared up its own backside (i.e., by ignoring science completely). Nonetheless, if quantum reality is the way many physicists say it is, then much conceptual analysis on this matter will either be wrong or simply inapplicable to the quantum domain.

(5) What is — or what constitutes — a world anyway?

Reference

Priest, Graham. (2002) ‘Logicians setting together contradictories: A perspective on relevance, paraconsistency, and dialetheism’.