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Synthese (2024) 203:211
https://doi.org/10.1007/s11229-024-04584-1
ORIGINAL RESEARCH
A logical challenge to correlationism: the Church–Fitch
paradox in Husserl’s account of fulfilment, truth, and
meaning
Gregor E. Bös1,2
Received: 11 December 2023 / Accepted: 28 March 2024 / Published online: 11 June 2024
© The Author(s) 2024
Abstract
Husserl’s theory of fulfilment conceives of empty acts, such as symbolic thought, and
fulfilling acts, such as sensory perceptions, in a strict parallel. This parallelism is the
basis for Husserl’s semantics, epistemology, and conception of truth. It also entails
that any true proposition can be known in principle, which Church and Fitch have
shown to explode into the claim that every proposition is actually known. I assess this
logical challenge and discuss a recent response by James Kinkaid. While Kinkaid’s
proposal saves one direction of the parallel for semantics, it gives up the parallelism for
truth. I spell out a different response which meshes naturally with Husserl’s account
of meaning. If the parallelism is restricted to a class of basic propositions, the truth of
non-basic propositions can be defined inductively, without leading to the paradox. I
then discuss objections that have been raised against a similar proposal by Dummett.
The result is that exegetically plausible and popular interpretations of Husserl’s cor-
relationism are indeed challenged by Church and Fitch. But when taking into account
the ‘logical adumbration’ of propositional blindspots, truth and possible fulfilment
can be connected without paradox.
Keywords Knowability ·Correlationism ·Husserl ·History of philosophy ·
Phenomenology ·Anti-realism ·Evidence ·Frederic Fitch ·Alonzo Church ·
Michael Dummett
BGregor E. Bös
gregor.boes@kuleuven.be; g.e.boes@tilburguniversity.edu
1Husserl Archives at the Institute of Philosophy, Katholieke Universiteit Leuven, Leuven,
Belgium
2Tilburg Center for Moral Philosophy, Epistemology and Philosophy of Science, Tilburg University,
Tilburg, The Netherlands
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1 Introduction
As the stage empties, a name tag remains behind: ‘the president’. It refers to the
same woman that everyone in the auditorium has just encountered as a charismatic
leader. But while reading the name tag represents her emptily, the audience had an
intuitively rich experience of the president ‘in the flesh’. Such pairings1between
empty and fulfilling acts play a central role throughout Husserl’s phenomenology. In
an 1893 manuscript, Husserl writes that symbolic representation exhibits a ‘deficit’,
striving for fulfilment (Husserl, 1979, p. 292; p. 411; cf. Husserl, 2009, p. 39; Husserl,
1891, p. 363; Husserl, 1901, VI, §21, p. 607). Eight years later, in the breakthrough
Logical Investigations, the pairing of empty and fulfilling acts continues to play a key
role (Husserl, 1901, I, §§9f; also VI, §13; also Husserl, 2002b, p. 88) and forms the
basis for Husserl’s account of perception (Madary, 2012, p. 148). As Rang puts it,
conscious representation has to be based on and oriented towards a complementary,
fulfilling intuition (Rang, 1975, p. 111). This pairing leads to different correlation
theses for Husserl’s semantics, notion of truth, and epistemology and even serves as
a guiding principle for phenomenology itself. A central commitment already before
Husserl’s development of the phenomenological reduction and his endorsement of
transcendental idealism, but also retained afterwards, the pairing and the correlation
principles that follow from it are relevant for philosophers in Husserl’s tradition more
broadly, including those who emphasize only the earlier or later period of his work.
To discuss this correlational metaphysics more precisely, I distinguish semantic and
alethic correlations in terms of real and ideal possibilities of fulfilment. The limit of
fulfilment is evidence (to be stated more precisely in the next section), and evidence
is the strictest form of knowledge. That any true empty representation can be fulfilled
therefore implies that every true proposition can be known. But from here it follows,
as Church and Fitch have shown, that every true proposition is known: this is either
called the paradox of knowability, or simply a philosophical “embarrassment” for
those who take truth to be essentially knowable (Williamson, 2000, p. 271) . I spell
out the Church–Fitch paradox and how it affects Husserl’s account before consid-
ering two ways to avoid such embarrassment. Kinkaid (2022) defends the semantic
correlation by turning it into a thesis about imagination, which separates it from com-
mitments about possible knowledge. While this avoids the Church–Fitch paradox, it
also either drops or trivializes the correlation between truth and the possibility of evi-
dent fulfilment. To retain a substantive characterization of truth, I propose a restriction
of Husserl’s correlation principles to a class of basic propositions. This approach fits
naturally with Husserl’s inductive characterization of meaning and extends Husserl’s
notion of ‘adumbrations’ to the treatment of propositional blindspots. The phenomeno-
logical context also allows to avoid objections to a structurally similar proposal that
was formulated by Dummett (2001). The discussion shows not only how an embar-
rassment from paradox can be avoided, but also how the use of symbols extends our
representational capacities.
1“Pairing”here refers to the relation between empty and fulfilling acts, not the technical sense of “Paarung”
that Husserl introduces to describe the constitution of multiplicities or the relation between empathizing
and empathized subject.
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2 Husserl’s pairing of empty and fulfilling acts
The pairing between empty and fulfilling acts leads to different correlation theses in
Husserl’s conception of semantics, truth, and epistemology. And because the pairing
ensures that the meanings of words can be clarified by intuition, it even underpins the
phenomenological battle cry ‘to the things themselves’:
Wir wollen uns schlechterdings nicht mit “bloßen
Worten”, das ist mit einem bloß symbolischen
Wortverständnis zufrieden geben [...]. Wir wollen
auf die “Sachen selbst” zurückgehen. An vol-
lentwickelten Anschauungen wollen wir uns zur
Evidenz bringen, [...] was die Wortbedeutun-
gen im Gesetzesausdruck meinen [...]. (Husserl,
1901, Introduction, §2, p. 10)
We can absolutely not rest content with ‘mere
words’, i.e. with a merely symbolic understand-
ing of words […]. We must go back to the things
‘things themselves’. We desire to render self-
evident in fully-fledged intuitions that what is here
given in actually performed abstractions is what
the word-meanings in our expressions of the law
really and truly stand for. (Husserl, 1900, Introduc-
tion to vol. 2, §2, p. 168)
This can be spelled out in terms of two different principles of correlation: one con-
cerning the meanings, the other concerning truth. As long as our representations allow
for intuitive fulfilment, we do not step beyond the boundaries of authentic thought; and
within these bounds, we think about possibilities, not just words. If we want to find out
whether our authentic thoughts are, in fact, true, we seek out what actually fulfils them.
This metaphysical picture has come to be called ‘correlationism’ (originally in Beck,
1928, influentially in Meillassoux, 2006), but also ‘ideal verificationism’ (Smith, 2003,
p. 186f.; Hopp, 2018, p. 632). These principles appear long before Husserl’s theory
of the reduction and exert their influence also on philosophers who are cautious about
Husserl’s later transcendental framework.
In semantics, the principle of correlation determines what constitutes a consistent
representation. The basic unit in Husserl’s theory of meaning is not the written or
spoken sentence, but act kinds that they motivate.2One can see the symbols of a
foreign script without understanding, but when they are interpreted, we pass right
through to what they represent. There is no intermediary step of visualizing (or even
seeing) what one is reading about: written language offers a determinate content while
remaining intuitively empty (‘sense-giving’ acts in Husserl, 1901, I, §14, p. 56). So
we should distinguish the three levels of symbol, empty representation, and intuitive
fulfilment. A perceptual act presents the symbols “a blackbird flies away”, which
motivates an empty representation. That empty representation then can be fulfilled in
the intuitive act of perceiving said blackbird.
Some perceptions of the blackbird are fuller than others, but there need not be a
single act type that provides the most fulfilment to a representation. “A blackbird flies
away” can be fulfilled by perceptual acts that present the blackbird from different
angles. What determines what a particular empty act represents may therefore not be a
2Husserl also discusses semantics at a subsentential level. Sentence parts such as ‘the knife’ or ‘Napoleon’
express nominal acts, which refer to individual objects. A strength of the pairing between empty and fulfilling
acts is that it can also give an account of the meaning of sentence parts. Others have said more about how
such relations between propositional and subpropositional meanings could carry over into a theory of truth,
for example via truthmaker theory (Zuidervaart, 2018, pp. 125f., 135f.). But to focus on the challenge from
the Church–Fitch paradox, I limit the discussion to propositions as expressed in full sentences.
