1
MEILLASSOUX’S CIRCLE; PARADOXES OF TOTALITY IN RECENT CONTINENTAL
METAPHYSICS
III. KAPLAN’S PARADOX
Meillassoux is frustratingly inexplicit about the connection between cardinality results in set
theory and reasoning about the set of all possible worlds. But it is clear that his argument has two
moments. He first states a version of Cantor’s Paradox.
But this series [of sets representing the increasing cardinal numbers] itself cannot be
totalized, in other words, it cannot be collected together into some ‘ultimate’
quantity. For it is clear that were such a quantitative totalization to exist, then it
would also have to allow itself to be surpassed in accordance with the procedure of
the grouping of parts [by taking the set of its subsets]. Thus, the set T (for Totality)
of all quantities cannot ‘contain’ the quantity obtained by the set of parts of T.
(Meillassoux 2008, p. 104).
Following Zermelo-Fraenkel set theory, he concludes that we should refuse to assert that the set
of all sets exists.
Consequently, this ‘quantity of all quantities’ is not construed as being ‘too big’ to be
grasped by thought - it is simply construed as not existing (ibid).
If we add to this the enthymematic premise that,
If a set is thinkable, then its powerset is thinkable,
we can get to Meillassoux’s conclusion that the totality of the thinkable cannot be said to exist
either.
2
Within the standard set-theoretical axiomatic, that which is quantifiable, and even
more generally, that which is thinkable - which is to say, sets in general, or whatever
can be constructed or demonstrated in accordance with the requirement of
consistency - does not constitute a totality. For this totality of the thinkable is itself
logically inconceivable, since it gives rise to a contradiction. We will retain the
following translation of Cantor’s transfinite: the quantifiable) totality of the thinkable
is unthinkable (ibid.).
Meillassoux never gives an explicit reason for thinking that this should entail that there is no set
of all possible worlds.
Moreover, Meillassoux realizes that some set theories, such as Quine’s NF,1 are probably
consistent and do quantify over sets of all sets. In making this admission, he weakens his
argument considerably,
What the set-theoretical axiomatic demonstrates is at the very least a fundamental
uncertainty regarding the totalizability of the possible. But this uncertainty alone
enables us to carry out a decisive critique of the necessitarian inference by destroying
one of the latter’s fundamental postulates: we can only move immediately from the
stability of laws to their necessity so long as we do not question the notion that the
possible is a priori totalizable (Meillassoux 2008, p. 105)
He seems to be arguing that affirming the necessity of laws of nature requires our talk of the set
of all possible worlds to have some form of a priori status. But the fact that there are so many
1
See Oksanen (1999) for an example of just this. Oksanen also shows that the Kaplan’s
cardinality argument was first discussed in print by Davies (1981) giving credit to Kaplan.
3
different set theoretic responses to antinomies shows that it does not. Put thusly, this is a
remarkably weak argument. A prioricity does not mean that there cannot be disagreement.
This problem is not dispositive though, as Meillassoux’s reasoning is remarkably similar
to an argument discovered by David Kaplan, one that like Meillassoux’s, trades on cardinality
considerations, but unlike Meillassoux’s: (a) explicitly connects the issue of the totality of the
thinkable with the totality of possible worlds, and (b) trades in logical necessity rather than a
prioricity. Given the way Kaplan’s argument patches the holes in Meillassoux’s, I do not think it
is an exaggeration to say that Meillassoux and Alain Badiou (2006; originally 1988), who
Meillassoux cites in this context, independently discovered Kaplan’s paradox.
Kaplan gives two arguments to show that (p)<>(q)(Tq  (p=q)) must be considered
to be logically false by standard modal semantics. His first2 argument tracks the
Badiou/Meillassoux argument closely. The sentences says that any proposition is such that it
there is a possible world where it uniquely has the property T in that world. So let T be the
property of being the only proposition being thought. Then Kaplan’s principle instantiated on T
would say that any proposition is such that there is a possible world where that and only that
proposition is being thought.
2
His second argument involves applying the above proposition to (p)(Tp → p) (everything
I'm now thinking is false). By the above proposition there should be a unique world where this
one proposition is being thought, but this gives rise to a liar type paradox. We think that
commentators (e.g. Bueno, Menzel, and Zalta (2013)), don’t mention this second argument
when talking about Kaplan’s Paradox because whatever one says about the liar paradox will
probably take care of this one.
4
Kaplan is not committed to the set possible worlds allowing this. Rather, he holds that
logic alone should not rule it out. This much more reasonable view ends up doing the work of
Meillassoux’s claim that our knowledge of the existence (or not) of the set of all possible worlds
should be a priori. And Kaplan is able to appeal to cardinality considerations in the same way
Meillassoux and Badiou do.
In standard modal semantics,3 propositions are identified with the set of worlds where
those propositions are true. So if we assume that the set of all possible worlds exists, then the set
of propositions is identical to the powerset (set of all subsets) of the set of possible worlds. But
since, by Kaplan’s principle, for each one of those propositions there is a world where it is
uniquely thought, the number of propositions must be less than or equal to the number of
possible worlds. But from Cantor we know that a powerset must contain more objects than the
set it is formed from. So we simultaneously have that the set of propositions is larger than the set
of possible worlds (since the former is the powerset of the latter) and that the set of propositions
is smaller or the same size as the set of possible worlds (since each proposition maps onto a
unique world). Contradiction!
Note how the gap in Meillassoux’s argument about the totalization of the thinkable and
the totalization of the set of possible worlds is patched by Kaplan’s taking as a premise the
3
“Actualist Realists” tend to do just the opposite, taking propositions as primitive and construing
possible worlds in terms of them. But Meillassoux’s concern about the totality of all possible
worlds cannot be avoided by adopting a variant of that view. Every variety of Actualist Realism
faces a version of Russell’s Paradox that we needn’t go into. Given what we say about Russell’s
Paradox in the next section, it is clear that Meillassoux won’t be able to reboot his argument by
appealing to the Russellian version. See Divers (2002), Chapter 15 for a discussion.
5
identification of propositions with sets of possible worlds. Once this is done Montague’s
reasoning converges with Kaplan’s.
Of course there are still many places one could, with some justification, cavil. One
moved by Kaplan’s Paradox might see it as impetus for developing an account of causal
necessity that did not involve totalizing the thinkable.4 Or one might utilize a theory of
propositional content that does not tie it to possible worlds, in the hope that one could then still
talk about causal necessity in terms of the set of possible worlds.5 We set these responses aside,
as responding to our tu quoque argument is far more critical to Meillassoux’s entire project.
IV. WHAT MEILLASSOUX SHOULD SAY ABOUT RUSSELL’S PARADOX
Meillassoux clearly models his response to Kaplan’s paradox on one of the standard responses in
set theory to Russell’s Paradox. In Zermelo-Fraenkel (ZF) set theory the universe of sets is
4
For example, Hiddleston (2005) reverses the Lewisian order of explaining causality in terms of
counterfactuals which are explained by possible worlds. For Hiddleston facts about causality are
fundamental with respect to the counterfactuals.
5
As far as we can tell, Brandomian inferentialists do not need to worry about this. For the
inferentialist propositional content is a function of inferential role, which proof theory makes
explicit. At least since Simpson (1994) we have had fully normalizable systems of modal logic
(for a Fitch style presentation see Cogburn (2011)). Such systems do utilize eigenvariables that
seem to refer to possible worlds and the accessibility relation on them. The inferentialist could
follow Hiddleston and account for these eigenvariables without possible worlds, or she could be
a realist about them. In neither case is propositional content tied to possible worlds in the way
that could get the Kaplan/Russell paradoxes off the ground.
6
constructed as a cumulative hierarchy via axioms from the bottom-up in a way that ensures that
paradox enabling sets (such as the set of all sets) do not exist. In naïve set theory any open
sentence defines a (possibly empty) set. But in ZF set theory an open sentence only defines a set
if the defined set is a subset of a set that exists in the hierarchy.
Meillassoux isn’t explicit about how he would actually formalize modal logic in light of
Kaplan’s paradox. But from the above quotes it is clear enough that approaches that are not
committed to a set of all possible worlds must be viable for his argument to go through.
However, if we carefully examine the mechanics of Russell’s Paradox, it becomes clear just how
problematic this strategy is for Meillassoux.