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211 Page 4 of 25 Synthese (2024) 203 :211
single best fulfilling act, but a set of best fulfilling acts. What kind of acts are in this set
depends on what is talked about; it may involve empathy, the understanding of a proof,
or introspection, among others (Sokolowski, 1974, pp. 18f. lists many examples). The
same holds for cases that are far removed from sensory perception. While sensory
perception can present individual objects, such as a knife or a table, also the proposition
‘the knife is on the table’ can be intuitively fulfilled. This kind of fulfilment is not
achieved by the senses alone, but requires categorial intuition. Categorial intuitions
can be built atop other categorial intuitions, and ultimately account for fulfilment of
propositions about abstract states of affairs, such as mathematical identities (Husserl,
1901, VI, §§40ff.), like a+b=b+a. Here again, we see the pairing between
empty and full acts: either the equation can be understood emptily, as symbols that
can be manipulated according to a set of rules that we remember; or the validity of
that identity can be fulfilled in categorial intuition.
Using symbols for empty representations has the great benefit that we can recom-
bine them into new representations. But how do we know that we created empty
representations and not just a new graphical ornament? For written language, the rules
of grammar determine which symbolic combinations lead to sentences. A sentence is
more than an ornament, but this can fall short of representation in different ways. On
the one hand, we can form grammatically correct sentences that are not meaningful,
such as ‘he laughed asymptotically’ because it is not even clear how itsparts combine.
On the other hand, there are contradictions, like “A and not A” or “there is a trian-
gular square”. While contradictions are not meaningless, they fail to express a “real”
meaning (Husserl, 1901, I, §15, p. 61): that is, whatever meaning is attached to their
symbols cannot correspond to a fulfilling act. With this further requirement, Husserl
distinguishes authentic (eigentlich) from inauthentic (uneigentlich) thought (Husserl,
1901, VI, §63). Inauthentic thought moves in sentences that are grammatical, so not
strictly meaningless. But inauthentic thought cannot be fulfilled. Authentic thought,
on the other hand, recombines only those empty representations that also respect the
possibility of their fulfilment. That all consistent propositions allow for their fulfilment
is ensured by pure laws of meaning.
Die reinen Gesetze der Gültigkeit der Bedeutun-
gen, der idealen Möglichkeit ihrer angemessenen
Veranschaulichung, laufen offenbar den reinen
Gesetzen parallel, welche die Verknüpfung und
Umwandlung ihrer eigentlichen kategorialen For-
men regeln. (Husserl 1901, VI, §63, p. 723)
The pure laws of the validity of meanings, the ideal
possibility of their adequate intuitive illustration,
obviously runs parallel to the pure laws governing
the combination and transformation of authentic
categorial forms. (Husserl, 2001a, VI, §63, p. 313)
This is the semantic correlation. That a proposition is consistent means the same as
it being metaphysically possible (Husserl, 1901, VI, §30, p. 633), only that ‘consis-
tency’ emphasizes the relationship between partial meanings, and possibility concerns
the compound meaning as a whole, together with its (intentional) object (Husserl,
1901, VI, §63, 117). The semantic correlation therefore expresses a metaphysical
commitment: an empty representation without the possibility of a fulfilling act does
not represent a metaphysical possibility.
Beyond semantics and modality, fulfilment also serves as the defining notion for
Husserl’s theory of truth and evidence.
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Die letzte Erfüllung repräsentiert ein Vollkommen-
heitsideal. Sie liegt allzeit in einer entsprechen-
den “Wahrnehmung” (wobei allerdings eine
notwendige Erweiterung des Wahrnehmungsbe-
griffs über die Schranken der Sinnlichkeit hinaus
vorausgesetzt ist). Die Erfüllungssynthesis dieses
Falls ist die Evidenz oder Erkenntnis im präg-
nanten Wortsinn. Hier ist das Sein im Sinne
der Wahrheit, der recht verstandenen “Überein-
stimmung”, der “adaequatio rei ac intellectus”
realisiert, hier ist sie selbst gegeben, direkt zu
erschauen und zu ergreifen. (Husserl, 1901,VI,
introduction, p. 540)
Th[e] final fulfilment represents an ideal of perfec-
tion. It always consists in a corresponding percept
(we of course take for granted a necessary widen-
ing of the notion of perception beyond the bounds
of sense). The synthesis of fulfilment achieved
in this limiting case is self-evidence or knowl-
edge in the pregnant sense of the word.Here we
have being in the sense of truth, ‘correspondence’
rightly understood, the ‘adaequatio rei ac intellec-
tus’ is itself given, to be directly seized and gazed
upon. (Husserl, 2001a, VI, introduction, p. 185)
We can “live through” the truth when an empty act represents an object in the
identical fashion that a fulfilling act presents it. This limiting case of fulfilment is
what Husserl calls ‘evidence’ or ‘knowledge in the pregnant sense of the word’ (cf.
Husserl, 2003, p. 159). To call an empty representation true means that such fulfilling
acts could be realized:
[D]ie Richtigkeit des Urteils im logischen Sinn
des Satzes: der Satz “richtet” sich nach der Sache
selbst; er sagt, so ist es, und es ist wirklich so. Darin
ist aber die ideale, also generelle Möglichkeit aus-
gesprochen, daß sich überhaupt ein Satz solcher
Materie im Sinne strengster Adäquation erfüllen
läßt. (Husserl, 1901, VI, §39.4, cf. Husserl, 1986,
pp. 108, 120; Husserl, 1929b, §90)
[T]he proposition ‘directs’ itself to the thing itself,
it says that it is so, and it really is so. In this
we have the expression of the ideal, and therefore
general, possibility that a proposition of such and
such a ‘matter’ admits of fulfilment in the sense of
the most rigorous adequation. (Husserl, 2001a,VI,
§39.4)
Adequate fulfilment can only present the truth (and this itself is evident, Husserl,
1901, VI, §39, p. 656). The notion of evidence is hence not a probabilistic relation
between propositions, as for the Bayesian, and it is not a feeling that accompanies
judgements when they are justified. Evidence refers to a special class of acts in which
the intended object is present and given how it actually is. What I am focusing on here is
the principle that connects truth with possibilities of evident fulfilment. Such an alethic
correlation has been ascribed to Husserl before (Tugendhat, 1970, p. 50f.; Soffer, 1991,
pp. 75, 89; Smith, 2003, p. 186f.; Bernet, 2003, p. 165; Hardy, 2013, p. 100; Erhard
2014, p. 102; Zahavi, 2017, p. 71f.; Mulligan, 2017, p. 93; Hopp, 2020, p. 122) and it
might be implicit in influential characterizations of a phenomenological conception of
truth (Sokolowski, 2000, p. 159; Jacobs, 2016, p. 259). I offer an explicit statement of
the semantic and alethic correlations below. But since Husserl’s conception of evidence
has been much discussed—in particular, with respect to its changes—I first consider
the alethic correlation after the Logical Investigations.
A main development is that the first notion of evidence is an act that identifies the
content of empty and fulfilling acts (Husserl 1901, VI, §39). Husserl later calls the ful-
filling act itself ‘evidence’ and gives it a form of priority.3The later work also discusses
that different subject matters might be given in acts of evidence with different struc-
tures (Husserl, 1939, p. 11f.). But these are considerations about distinctions between
3Tugendhat (1970, p. 94) and Lohmar (1997) find this priority already in the Logical Investigations.Bernet
(2003, p. 155) emphasizes the role of synthesis, while Byrne (2021, p. 140f.) traces the shift to a monothetic
account of fulfilment and evidence.
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211 Page 6 of 25 Synthese (2024) 203 :211
different types of evidence and their structure; they are orthogonal to the idea that
every true empty representation has a (set of) complementary fulfilling presentations.
Husserl’s notions of adequate and apodictic evidence have also created much dis-
cussion (at book-length in Levin, 1970). I now have to briefly introduce some of
these technical debates in Husserl scholarship to show that the alethic correlation,
despite Husserl’s progression in these topics, continues to play an important role in
his later work. First, this concerns the role of apodictic evidence; second, Husserl’s
late transcendental foundation of logic, and third, the fallibility of evident judgement.
To introduce the terminology, consider that fulfilment can be partial. A quick glimpse
of the blackbird provides less complete fulfilment of ‘a blackbird flies away’ than
undisturbed observation. Such increasing degrees of fullness specify a partial order-
ing of acts, at the limit of which Husserl locates adequate evidence (Husserl, 1901,
VI, §16, p. 598). In the mathematical sense of ‘limit’, a series of numbers with the
limit πapproximates πto arbitrarily small differences, while πnever appears in that
series. This is how adequate evidence can be the limit for evident experiences, even
if there are always further perspectives on the same blackbird that would add to what
we have seen so far (cf. Husserl, 1913, §143). Apodictic evidence on the other hand
is such that we cannot conceive of a reason to doubt it (Husserl, 1929a, §6), similar to
what other philosophers might call ‘certainty’. We may for example wonder whether
far-fetched thought-experiments with brains in vats constitute such reason to doubt,
and whether this undermines apodicticity. In the search for the ultimate foundation
of knowledge, it becomes relevant whether apodictic evidence is possible without
adequacy and whether it can be achieved at all (Heffernan, 1998, p. 62). But I am
concerned here with the idea that the emptiness of a representation can always be
fulfilled. This is compatible with the idea that the best possible fulfilment does not
realize the ideals of adequacy or apodicticity, and it is compatible with not knowing
whether any given fulfilment allows further improvement.
One may still wonder whether Husserl’s Formal and Transcendental Logic reveals
a naïvety in formal logic that prohibits an explicit statement of the alethic correlation.
Husserl considers formal logic a positive science, insofar as it presupposes the reality
of the world and that there are absolute truths (Husserl, 1929b, §105). This creates
a critical distance between Husserl and the notion of truth as it is used in a formal
framework. My considerations, however, are focusing on Husserl’s understanding of
propositional truth, not what he says about subpropositional relations of fulfilment.
And even in the Formal and Transcendental Logic, truth remains centred around the
ideal of adequation between empty intention and fulfilling intuition. In the case of
formal logic, the principle of excluded middle is explicated as the claim that any
meaningful statement can either be brought to adequate fulfilment or is evidently
disappointing, a fulfilment of its negation (Husserl, 1929b, p. 90). Transcendental
logic is ‘critical’ of such assumptions about truth, in the sense that it suspends the
presumption of objective validity.
It is no small feat to draw out the consequences of suspending that presumption.
At the idealistic end of possible interpretations, it might appear that to consider a
judgement that p true, it has to be matched to the subjective activity which made it so,
that p is true (Husserl, 1929b, §46). This would constitute a sea change about what
underwrites the truth of our judgements—no mind-independent but knowable states
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Synthese (2024) 203 :211 Page 7 of 25 211
of affairs, but sedimented activities of transcendental consciousness—but despite this
change in truthmakers, truth would still be spelled out in terms of possible fulfilment.
If anything, the connection would be even closer, since possible fulfilment were then
not only correlated with truth, but constitute it like bricks constitute a wall. So even in
this extreme case, any truth of an empty representation would remain coordinated with
a fulfilling presentation. With a small exception, this will be all I wish to say here about
transcendental logic and transcendental idealism.4The rest of this essay operates at a
level of naivety that is shared with formal logic and the empirical sciences, to discuss
a consequence of Husserl’s thought at that level. This does not mean that there is an
incompatibility with the Formal and Transcendental Logic: the critical project does not
aim to ‘surrender’ (preisgeben) what formal logic and empirical science presuppose
(cf. Husserl, 1929b, §80, p. 206).
Formal and Transcendental Logic also contains a famous remark that might appear
to question the assumption that evidence implies truth:
Selbst eine sich als apodiktisch ausgebende Evi-
denz kann sich als Täuschung enthüllen und setzt
doch dafür eine ähnliche Evidenz voraus, an der
sie “zerschellt”. (Husserl, 1929b, §58)
Even an ostensibly apodictic evidence can become
disclosed as deception and, in that event, presup-
poses a similar evidence by which it is “shattered”.
(Husserl, 1969, §58)
But the second half is crucial: evidence disappoints only where we need to have
found better, more complete evidence. This rather reaffirms the idea that every truth is
connected with a possibility of evident fulfilment: If purported evidence disappoints,
this means that we have not yet reached the last rung in the ladder of improving
fulfilments. So even in Formal and Transcendental Logic, truth entails the possibility
of an evident fulfilment, and if purported evidence disappoints, there must be more
complete evidence that does not disappoint. This is in no tension with the idea that
the best fulfilment presents the truth—what I call the alethic correlation. This best
fulfilment need not amount to apodictic or adequate evidence: seeing the blackbird
can present the truth intuitively, even if there are hidden sides of that bird, so that the
limit of adequate fulfilment still points beyond it. For the lack of a better term, let me
call the best achievable level of fulfilment ‘evident fulfilment’.
Now we can explicitly state the two correlation principles. The semantic correla-
tion Corr-Sem is about any consistently combined meaning. The alethic correlation
Corr-Al is about any true proposition.
Corr-Sem A proposition is consistent if and only if it is possible that an act intuitively
fulfils that proposition. (ideal possibility of evident fulfilment)
Corr-Al A proposition is true if and only if it is possible that an act intuitively
fulfils that proposition. (real possibility of evident fulfilment)
Husserl also correlates the existence of individual objects with the possibility of
directly experiencing them (Husserl, 2001b, p. 157), and holds that any existing object
is the subject of true propositions (Husserl, 2003b, p. 146). Moreover, he endorses a
4See Tugendhat (1970, p. 243f.) about the relation between truth in the empirical sciences and truth in
genetic phenomenology. Tugendhat also warns of the late Husserl’s tendency to prioritize the latter over
the former.
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correspondence between true propositions and obtaining states of affairs5(Husserl,
1906, §14, p. 53; Husserl, 1900, p. 230f; Husserl, 2013, p. 78f; Husserl, 2001b,p.
154). Together with Corr-Al, this leads to an ontological correlation that connects
possible fulfilment with obtaining states of affairs, which is a good candidate for inter-
preting Husserl’s transcendental idealism without a subjective creation of truthmakers
(Husserl, 2003b, p. 146). But I want to proceed in smaller increments, maintaining
distinctions between what we can represent, what we mean by truth, and whether
these boundaries of our representation coincide with those of reality. It is possible,
for example, to endorse a correlation between truth and possible experience without
endorsing a similar correlation between mind and world (a similar point is made for
semantic anti-realism by Wright, 1992, p. 159, for Peircean verificationism by Misak,
1995, p. 118, for Husserl by Hopp, 2020, p. 291). In what follows, I put aside the
ontological correlation and Husserl’s transcendental idealism. The focus is rather on
the pairing of empty and fulfilling acts, which Husserl endorsed before and after his
explicit turn to transcendental idealism.
The distinction between a semantic and an alethic correlation immediately shows
that ‘possibility of evident fulfilment’ has to mean different things. I here use Husserl’s
terminology as follows: Ideal possibilities (♦I) are only constrained by essential laws
and concern anything that could be the case. Real possibilities (♦R) are a subset of the
ideal possibilities. Soffer (1991, p. 75) uses ‘real possibility’ to refer to possibilities of
knowledge within (practical) reach. This use of ‘real possibility’ might be common in
the literature, but it does not allow to distinguish possible fulfilment in mere phantasy
and the positing acts of evident fulfilment (Husserl, 2002a, §48, pp. 178ff.). And with
that distinction, we can also separate the semantic and alethic correlations.
Husserl’s official account characterizes real possibilities as those ideal possibilities
that have been motivated (Husserl, 2020, p. 203; Husserl, 1973, §84, p. 292f. Husserl,
1913, §47). I think there are serious problems with this proposal (see Bös, manuscript)
although it can perhaps be radicalised into a “rejection of the hypostatization of possi-
bilities” (Zhok, 2016, p. 232), according to which actual experience creates the room
for possibilities. Fortunately, this need not be decided here, because after illustrating
what these notions of possibility amount to, they can be treated as primitives.
Husserl describes real possibility as ideal possibilities with an additional constraint
from reality: and this additional constraint just seems to be the way that the world
actually is (Husserl, 2002a, §61, p. 269; see also Husserl, 1973, p. 292f.). If there is
one apple left on the tree but nobody is looking, it is a real possibility of evidence
to look and see that there is a single apple left. When somebody says ‘there are two
apples on the tree’, there is no corresponding real possibility of fulfilment, hence this
statement is false. But seeing two apples remains an ideal possibility of fulfilment,
which distinguishes this statement from the lack of fulfilment of a contradiction.
After setting aside the ontological correlation and an issue about a distinction
between modal terms, we can look at a new challenge to Corr-Al, which will occupy
us for the rest of this essay. Evident fulfilment, even where it does not achieve ade-
5In the context of Husserl, states of affairs can also fail to obtain, so that “obtaining states of affairs” is
not pleonastic. Appearances to the contrary are due to Armstrong, who uses ‘states of affairs’ like ‘facts’
(Textor, 2021, Introduction and Historical Appendix). For a phenomenological metaphysics of states of
affairs, see (Reinach, 1911).