IVa. Russell’s Paradox as the Canonical Inclosure Paradox
Graham Priest’s great discovery is that an astonishing number of traditional paradoxes fit the
following schema:
Priest’s Inclosure Schema:
(1)
Ω = {y; φ(y)} exists and ψ(Ω)
Existence
(2)
if x  Ω and ψ(x)
(a)
δ(x)  x
Transcendence
(b)
δ(x)  Ω
Closure
In Beyond the Limits of Thought he gives values for φ, ψ, and δ to derive the paradoxes of
Russell, Burali-Forti, Mirimanoff, Kant (according to Priest’s reconstructed “fifth antinomy”),
König, Berry, Richard, Berkeley, Weyl, Montague, as well as the traditional liar paradox. In
addition, he is able to present a guerilla retelling of the history of philosophy (including Plato,
Aristotle, Cusanus, Aquinas, Anselm, Leibniz, Berkeley, Kant, Hegel, Cantor, Russell, Frege,
Quine, Davidson, Derrida, Wittgenstein, Heidegger, and Nāgārjuna) in terms of the schema.
7
For Priest, Russell’s Paradox has a pride of place, in part because it is “the heart of
Cantor’s Paradox” and “undoubtedly the simplest of all the set-theoretic paradoxes” (Priest 2006,
129). We will explain the connection with Cantor below, but Priest’s key insight is that the
“Russell set,” the set of all sets that are not members of themselves, is arrived at by applying
Cantor’s own diagonalization function to the identity function of the set of all pure sets.6 First,
we define diag in the usual manner. Where fα is a one-place function defined over the set α,
diag(fα) equals the set of x in α that are such that x is not a member of fα(x):
diag(fα) = {x  α | x  fα(x)}
This is the key function that Cantor constructed to show that the cardinality of any set is less than
the cardinality of the set of all of that set’s subsets. Now if we let id be the function that takes
every object to itself, we have:
diag(idα) = {x  α | x  idα(x)}
But since by definition idα(x) = x, we can replace idα(x) with x in the above, giving us:
diag(idα) = {x  α | x  x}
Now assume that α is V, the set of all pure sets. Since V contains everything the set of x in V is
the same as the set of all x.
diag(idV) = {x  V | x  x} = {x | x  x}
The Russell set.
And now we can consider Priest’s inclosure schema for Russell’s Paradox. We should
note that part of what makes Russell’s paradox the simplest such one is that it is in the family of
6
This is pretty insightful. The way Russell’s Paradox is usually presented is by noting that if the
set of all sets exists then the Russell set would also exist as a subset of it. Priest shows that this
way of presentation is also an instance of the inclusure schema (Priest 2006, 130).
8
paradoxes (including the Burali-Forti and Mirimanoff paradoxes, and Kant’s 5th Antinomy)
where ψ can be a trivial property such as being self-identical. Thus we don’t need to represent it
in the inclosure schema. Also, since Ω = {y; y  V} is equal to V, we can simplify the inclosure
schema thusly:
Priest’s Inclosure Schema for Russell’s Paradox:
(1)
V exists
(2)
if x  V
Existence
(a)
diag(idx)  x Transcendence
(b)
diag(idx)  V Closure
The contradiction is arrived at by the characteristic self-application of (a) Transcendence and (b)
Closure to V itself, which yields the contradiction (a) diag(idV)  V and (b) diag(idV)  V. Note
that this is licensed because any set is a subset of itself and Transcendence and Closure apply to
all subsets of V. From the nature of the contradiction we can see why Priest uses the phrases he
does. Once applied to V, the Transcendence lemma shows that the diagonalizing function yields
a value external to the postulated totality (the set of all sets), while the Closure lemma shows that
the same function yields a value inside the postulated totality.
Clearly the self-application yields a contradiction. The interesting work then is always
demonstrating Transcendence and Closure with respect to all of the subsets of the totality in
question. In the case of Russell’s Paradox, Closure follows immediately. Since V is the set of all
pure sets, any pure set is an element of it by definition. Transcendence is a bit trickier, but in the
case of Russell’s Paradox, easily formalizable in a Fitch style system, if we make one
assumption:
1. z(z = {y  z | y  y}  {y  z | y  y})
FACT
9
This says that any set is the union of two of its subsets: (1) the one composed of elements of that
set that are members of themselves, and (2) the one composed of elements of that set that are not
members of themselves. Since, by the law of bivalence a set either is a member of itself or is not,
this exhausts the possibilities and so hence the union of the two subsets is equal to the superset.