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quacy, is a particular way of knowing, namely knowing with intuitive fullness (Husserl
1900, §6, p. 28). If every true empty representation can be brought to evident fulfil-
ment, this implies a fortiori a thesis about the scope of what can be known: for every
true proposition, it is possible to know that proposition, namely by realizing an act of
evident fulfilment. The Church–Fitch paradox can be formulated as an argument to
the effect that such possible knowledge entails that every truth is actually known. I
first introduce the paradox as an argument in modal epistemic logic, commenting on
the justification for each step. Then I illustrate the structure of the argument in natural
language before discussing ways in which it can be addressed.
3 The Church–Fitch paradox
What is known as the Paradox of Knowability goes back to Fitch (1963), who, in
beautiful irony, credits it to an anonymous 1945 referee report for a paper that was
never published. In 2005 this referee was identified as Alonzo Church (Salerno, 2009,
pp. 13, 36). The paradox challenges the conceptual connection between truth and
possible knowledge. Let Kp stand for somebody, somewhere, at some time knows
that p, and let ♦stand for a suitable notion of possibility.6The schema according to
which any true proposition can be known,
Universal Knowability p→♦Kp
then collapses into the omniscience schema,
Omniscience p→Kp
according to which every proposition is known. Since these are schemata, arbitrary
propositions can take the place of p.
The Church–Fitch paradox does not depend on the scope of the modal operator,
so we can leave aside the earlier complications about the relation between ideal and
real possibilities. The only assumptions are that knowledge is factive: Kp →pand
distributive: ∀p,q:K(p∧q)→Kp∧Kq. Factivity simply means that one can
only know propositions that are true. Distributivity means that knowing a conjunction
entails knowing each conjunct. With these properties for the knowledge operator, it
follows that there are ‘no known unknowns’, in the specific sense that it cannot be
known that a proposition is true and never known.
1. K(p∧¬Kp)(assumption)
2. Kp∧K¬Kp (1., distributivity of K)
3. Kp∧¬Kp (2., Factivity of K. Contradiction)
4. ¬K(p∧¬Kp)(1.–3., discharging 1.)
5. ¬K(p∧¬Kp)(1.–4., theorems are necessary)
6. ¬♦K(p∧¬Kp)(5., duality of and ♦)
6K,and ♦are propositional operators, in the sense that for any proposition p,Kp,pand ♦pare
also propositions. Their interpretations are ‘It is, was, or will be known that p’, ‘It is necessary that p’
and ‘It is possible that p’. For a philosophical introduction to modal logic, see (Girle, 2009,chs.1,9,12).
Discussions of Husserl and modal logic are found in Mohanty (1984), Spinelli (2021). For an overview of
the Church–Fitch paradox, see (Brogaard & Salerno, 2019) and the articles collected in (Salerno, 2009).
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The properties of Kalone make it impossible to know a proposition p∧¬Kp,for
arbitrary p. Like a proof of 720 =2·3·4·5·6, this derivation can always be made. The
‘theorem’ it establishes therefore holds necessarily, which was used in step 5. The last
line uses the equivalence of ‘necessarily not’ and ‘not possibly’. With this ‘no known
unknowns’ lemma, Omniscience follows quickly.
1. p→♦Kp (Universal Knowability)
The schema can be applied to arbitrary propositions, including for any proposition p,
the more complex proposition p∧¬Kp.
2. (p∧¬Kp)→♦K(p∧¬Kp)(from 1.)
The lemma we just derived did not depend on what pwas, so we can use it here as
well.
3. ¬♦K(p∧¬Kp)(‘no known unknowns’ lemma)
4. ¬(p∧¬Kp)(from 2., 3.; modus tollens)
5. p→¬¬Kp (→-introduction)7
6. p→Kp (from 5.; double negation elimination. Omniscience)
We have shown how the thesis that every true proposition could be known leads to
the claim that every truth is, was, or will be actually known. This is a much stronger
coordination between mind and world than what Husserl could have wanted to endorse.
Even in his attempt to prove transcendental idealism, certainly one of the places where
Husserl’s idealism is the most unadulterated, he writes that objects are possible “with-
out my [thinking] of it or anyone else’s thinking of it” (Husserl, 2003b, p. 146). Such
objects would make propositions true that nobody knows in fact (although they all
could be known). Speculating about an omniscient being does not help either, since
the same problem would arise for a reinterpretation of Kas ‘known by a finite being,
at some point, at some time’.
As an informal illustration of the Church–Fitch paradox, consider Bolzano’s blos-
soming tree (Bolzano, 1837, §25, p. 84; Beyer, 2019, p. 69). Imagine that in a
long-abandoned monastery, we find a dying almond tree, dropping its last petal as we
enter the courtyard. “Nobody knows how many petals were on this tree last spring”,
we think to ourselves. This thought itself has its determinate truth or falsity because it
corresponds or fails to correspond to a state of affairs: We do not know the number of
petals, nor does anyone else. Also in Husserl’s terms, there is no issue with thinking
of a state of affairs that makes judging a particular ncorrect, and judging any other
number incorrect. But it is enough for the Church–Fitch paradox to arise. If there
is a truth about the number of the petals on the tree, and it is also true that nobody
knows, has known, or will know this number, these form an unknowable conjunction:
a proposition that represents an obtaining state of affairs but cannot be known (and
therefore cannot be known with evident fulfilment). In phenomenological terms, we
have constructed a symbolic expression which can be interpreted as an empty rep-
resentation, but which does not allow for evident fulfilment. Yet this is not a case
7From line 4., assuming pand ¬Kp leads to contradiction. If we discharge the assumption ¬Kp,we
have a proof of ¬¬Kp under the assumption that p, which permits the introduction of the conditional.
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of inauthentic thought, because no contradiction is involved: for some pn, the empty
representation has a corresponding state of affairs. Unlike Meillassoux’ (2006) much
discussed argument from ancestrality, the Church–Fitch paradox is not restricted to
scientific statements about time before sentient life, but arises for all kinds of trivial
propositions. For any true proposition that nobody actually knows in past, present
and future, there is a logical conjunction that nobody could possibly know. We do not
need to go as far as the Big Bang; challenges to correlationism already arise from the
myriads of trivial truths that we never cared to ask about.
It is a classical topic in Husserl’s phenomenology to criticize formalized thought and
its deadends (Husserl, 1936, §9). But Husserl’s countermeasure, echoed in the return
to ‘the things themselves’, precisely presupposes the pairing of empty and fulfilling
acts that leads to the Church–Fitch paradox. So I do not think that Husserl’s account of
formalization in the Crisis will suffice, we need to substantially engage with it. Most
responses fall into one of three camps, they either
1. Revise the logical properties of the epistemic operator,
2. Reject the inference principles of classical logic, or
3. Restrict the scope of knowability.
The epistemic operator in the literature on the Church–Fitch paradox is either the
knowledge operator Kor a generalized factive and distributive operator. In Sect. 2
I introduced evident fulfilment as a best possible case of fulfilment which does not
need to amount to adequate or apodictic evidence. I have taken evident fulfilment to
imply knowledge of what is evidently fulfilled, but the paradox could be formulated
analogously as long as evident fulfilment is factive (ensuring the truth of what is
evidently fulfilled) and distributive (evident fulfilment of (p and q) entails the evident
fulfilment of p and the evident fulfilment of q). In the phenomenological context, the
first strategy would be to revise the logical properties of fulfilment so that the best
possible kind of fulfilment does not imply truth.8This might be motivated by the late
Husserl’s concerns about the possible disappointment of what appears to be apodictic
evidence.
But I think it is important to distinguish here between first and second order knowl-
edge. Undeniably, we sometimes believe to know something, and it turns out that we
were wrong. But the correlation theses are about what we actually judge, not whether
we always know if we have judged evidently or not. How well introspection can deter-
mine our own epistemic position is a different question. For fallibility to be relevant to
the Church–Fitch paradox, we would have to take the best possible cases of evidence
to be compatible with the falsity of what they support. This is only possible if the
notion of evidence is completely separated from the notion of truth. It would then be
simpler to give up Corr-Al entirely, since any connection between truth and evidence
would need to be explained differently.9
8From a logical point of view, it would also be an option to deny distributivity, i.e. the principle that a
fulfilment of p and q implies the fulfilment of pand the fulfilment of q. But not only is such a response ad
hoc and difficult to understand, Williamson (1993) also constructs a version of the Church–Fitch paradox
that works without distributivity.
9Mertens (1996 pp. 143ff., 213ff.) develops a fallibilist interpretation of Husserl. Likewise Berghofer
(2018) considers fulfilment only as a source of justification. A replacement for Corr-Al in this context
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Husserl writes that evidence is knowledge ‘in the narrowest sense’ (Husserl, 1900,
p. 29; Husserl, 2001a, VI, introduction, p. 185), and I take evident fulfilment to be
a form of intuitively full knowledge. But ‘knowledge’ is undeniably factive: “He
knows that I am tall, but that is not true” is either contradictory or shows a confusion
of knowledge and belief. That this is not as obvious in “She judges evidently that
I am tall, but that is not true” is due to the ambiguity of the world “evidence”. In
Sect. 4I discuss a sense in which a logical revision of fulfilment can save a version of
Corr-Sem,butCorr-Al requires a factive notion of evident fulfilment.
Instead of revising the logical properties of evident fulfilment, one could also seek
the flaw in the rules of inference of classical logic. Such a response has been pursued
for example by Dummett (2007,2009) and expanded by Bermúdez (2009). In the
formulation offered here, only the double negation elimination in the last step is not
intuitionistically valid. Dummett, in any case, takes the penultimate line to express an
intended intuitionist characterization of truth: That a proposition is true implies that
there is no proof that it cannot be proved (Dummett, 2007, p. 348). In other words, the
truth of a proposition implies that coming to know that truth always remains open.
Affinities between phenomenology and intuitionist logic appear in the work of
Hermann Weyl and Oskar Becker. Given their connection to Husserl, one may there-
fore wonder if the intuitionist response is attractive as an interpretation of Husserl’s
metaphysics. If Husserl can be considered a mathematical platonist, then surely not
of a ‘naïve’ kind, as he attempts to spell out the metamathematical conditions under
which mathematicians can symbolically construct new domains (see the double lec-
ture, Husserl, 1891, pp. 430–451). But he understands mathematics and logic to study
abstract objects and ideal states of affairs (Kinkaid, 2022, p. 1017). And the princi-
ples of formal logic that he endorses are classical, including the elimination of double
negation (Husserl, 1901, VI, §34, p. 642; Husserl, 2001b, p. 243). Even Formal and
Transcendental Logic reaffirms, at the formal level, the principle of excluded mid-
dle (Husserl, 1929b, §79; Mohanty, 1999, p. 192f.). Whereas Dummett’s intuitionist
response fits with his wider revision of logic and his programme in the philosophy of
mathematics, it would lack motivation in the context of Husserl’s philosophy.
Arestriction, on the other hand, is less invasive. The general idea is that the paradox
arises from the unrestricted quantification over all propositions, whether formulated as
a principle for knowability or possible evidence. A main proponent of such a strategy
is Tennant, who restricts the knowability thesis to propositions that can be known
without contradiction (Tennant, 1997, p. 273). This kind of response is much more
convincing if it does not just respond to a paradox, but follows from general principles.
I spell out such a strategy in Sect. 5.
4 Fulfilment in Imaginative Illustration
Kinkaid observes that Husserl’ssemantic correlation has a general problem with propo-
sitions which have come to be called ‘blindspots’ (after Sorensen, 1988). A blindspot
could be a general principle that every true proposition can be justified. Douven (2007) defends such a
principle from a Bayesian perspective. But in what follows, I am interested in pursuing the version of the
correlation that also connects fulfilment and truth.
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Synthese (2024) 203 :211 Page 13 of 25 211
proposition is consistent, but inaccessible to some propositional attitude. The most
famous example is Moore’s “It is raining, but I do not believe it”, which is inaccessi-
ble to the propositional attitude of belief (Kinkaid, 2022, p. 1019). The Church–Fitch
paradox exploits that p∧¬Kpis a blindspot for knowledge. As a blindspot for knowl-
edge, it is also a blindspot for evident fulfilment: so it is meaningful, possibly true,
but cannot be judged evidently. In response, Kinkaid (2022, p. 1022) offers an elegant
revised principle:
K-Rev All consistent propositions can be intuitively illustrated.
This principle is weaker than Husserl’s original correlation between intention
and fulfilment, which includes the ‘possible knowledge-use of meanings’ (‘mögliche
Erkenntnisfunktion der Bedeutungen’, Husserl, 1900, I, §29, p. 227; Husserl, 1901,
I, §29, p. 101). Kinkaid’s revision avoids the Church–Fitch paradox by substituting
the factive possibility of evident fulfilment with the non-factive possibility of intu-
itive illustration.10 Intuitive illustration can happen through non-positing acts, such as
imagining a state of affairs that would make the proposition true (Kinkaid, 2022,p.
1023). Whereas evident fulfilment vouches for what it presents, acts of imagination
do not in general have such “positing” character. That imagination is not a positing
act also means that imagination is not factive. In terms of the strategies outlined in
Sect. 3, this is similar to a revision of the logical operator on the right-hand side of the
correlation: the truth of a proposition entails that an act with that propositional content
is possible, but this act has no bearing on what is the case.
The positing character of evidence concerns object and subject of experience alike.
‘I do not exist’ or ‘There is an unimagined tree’ can be intuitively illustrated by
imagining a world in which there is nobody or where there is a tree but nobody who
imagines it. One could describe this process as a separation of the phantasizing from
the phantasized ego, which in phenomenology has been discussed as ‘ego-splitting’
Cavallaro (2017).11
This is an interesting lesson about the scope of imagination, but it also reverses a
priority between evidence and imagination. The official account has it that the non-
positing acts of phantasy are understood as a modification of the positing acts of
evidence (Husserl, 1996a, p. 115; Husserl, 1901, VI, §30, p. 633; Husserl, 1980,
p. 590; Husserl, 1913, §104; Tugendhat, 1970, p. 40; Hopp, 2020, pp. 238, 291).
Imagination allows us to learn about possibility because we can imagine what kind of
evidence we could have. We are able to imagine the kind of evidence we would have
if the door were green, even if the actual door is red. What we have really imagined is
10 A small terminological point: In the passage that Kinkaid cites for the notion of ‘intuitive illustration’
(Veranschaulichung), Husserl indeed distinguishes it from ‘intuitive fulfilment’. Husserl’s argues that not
all fulfilment has to be an illustration, which he associates with imagery. Symbolic representations can
provide fulfilment, for example when breaking 534down into 53·53·53·53and from there towards
5=4+1,...2=1+1 (Husserl, 1901,VI, §§17f.), yet they would not be illustrations. But to simplify the
terminology, I follow what is intended in Kinkaid’s usage: intuitive illustration need not provide imagery.
11 One might worry about intuitive illustration for sentences whose evaluation ‘take us back’ into the world
from which we are imagining. “I am not actually imagining anything” could be a case in point. But this
seems to depend on too many assumptions, in particular about the semantics for “actually”. And we could
still imagine someone in a different world to utter this sentence truly: although I would be falsifying this
sentence by intuitively illustrating it, I can imagine a state of affairs in which someone would utter it truly.
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the possibility to have evidence that the door is green (♦Ep, with Eas a propositional
operator for ‘It is evident, that’). Since the evident judgement that pimplies the truth of
p,itfollowsthatpis possible (♦Ep ♦p). Propositional blindspots, however, show
that this cannot be the full story. There are propositions we understand but that cannot
be posited in an evident act: ♦(p∧¬Ep)but not ♦E(p∧¬Ep). Thus, blindspots
illustrate that symbols can be combined into meaningful empty representations that
we could not have arrived at by positing a state of affairs and then neutralizing that
commitment.
Kinkaid interprets Corr-Sem along the lines of Dummett’s manifestation require-
ment. Its role is to ensure that we can demonstrate our understanding of the concepts we
use by a manifestation of their meaning (Kinkaid, 2022, p. 1022). Intuitive illustration
is a less demanding manifestation than evidential fulfilment. This avoids counterexam-
ples from blindspot propositions for evidence, but it also drops the correlation between
truth and possible fulfilment (together with any claim about the scope of knowledge).
In short, Kinkaid’s revision of the semantic correlation does not save Corr-Al from
paradox. But could the proposal offer a restriction that saves a version of Corr-Al?
Kinkaid already states that he intends to “restrict ideal verificationism to acts to which
the expression is accessible” (Kinkaid, 2022, p. 1019), where ideal verificationism
is a label for Husserl’s semantic and alethic correlations. Although this phenomeno-
logical “restriction strategy” (Kinkaid, 2022, pp. 1012, 1018) does not restrict the
domain of propositions over which Corr-Sem quantifies, Kinkaid has already identi-
fied blindspots as a class of problematic propositions. One could think that this entails
a restriction strategy for Corr-Al: all true propositions have a possibility of evident
fulfilment, except for blindspot propositions.