We continue:
2. | x  V
assumption for  introduction
3. | | diag(idx)  x
assumption for  introduction
4. | | x = {y  x | y  y}  {y  x | y  y}
1  elimination
5. | | diag(idx)  {y  x | y  y}  {y  x | y  y}
3,4 = elimination
6. | | | diag(idx)  {y  x | y  y}
assumption for  elimination
7. | | | diag(idx)  diag(idx)
6 definition 
8. | | | diag(idx)  {y  x | y  y}
6 definition of diag(idx)
9. | | | diag(idx)  diag(idx)
8 definition 
10.| | | 
7, 9  elimination
11.| | | diag(idx)  {y  x | y  y}
assumption for  elimination
12.| | | diag(idx)  diag(idx)
11 definition 
13.| | | diag(idx)  diag(idx)
11 definition diag(idx)
14.| | | 
12, 13  elimination
15.| | 
5, 6-10, 11-14  elimination
16 | diag(idx)  x
3-15  introduction
17. x(x  V → diag(idx)  x)
2-16  introduction
10
We (2) start with an arbitrary x which is a subset of V, and (3) assume for reductio that the
diagonalization on the identity function applied to that x is itself a member of x. Then, (4) note
that the x in question will be equal to the union set of two subsets, one consisting of members of
x that are members of themselves and one consisting of members that aren’t. Since we’ve
assumed that the diagonalization set is a member of x it follows that (5) it is a member of this
union. But then if we reduce to absurdity the assumption that it is in either member of the union
(6-10, 11-14) we will have reduced to absurdity the assumption that it is a member of x (15), and
hence (16, 17) proved that for any subset x of V the diagonalization of the identity function on x
is not a member of x. The two subproofs (6-10, 11-14) both straightforwardly hinge on the
definition of diagonalization and set membership.
A typical response to such paradoxes is to refuse to assert the Existence of the totality in
question. Kant’s original response to his mathematical antinomies (discussed in Chapters Five
and Six in Beyond the Limits) is the model of how to attempt such a thing, and ZF set theory is a
modern day version of Kant’s gambit. But there are other possibilities. The problematic open
sentences in ZF set theory are in von Neumann’s set theory expressible as proper classes, which
are like sets but not prohibited from being members of anything. Thus Closure is blocked, since
it cannot apply to the proper class V. And the proof to Transcendence can be blocked by
adopting weaker logics, such the De Morgan logic developed by Hartry Field in Saving Truth
From Paradox.
Priest notoriously accepts Existence, Closure, and Transcendence, holding that inclosure
paradoxes are true paradoxes. When critiquing alternative approaches he appeals to two
principles: (1) the Principle of Uniformed Solutions (PUS) which states that similar paradoxes
should have similar solutions, and (2) the Domain Principle, which in its simplest formulation
11
states that “For every potential infinity there is a corresponding actual infinity (Priest 2006,
124).”
When Priest actually uses the Domain Principle he intends something stronger than
Cantor’s principle, for example,
. . .for any claim of the form ‘all sets are so and so’ to have determinate sense there
must be a determinate totality over which the quantifier ranges. It would clearly be
wrong to suppose that this totality is a set satisfying the axioms of Zermelo-Fraenkel
set theory, or of some other theory of sets; but that there is a well defined totality
seems to me to be undeniable. Moreover, it is clearly a totality that we can think of
as a single thing, since we can legitimately refer to it as that totality: the totality of
sets (Priest 2006, 281)
Of course Priest doesn’t just restrict himself to set theoretic paradoxes in the book, and from his
discussion it is clear that he takes the Domain Principle to apply to any kind of thing.
Priest’s Domain Principle:
For any claim of the form “all xs are so and so” to have determinate sense, there
must be a determinate totality over which the quantifier ranges. We can refer to this
totality and add it to the group of objects we quantify over.7
If this is correct then standard ways of blocking Existence are prohibited. The collection of all
sets exist since we make claims about all sets.8
7
Put this clearly, the principle is suspiciously similar to Frege’s Comprehension Axiom, which
entails that the set of all sets exists. See also Priest’s (2005) discussion of the Characterization
Principle that holds that for any property there is some possible object that this property is true
of.
12
Priest takes Kant to have first argued for the Domain Principle and also shows how its
application allowed Cantor to construct the ordinal numbers. Priest’s extends Cantor’s own
argument (2002, pp. 123-127). Consider a sentence with a variable in it. The determinate sense
of the sentence will depend upon the collection of things the variable ranges over.