On considering the definition of a blindspot, however, this collapses into triviality.
A proposition pis a blindspot with respect to an attitude A if p is consistent but
inaccessible to A (Kinkaid, 2022, p. 1020). Sorensen writes a little more, stating that a
proposition pis a knowledge blindspot for Sat tif and only if pis consistent, true, the
subject S is absolutely epistemically thorough at time t, and yet p cannot be known by
subject S at time t (Sorensen, 1988, p. 52f.). Let us consider the blindspots that hold for
all subjects at all times. If we exclude propositional blindspots from the correlation
between truth and evident fulfilment (Ep), this would exclude all propositions for
which ¬♦Ep. But as a restriction of the left-right direction of alethic correlationism,
this yields:
∀p:p→♦Ep except when ¬♦Ep
which is not more informative than ‘I can lift every weight, except for the weights that
I cannot lift’—nothing to boast about. Maybe this could be refined by distinguishing
the modalities involved. In Sorensen’s account, the notion of possibility in question is
determined by ‘background constraints’ that can include the laws of logic and physics
or principles of psychology. But neither Kinkaid nor Sorensen get more specific than
this, and a puzzle would remain in any case: if alethic correlationism characterizes an
essential link between evidence and truth, why would this characterization not extend
to true blindspot propositions? Fortunately, there is also a different restriction strategy
for Corr-Al which grows naturally out of Husserl’s semantics.
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5 A phenomenological restriction strategy and an inductive
characterization of propositional truth
Husserl often focuses his investigation on the study of the ‘basic kinds’ of a domain. To
elucidate the meaning of complex scientific statements, we need to follow a ‘guideline’
(Leitfaden) of basic objects (Husserl, 1996, p. 329; Husserl, 2003a, p. 222). The
parallelism between empty acts and the possibility of fulfilment is a case in point.
Husserl first affirms the parallel between symbolic representation and fulfilment for
the symbolic connectives, which are ‘primitive types’ of categorial intuition (Husserl,
1901, VI, §63, p. 721). Once we have established such primitive types, they can be
applied to arbitrary empty representations, such as ‘there is a dog’ and ‘there is no
dog’. Husserl here separates grammatical correctness from possibility in terms of
possible fulfilment. Grammatically correct but unfulfillable representations, like ‘A
and not A’ are ‘inauthentic’ (uneigentlich) meanings. This should concede that we can
distinguish between different kinds of contradictions (like Marty argued), so possible
fulfilment is not really what determines meaningfulness (Husserl, 1901, I, §15, p. 61).
But Husserl considers the fulfillable meanings to be those that are not contradictory;
which for him means that they describe possible states of affairs. This requires that the
possibility of fulfilment is not only important for justifying that a connective like ‘and’
can connect arbitrary propositions, but also that there will be corresponding complex
fulfilments wherever that combination is not contradictory. And this is what we find
in Husserl’s ‘ideal of a logically adequate [angemessenen] language’, for which the
contradiction-free composition of empty meanings follows exactly the rules by which
fulfilling presentations can be combined (Husserl, 2001a, VI, §63, p. 311, Husserl,
1901, VI, §63, p. 721).
Even before considering the Church–Fitch paradox, there are reasons to wonder
if this more ambitious parallel should really obtain. Simple examples involve quan-
tification over finite domains. Trapped in a hut during a hail storm, one may wonder
whether all windows are still intact (Hopp, 2018, pp. 636f.). But no matter how fast
one moves around, checking one window always precludes checking another. While
empty representations about each individual window can be fulfilled, these fulfilments
are not compossible. Nevertheless, there is no difficulty in symbolically representing
all of this in the single sentence ‘all the windows are unbroken’, and of course this
representation is not contradictory. While the hail storm case leaves open whether
some kind of idealization or a fanciful mirror setup would allow for a single intu-
ition to fulfil the empty intention, the Church–Fitch paradox takes this objection to an
extreme where fulfilment is clearly impossible.
So there is reason to doubt the strict parallelism between the composition of empty
meanings and intuitive fulfilment. But this parallelism is not always expressed so
rigidly. In the 1905 lecture on meaning, Husserl allows en passant that a symbolic act
may have its intuitive counterpart not in a united act, but a bundle of acts:
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[Es] besteht die Eigentümlichkeit, dass zu jedem
symbolischen Akt ein ihm entsprechender oder
ein Bündel ihm entsprechender intuitiver Akte
aufzuweisen ist derart, dass beiderseits dieselbe
Gegenständlichkeit, und in völlig gleichem Sinn
vorstellig ist. (Husserl, 2002b, p. 102)
[There is] the peculiarity, that for each symbolic
act, we can present [aufweisen] a corresponding
act or a bundle of corresponding acts, such that in
both cases, the same object is represented, and it is
represented in a completely equal manner. (trans-
lated by the author)
Such ‘bundle parallelism’ suggests that not every symbolic representation can be
fulfilled in a single act; thus, there might be incompossible presentations of an emp-
tily represented state of affairs. And in other contexts, phenomenologists take this for
granted. In the phenomenology of perception, it is perhaps the central idea that the
same intention (‘the house is red all over’) is only fulfilled in adumbrations, meaning
that the fulfilment of one side of the house precludes the fulfilment of another. What the
Church–Fitch paradox reveals is that there can be a structure of ‘logical adumbration’:
rather than the perspectival nature of perception, it is the logical structure of a propo-
sition that precludes its fulfilment in one blow. What I am proposing here is such a
‘bundle parallelism’ between propositions and their fulfilment that takes these logical
adumbrations into account. This makes it easier to account for the possible fulfilment
of logically complex statements (cf. Tugendhat, 1970, p. 135f.). For a house with six
windows, the sentence ‘all windows are unbroken’ would not need to be fulfilled in
a single act with content p1∧ ···∧ p6, but in a bundle of acts that have the contents
{p1,..., p6}. The parallelism between empty and fulfilling acts is then not understood
as a claim about all symbolic representations, but as a thesis about the elements that
can be combined. This leads to a different interpretation of the alethic correlation.
(I) A basic proposition pis true if and only if it is a real possibility that an act
evidently fulfils p.
Regarding the Church–Fitch paradox, this constitutes a phenomenological restric-
tion strategy, in the sense that it restricts the scope of “all” in the correlation between
truth and the real possibility of fulfilment. The truth-conditions for non-basic propo-
sitions need to be supplied by further principles; but these are anticipated in Husserl’s
lectures on logic. Under the label propositional mathesis, Husserl develops a theory
of all truths that are based in the concept of proposition.12 Like algebra contains rules
for the transformation of mathematical statements, the propositional mathesis spells
out the rules by which propositions can be combined into new propositions. These
compositional principles can also spell out how the truth of complex propositions
depends on truths that are related to possible evidence. Nowadays one might say that
they define truth-functionally complex propositions. Husserl speaks of a ‘functional
form’ that does not change the meaning of the propositions on which it operates, but
‘functionally enriches them’ (Husserl, 2003a, p. 208). The liberal reformulations here
follow the lectures on logic and the theory of judgement (Husserl, 2001b, p. 239f.; see
also Husserl, 1896, §§36ff.; Husserl, 2002b, p. 152ff.).
12 ‘Die propositionale Mathesis will die allgemeinen Wahrheiten systematisch entwickeln, die im Begriff
des Satzes überhaupt gründen’ (Husserl, 2001b, p. 239). Husserl speaks here of ‘sentences’ in Bolzano’s
sense. This is a notion of sentence where a successful translation from French to German does not affect
the sentence that is expressed (Husserl, 2001b, p. 59). Since ‘sentence’ is nowadays rather understood as a
symbolic expression type, I speak of ‘propositions’.
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(II) A conjunction p∧qis true if and only if pand qare true.13
(III) A disjunction p∨qis true if and only if at least one of pand qis true.14
(IV) A hypothetical p→qis true exactly if p, then q.15
(V) A negation ¬pis true if and only if pis not true.16
(VI) An existential quantification ∃Dx:p(x)is true if and only if the domain Dof the
function p(x)ranges over at least one value of xthat yields a true proposition.17
(VII) A universal quantification ∀Dx:p(x)is true if and only if the domain Dof the
function p(x)ranges only over values of xthat yield true propositions.18
By adding these additional clauses, Corr-Al can be restricted to a class of basic
propositions, while leaving the truth of complex propositions well-defined. In particu-
lar, this means that p∧¬Kpis not in the class of basic propositions, and therefore need
not be fulfillable, and therefore step 4 in the Church–Fitch argument fails. The truth
of ‘all windows are unbroken’, and Tugendhat’s worry about sentences like ‘there is
no devil’ are also taken care of (1970, p. 135f.). But the new distinction between basic
and non-basic propositions deserves clarification. Basicness is an ambiguous concept,
and we can distinguish syntactic, semantic, and epistemic notions of basicness that
need not coincide. Syntactic basicness is based in the structure of the symbols that
make up our sentences. Semantic basicness would need to identify meanings by which
more complex meanings can be expressed. Epistemically basic propositions could be
understood as those that are immediately justified or those that serve the justification
of epistemically non-basic propositions. Which kind of basicness is operative in the
phenomenological restriction strategy?
Occasionally, Husserl marks out simple sentences as those that have only non-
sentential parts (see Husserl, 2001b, p. 200; Husserl, 2003a, pp. 200 and 101) “If
God exists, the sinners will be punished” is a composite sentence, because its part
‘the sinners will be punished’ by itself is a sentence. Despite Husserl’s general use
of ‘Satz’ to refer to propositions (see footnote 12), this seems to express a form of
syntactic basicness. So one may wonder whether non-basic propositions are exactly
those that are expressed in syntactically non-basic sentences.
But the relation between the structure of the expressing symbols and the expressed
propositions is more complex. Take the sentence ‘Carl is a grandparent’. This could
13 “For an arbitrary sentence A and an arbitrary sentence B, AB is a third sentence. It uniformly says: both
is valid.”( Husserl 2001b, 239. All translations by the author).
14 “Two arbitrary sentences determine a third in the form ‘A or B’, that means ‘one of both is valid’.”
(Husserl, 2001b, p. 239).
15 “If the sentence A is valid, so the sentence B.” Husserl also shows the equivalence of p→qand
¬(p∧¬q)(Husserl, 2001b, p. 244, corollary 25).
16 “We express the negation of a sentence with the index 0. Thus A0(!)means: A is not true.” Negation is
understood classically, with ¬¬p↔p(Husserl, 2001b, p. 243, axiom X).
17 “
xy
f:There are variable systems, xy, where … is fulfilled.” (Husserl, 2001b, p. 239).
18 What Husserl says about universal quantification is based on an axiom about permissible variable
substitutions into general sentences. “If a general sentence
x1...xn
f(x1...xn)is valid with regard to the
terms x1...xn, any sentence is valid that we obtain from substituting any or all variables x1...xnwith valid
functions of new variables χ1...χ
0, and that new sentence is generally valid with respect to the variables
χ1...χ
0” (Husserl, 2001b, p. 240, axiom α). I have attempted a simpler formulation for the semantics of
universal quantification.
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211 Page 18 of 25 Synthese (2024) 203 :211
be understood to express either a simple proposition, or a hidden complex proposition,
like ‘Carl is a parent and one person, to whom Carl is a parent, is a parent’. Arguably, we
could understand grandparenthood entirely in terms of parenthood. But the symbols
that form the sentence ‘Carl is a grandparent’ reveal no such logical structure. And
a simple syntactic form can be introduced at will. If we call the grandparent of a
cousin who is not your own grandparent your ‘grousin’, then ‘Carl is a grousin’ is
syntactically simple. Therefore, syntactic simplicity can serve at best as a necessary
condition for propositional basicness. Nevertheless, similar restriction strategies have
been classified as ‘syntactic’ responses to the paradox (Brogaard and Salerno, 2019).
This description is natural within a propositional calculus, where the basic propositions
are represented by a single propositional variable (p, q, …), and non-basic propositions
can contain multiple propositional variables (p∧q,...). But such a formal calculus
has already decided which propositions are basic and which are not.19
Since the syntactic form of the expressing sentence is insufficient to determine
whether a proposition is basic, we have to look elsewhere. Epistemological basicness
does not seem to fit either, as there are complex propositions that are easier to find out
than their constituents. It is easier to know with evidence that ‘either I carry the virus,
or the test has malfunctioned’ than to find out about either of these disjuncts.
What remains is a notion of propositional basicness that depends on the meanings
involved. Language evolves, and new terms can be introduced on the basis of old ones,
and the traces of such complication can disappear. An apparently basic proposition
can reveal hidden complexity, once we inquire into the origin of its meaning. Such
inquiries, which have been discussed under the labels of genetic and generative phe-
nomenology (Steinbock, 1995), do not aim to establish psychological facts about a
subject or a community. They rather constitute a re-living of the creation of meanings
that have been bequeathed to a community, and on which formal logic and empiri-
cal science are built (Husserl, 1939, §11, p. 47f.). That re-living can either result in
criticism or the taking of responsibility for the inherited meanings, which otherwise
constitute an ‘anonymous’ presupposition (Landgrebe, 1982, p. 76). The restricted
alethic correlation holds that all propositions can either be intuitively fulfilled or they
are traceable to intuitively fulfillable meanings. But since the notion of propositional
basicness cannot be applied mechanically, for example by specifying a function on
the representing symbols, it should be expected that there will be disputable cases.
These disputes will concern what we consider evident fulfilment and how new terms
are introduced, in particular through scientific theories. I do not think that a correla-
tion between truth and basic propositions thereby puts theoretical language into an
empiricist straitjacket, for example by taking basic propositions to be assertions about
Carnapian ‘Ur-experiences’ (Carnap, 1928), but this is to be discussed elsewhere.
Restricting Corr-Al to basic propositions makes it less demanding about knowabil-
ity; any issues with the semantics for scientific terms would have arisen equally for
unrestricted correlationism.
Instead of turning to such general issues, I want to use the rest of this paper to
discuss specific objections about this particular way of addressing the Church–Fitch
19 And even here, it seems that we can just define r=p∨qto have a non-basic proposition which is
represented by a single propositional variable.
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Synthese (2024) 203 :211 Page 19 of 25 211
paradox. In the context of his intuitionist project, Dummett (2001) originally defended
a similar restriction strategy, before simply accepting the argument’s penultimate step
(∀p:p→¬¬Kp) as the desired intuitionist characterization of truth (Dummett,
2007). In the period that Dummett endorsed this restriction strategy, objections were
raised that need to be considered here as well.
Dummett’s proposal is originally presented on merely two pages, which invites the
suspicion that it constitutes an ad hoc response to the paradox, rather than an account
that is motivated in general principles. Husserl on the other hand outlined his propo-
sitional mathesis before the paradox was known to him or indeed anyone else. The
phenomenological descriptions consistently prioritize basic cases of experience, and
a restriction of Corr-Al to basic propositions also addresses issues with proposi-
tions that are not related to the paradox, like ‘all windows are unbroken’. Restricting
Corr-Al to a class of basic propositions is therefore well motivated in Husserl’s
semantics, and not just a targeted response to the Church–Fitch paradox.
More substantial objections begin by asking whether “it is a real possibility that
an act evidently fulfils p” is itself a basic proposition. In formal shorthand, we can
ask how the possibility operators ♦R,♦Iand an operator Efor evident fulfilment
interact with propositions. Unlike the other logical symbols we considered, the truth
of ♦Ip,♦Rpand Ep cannot be expressed as a function of the truth of p. Adding a
supplementary clause in the style of (II)–(VII) therefore would not seem to help. But
Husserl has written about different methods for finding truths about possibility. The
use of imaginative illustration, as in Kinkaid’s revised principle, is one of them. One
can also begin with the essential laws that ground necessary truths, and then consider
anything that is not in contradiction with these laws to be possible (Husserl, 1996, §43,
p. 218f.). There are different ways to spell this out, but one may end up articulating
a way in which it could become evident that ♦Ip. This could then be used to give an
account of the truth of ♦Ip, for example:
(VIII♦?) A statement about ideal possibility ♦Ipfor a basic proposition pis true if it
is a real possibility (♦R) that pis completely intuitively illustrated.
Formally, (VIII♦?) looks like an instance of (I). But it might be preferable to treat it as a
supplementary clause, since considering ♦Ipas a basic proposition leads to recursion
for propositions like ♦I♦Ip,♦I♦I♦Ip, etc. I also becomes apparent here that the
use of imagination and eidetic laws will only help us to learn about possibilities, not
contingent facts. What more can be said about real possibilities remains a different,
and in my view, still open question.
We can treat Ep analogously to ♦Ip, by introducing a supplementary clause about
acts that make the truth of Ep evident. 20
(IXE?) A statement about evident fulfilment Ep is true if and only if it is a real possi-
bility that an act of reflection or empathy evidently fulfils that Ep.