For example, consider the claim ‘Let z be a root of the equation ax2 + bx + c = 0.
Then z has at least one value.’ This is true if z may be complex; false if z must be
real (Priest 2006, p. 125)
Since the truth value of a sentence is a function of its sense, given the way the world is. The
sense of a sentence containing a variable is only fixed by determining what the variable ranges
over. Clearly then, if there is no determinate totality over which the variable ranges, the sentence
will not have a determinate sense.
This is why Aristotle’s doctrine of the idea that there is only a potential infinity makes no
sense. The sentence that every finite number is such that we can construct a greater number is
itself a sentence about the infinite collection of numbers. The Domain Principle should thus be
understood as entailing the Hegelian idea that one cannot talk about parts as parts without
referencing the whole of which these parts are parts. For if a different whole were referenced
then the meaning of phrases referring to all of the parts would be different.
IVb. Meillassoux, Russell’s Paradox, and the Domain Principle
8
Priest (2006, p. 164) argues that the standard Von Neumann method of blocking Closure
actually ends up blocking Existence for the paradox run on classes.
13
Meillassoux’s argument against correlationism crucially involved a Priestian move, taking a
sentence uttered by the transcendental subject to be about the transcendental subject. We gave
this as step 9 in our exegesis of Meillassoux:
9. But the empirical/transcendental distinction will only work for the correlationist if
there are good reasons not to apply A to the very transcendental subject who is
asserting A, “Event Y occurred x number of years before the emergence of human
beings (understood as transcendental subjects).”
And Meillassoux’ reasoning here was again thoroughly Hegelian/Priestian. The transcendental
subject’s finitude is motivated by taking into account the manner in which the transcendental
subject is bounded. But we can only determinately refer to such boundaries if we refer to the
whole in which the subject is situated. As argued above, it is precisely this move that leads
Meillassoux to title his book After Finitude.
Meillassoux is either here tacitly assuming the Domain Principle, or his argument against
correlationism is fallacious. For the correlationist could clearly respond to him analogously to the
way Kant responds to the mathematical antinomies. A subject’s finitude is made sense of relative
to a greater finitude. My n number of years on earth make sense in part because of the n + 2
years that sandwich them. But a greater finite understanding can make sense of those n + 2 years.
And this can clearly be iterated to any moment in space and time.
Such a response only fails if Meillassoux intends to be invoking the Domain Principle. In
talking about finite amounts of time and space, the correlationist is quantifying over all times and
places. For her claims to have determinate sense then this object, the objective universe of space
and time, must also exist and be such that we can meaningfully refer to it.
14
What goes for the universe goes for the universe of sets, and vice versa. It is entirely
unclear why the Domain Principle should not apply to talk about sets, but should apply to talk
about spatial and temporal boundaries. When we return to Kaplan’s Paradox we will see how this
puts Meillassoux in an unstable position.
V. WHAT MEILLASSOUX SHOULD SAY ABOUT KAPLAN’S PARADOX
If Priest is right that Russell’s paradox is “the heart of Cantor’s paradox” then one might think
that Priest’s Principle of Uniform Solution entails that what one says about Russell’s paradox is
exactly what one should say about paradoxes involving cardinality.
Let B be the set of all (pure) sets. . . Any member of P(V) is a set, and hence P(V) is
a subset of V. Conversely, any member of V is a collection of sets, and so is a
member of P(V), and hence V is a subset of P(V). It follows that P(V) = V; and in
this case there is a one-to-one maping between V and P(V), viz., the identity map
(the map that maps everything to itself). But as we saw in 8.3, Cantor showed that
for any set, x, there can be no such mapping between x and P(x). This contradiction
is now called ‘Cantor’s paradox’. Cantor did, indeed discover it, though he never
published it officially.
Cantor’s paradox can be stripped down to its essence. As we saw in 8.3, Cantor’s
proof that there is no one-to-one correspondence between x and P(X) takes an
arbitrary such correspondence, f, and deduces a contribution by considering whether
a swet w is a member of f(w), where f(w) is {y  x; y  y}. Let us write this as x.
Now if x x then x. x. Hence x x. It follows that x  x [Transcendence] or
we would have x x. But if x is any subset of V, x is a subset of V. Hence x V
15
[Closure]. In Cantor’s paradox we take V itself for x [self-application]. We then have
both V  V and V  V (Priest 2006, p. 129).