Formally, this would mean that Ep ↔♦RE(Ep). This might appear like a strong
internalist commitment, but this appearance can be lessened, if one is so inclined, by
20 When formulating the Church–Fitch paradox for Einstead of K,Ep would have to be read as ‘It is
evidently judged by someone, at some time, that p’, thus with an implicit quantification over subjects and
times. A formula Ep without quantifiers would therefore have to bind variables by specifying a subject and
a time.
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211 Page 20 of 25 Synthese (2024) 203 :211
distinguishing the truth-conditions for evidence from the truth-conditions for believing
to have evidence. Take the evident judgement for the proposition ‘There is an apple in
front of me’ to be based on an act of perception. Whenever this apple-perception occurs,
we could reflect on what we are visually experiencing and judge with evident fulfilment
that we are judging with evident fulfilment. But this is compatible with there being
other scenarios, where we only believe that our judgement is evidently fulfilled. All
that we need is that, in the good cases, a reflection on that act of judgement is possible.
That reflection, however, would be a separate judgement about one’s own state of
evidence. And there is still room to consider what counts as evident fulfilment beyond
acts of reflection. Acts of empathy, for example, could serve as evident fulfilment of
sentences about evident judgment, even for creatures who lack conceptual or reflexive
capacities. There remain open questions, but these arise equally for the unrestricted
version of Corr-Al.
More specifically relevant is the suggestion by Brogaard and Salerno (2002) that
a restriction to basic propositions leads to new paradoxes. Their ‘revenge paradox’
depends on an inference ♦♦E(Ep)♦E(Ep). In terms of contemporary modal
logic, such an inference principle holds if the accessibility relation between possible
worlds is transitive. It is not trivial to translate such a property from possible-world
semantics into the phenomenological way of thinking about possibilities. But ‘intuitive
illustration’ as discussed in Sect. 4seems to make good sense of it. If I read about
Eddie’s childhood and how he liked to read stories about being a knight in shining
armour, it seems that I have inuitively illustrated a possibility in which somebody is
intuitively illustrating a possibility. The intuitive illustration of this possibility seems to
require filling in Eddie’s intuitive illustrations as well. Therefore, intuitive illustration
is transitive: I could as well switch to imagine what Eddie is imagining; whereas I
am at a loss when I try to illustrate ‘Eddie imagined something that nobody could
imagine’. This suggests that ♦I♦Ip♦Ip. What is possible in a possible world
should also be possible in the actual world.
But only ideal possibilities are transitive in this sense—we have already seen that
the real possibilities of evidence work differently. The possible worlds where we know
more are subtly or not-so-subtly different from the actual world. Think of a pupil in
a chemistry class. The instruction is to measure the concentration of ions in a liquid,
and to determine if the saline solution has been saturated. The pupil knows that his
solution is saturated when any added salt settles on the ground, rather than dissolving.
As it happens, the solution is not saturated. It is a real possibility to trickle salt into
the liquid and watch it disappear. At the same time, the student could also measure
the saline concentration and read a value ρaoff the display: so it is a real possibility
to determine that the density of solved particles in the solution is ρa.Now,given
that it makes sense at all to talk about the real possibilities that obtain “within” or
“from” other real possibilities, then the student who just watched salt dissolve can
also measure the saline concentration, with result ρb. This does not mean that the
actual student has a real possibility of measuring the concentration ρb—after all, the
contingently unknown truth about the particle density was ρa.
‘Possible’ is transitive for ideal possibilities: what can be successfully imagined
is not affected by where it is imagined from. Real possibilities are more fickle. They
reflect how the contingent facts about the actual world select from the totality of
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Synthese (2024) 203 :211 Page 21 of 25 211
ideal possibilities, and this selection can change with stepping from the actual world
to a really possible world. So although the case of ideal possibilities might make it
tempting to treat all possibility operators as transitive, this does not apply to the kind of
possibility we need for correlating truth with evidence. Therefore, the revenge paradox
does not arise.
Rosenkranz (2004) argues more generally that Brogaard and Salerno (2002)have
demonstrated the incompatibility of two inference rules that they assumed in addition:
♦-Factivity ♦REp p
Closure ♦REp ∧(Ep →Eq)♦REq
We are looking for a correlation between truth and the possibility of evident judge-
ment, so we also want the real possibility of evidence to imply the truth of its content.
This is just ♦-Factivity, which should therefore be endorsed. The principle itself
might require a form of restriction, since finding things out usually changes the world
and it is not clear that the factivity of ♦REis without problems (Schlöder, 2021;
Heylen, 2022, p. 2251f.). But this is only to say that phenomenologists who want to
endorse a correlation between truth and evidence have good reason to find a defensi-
ble version of ♦-Factivity, and this will greatly depend on the further theory of real
possibilities of evidence.
Closure resembles a valid principle that relates possibilities and necessary condi-
tionals: ♦Ip∧(p→q)♦Iq, but like transitivity, Closure does not work for real
possibility. Take a fresh lottery scratch card, which has not been scratched yet. You
know that, once it has become evident that the ticket is a winner, it has also become
evident that the ticket has been scratched, because that is the only way anyone could
find out that a ticket is a winner. This conditional is a ‘real necessity’: there is no real
possibility (¬♦R¬) for seeing that a ticket is a winning ticket without seeing that it
has been scratched. Now looking at the unscratched ticket in front of you, a few rubs
with a coin are all that stands in the way of seeing that the ticket is a winner. It is
therefore a real possibility to know that the ticket is a winner. Given the real necessity
of the mentioned conditional, Closure would allow to infer that it is a real possibility
to see that the ticket has been scratched. But we have already endorsed factivity: real
possibilities of evidence obtain only for finding out truths—and the reason we do not
know that we have a winner is precisely because the ticket not been scratched yet.21
Insofar a correlation between truth and possible evidence is a reason to hold onto
♦-Factivity,Closure becomes suspicious. And without Closure, there remains
little room where new paradoxes could arise.
21 Closure may be more plausible if the required necessity is conceptual or logical necessity. But it seems
that the ‘matter of fact’ that evidence of winning is evidence of scratching, can easily be turned into such
a conceptual necessity (adapted from Rosenkranz, 2004, p. 71). For p: the ticket is a winnner and q: the
ticket is scratched, it can be true as a matter of fact that p→q. Then, assuming there is a real possibility
of finding out about this matter-of-fact implication and p,wehave♦RE(p∧(Ep →Eq)). But since E,
as a special case of knowledge, is factive and distributes over conjunction, we have a conceptual necessity:
(E(p∧(Ep →Eq)) →Eq).Closure then entails again that it is a real possibility to see that the card
is scratched—which does not mix with ♦-Factivity.
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211 Page 22 of 25 Synthese (2024) 203 :211
6 Conclusion
Common and textually supported interpretations of Husserl’s correlationism indeed
lead to a knowability principle which generates the Church–Fitch paradox. Kinkaid
avoids this by considering only non-positing possibilities of intuitive illustration. Such
a revised principle is intended to save a sense in which our grasp of consistent proposi-
tions can manifest experientially; but as such it only concerns fulfilment and possibility,
not the relationship between truth and evidence. I proposed a restriction strategy
which grows naturally out of Husserl’s inductive characterization of propositions.
This response can be formulated in terms of possibilities of evidence, which allows to
maintain an alethic correlation. Objections that were raised for a structurally similar
proposal by Dummett have been addressed or do not apply. Alleged revenge para-
doxes rely on transitivity and closure principles that phenomenologists have reason to
do without. It remains ambitious to correlate truth and possible evidence, even after a
restriction to basic propositions; but it is no longer paradoxical.
Acknowledgements Research for this article was funded by KU Leuven through the post-doctoral mandate
3H220352, Phenomenology and the Scientific Image of the World, and by King’s College London through
PhD funding from the faculty of arts and humanities. The manuscript has greatly benefited from a workshop
on the concept and scope of knowability, organized by Jan Heylen at KU Leuven in June 2023. Discussions
with Jan Heylen were invaluable in developing this paper, as was the support of Mark Textor and Julia
Jansen. The article also greatly benefited from the reports of two anonymous reviewers, and I am grateful
for discussions with, among others, Emanuela Carta, Kristine Grigoryan, Carlo Nicolai, David Papineau,
Francesco Praolini, Filippos Stamatiou, Odysseus Stone, and Dan Zahavi.
Declarations
Competing interests The author has no competing interests.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence,
and indicate if changes were made. The images or other third party material in this article are included
in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If
material is not included in the article’s Creative Commons licence and your intended use is not permitted
by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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