Of course the stripped down version just is Russell’s Paradox.
While Priest’s insight is important, it would be a mistake to use this connection to apply
the Principle of Uniform Solution from Russell’s Paradox to cardinality paradoxes. Kaplan’s
proof only relies on the fact that a set x is smaller than its own powerset. To prove this, Cantor
assumes for reductio that there is a function f that maps each member of x onto a member of x’s
powerset. Then he shows that diag(fx) yields a set that is in the powerset of x, but not in the range
of f. But that means that any such f will not be an onto function, since things in the codomain of f
(the powerset of x) will not be in f’s range (the collection of objects that f actually maps
members of x onto).
Diagonalization applied to arbitrary functions superficially resembles Priest’s
transcendence, but it is not a case of it. For transcendence to hold with respect to a function g and
some postulated totality y it must be the case that for every subset of the totality g maps into
something not in that subset. But consider the function s that takes every set into its singleton set
applied to {, 1, 2}. s = {}, s(1) = {1}, s(2) = {2}. But then diag(s{, 1, 2}) = , which is a
member of {, 1, 2}. What’s important about diagonalization is that it yields an object not in the
range of the original function. But this can only give you transcendence in Priest’s sense when
the range of the function includes the domain.
Nonetheless, Kaplan’s Paradox is still quasi-Priestian. His inflationary principle
(p)<>(q)(Tq  (p=q)) allows him to take any set of possible worlds and generate another set
that can’t possibly be a subset of the set of worlds. Thus, where M is the multiverse, P(x) is the
16
powerset of x, and k(y) takes a set of sets of worlds and generates a new world for each world in
that set, we have:
Priestian Inclosure Schema for Kaplan’s Paradox:
(1)
M exists
(2)
if x  M
Existence
(a)
(k(P(x))  x) Transcendence
(b)
k(P(x))  M
Closure
The Kaplan function generates a set that is equinumerous with the set it is applied to. But the
powerset of a set is always bigger than the original set. Moreover, since we know that a subset is
never larger than its superset, the Kaplan function applied to the powerset of a set x will yield a
set that is not a subset of that set x [Transcendence]. And since the output of the Kaplan function
is a set of worlds, it is a subset of the set of all worlds. Then if, apply Transcendence to M, we
get (k(P(M))  M) and k(P(M))  M. Contradiction.
We think that the two arguments are homologous enough that it would be odd to reject
Existence of the totality of possible worlds while accepting the inconsistent totality of the set of
all sets. But, since there dishomologies we don’t take this intuition to be dispositive. Much more
relevant is the fact that the Domain Principle applies to Kaplan’s Paradox just as much as it does
to Russell’s Paradox. Meillassoux can only present his own philosophy of contingency by
quantifying over possibilities. For Meillassoux, many states of affairs that the rest of us regard as
impossible are actually possible. But if he’s going to talk about possibilities, as he must to
articulate his own philosophy, he must talk about the totality of possibilities.
In this context it is important to realize just how correlationist Meillassoux becomes
when he refuses to totalize the collection of possibilities. For example, in this passage he argues
that Kant wasn’t correlationist enough!
17
This ignorance [of whether the possible can be totalized] suffices to expose the
illegitimacy of extending aleatory reasoning beyond a totality that is already given in
experience. Since we cannot decide a priori (i.e. through the use of logicalmathematical procedures alone) whether or not a totality of the possible exists, then
we should restrict the claims of aleatory reasoning solely to objects of experience,
rather than extending it -as Kant implicitly does in his objective deduction - to the
very laws that govern our universe, as if we knew that the latter necessarily belongs
to some greater Whole (Meillassoux 2008, p. 105).
But Meillassoux never defends the claim that Kantian refusal to totalize is necessary with respect
to the totality of the possible, but impermissible with respect to the totality of space-time. His
argument against correlationism only works given the impermissibility with respect to spacetime. But his argument to contingency then uses the very gesture he prohibits earlier.
VI. MEILLASSOUX’S CIRCLE
say this is the only bit of the book relevant to the issue. if he had an argument against dialetheism
then might say Domain Principle applies neither in Russell’s nor Kaplan’s Paradox.
But his argument is question begging.
CONCLUSION
Garcia and Gabriel how issues of totality are again at the forefront of continental philosophy.
References:
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