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αν

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THE EPISTEMIC INJUSTICE OF 
EX CONTRADICTIONE QUODLIBET

SHERRY TSENG

The principle of ex contradictione quodlibete stipulates that from contradiction, 
all propositions follow. From this, all explode into triviality; hence, the aversion 

towards contradiction. However, our social selves are mired with inconsistency and 
contradictions and identities built on a spectrum. The assumption of triviality from 
contradiction in formal logic makes it such that the contradictions found within 
natural language on our social identities equally trivializes those contradictory 
aspects, and thereby, inflicts an epistemic injustice. 

I argue that if natural language is to be formalized, then there exists a moral imperative 
to defer to paraconsistent logic, specifically in cases of linguistic inconsistency relevant 
to aspects of social identity. The conditionality of the claim proves important: I do not 
defend the assertion that natural language can be formalized—that is a philosophical 
and technical anthology in its own right. Rather, I would like to undertake the 
normative project of highlighting what I take to be a necessary condition for the 
formalization of natural language. The argument is as follows: the rejection of 
inconsistency denies the expression of social experiences lying outside the binary. It 
presupposes a singularity of social experience, and in assuming this, inflicts epistemic 
injustice. To a further extent, this jeopardizes social justice and political freedom via 
its hindrance to the dialogical basis of democracy. In its acceptance of inconsistency 
without triviality, we ought to accept paraconsistent logic, understood under a larger 
framework of logical pluralism, as a strong antidote to the harms outlined above. 



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The urgency of this demand emerges from the significant overlap between formal 
and Boolean logic with the implications of the former largely carrying over to the 
latter. The premises of big data and artificial intelligence, grounded in Boolean logic, 
have their linguistics subsumed under natural language processing (and thereby 
formal logic). This trend persists even as developments in the field have shifted from 
rule-based algorithms to statistical models and vector representations. Through its 
adoption of formal logic’s views on inconsistency, the future of technology has then 
rendered itself vulnerable to these aforementioned harms, and by way of algorithmic 
learning, will only experience its problems perpetuated and compounded further. 

The essay begins in §I with an introduction of epistemic injustice and its associated 
harms, of which I specifically focus on illocutionary silencing. With these conceptual 
resources, §II demonstrates how the assumption of triviality as a consequence of 
contradiction inflicts epistemic injustice in the form of illocutionary silencing. §III 
continues by offering a positive solution in the form of paraconsistent logic, and 
though accounts of this form of logic are wildly disparate—tied only by the common 
thread of non-explosion—I believe that this one thread is a moral commitment 
necessary to make. 

§I Epistemic Injustice

Introduced by Miranda Fricker (2007), epistemic injustice is an injustice arising from 
dissimilarities in individual and collective epistemic resources. Fricker then proceeds 
to divide this into two camps: testimonial and hermeneutical injustice. 

1. Testimonial Injustice: “wherein a speaker receives an unfair deficit or credibility 
from a hearer owing to prejudice on the hearer’s part.” (Fricker 2007, 9)

Patricia Williams, a professor at Columbia University Law School, demonstrates a 
paradigmatic case of this in her book The Alchemy of Right and Race, wherein she 
recounts a personal, anti-black, racist experience.  Yet, upon retelling this event, she 
would often disbelieve herself—a consequence perhaps in no small part attributable to 
the prejudicial stereotypes of African Americans as “liars” or “paranoid,” consequently 
leading Fricker to discern that she has suffered an instance of testimonial injustice. 

2. Hermeneutical Injustice: “wherein someone has a significant area of their social 
experience obscured from understanding owing to prejudicial flaws in shared 
resources for social interpretation.” (Fricker 2007, 148)

Sexual harassment is a common example of this second form of epistemic injustice. 
Prior to its conceptualization, many of those victimized lacked the epistemic resources 



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to articulate their experiences, which were then previously rendered unintelligible. 
Instead, their discomfort would be ‘interpreted’ as overly prudish or lacking in sense 
of humor, henceforth exemplifying a hermeneutical injustice. 

Of note here is the distinction between hermeneutical and testimonial injustice 
in the collectivity of epistemology. In the hermeneutical form, the injustice arises 
from a deficit in the shared pool of knowledge, whereas in testimonial form, the 
injustice may be rooted in a singular repository of it. In the example given for the 
hermeneutical, society lacks the conceptual resource of sexual harassment itself—an 
absence that points to a structural and collective inequity in epistemology. Conversely, 
in the case of testimonial injustice, Williams’s example does not causally trace (at 
least necessarily) to a flaw in a shared resource, but instead, may be attributable to 
one individual’s racist beliefs and attitudes. And still, the two forms are nonetheless 
deeply intertwined: the hermeneutical may lead to the testimonial and the testimonial 
may be a manifestation of the hermeneutical. What follows from these injustices are 
harms of both an epistemic and pragmatic nature. The excerpt below focuses on one 
harm of illocutionary silencing, as proffered by Rae Langston: 

“If you are powerful, you sometimes have the ability to silence the speech of the powerless. 
One way might be to stop the powerless from speaking at all. Gag them, threaten them, 
condemn them to solitary confinement. But there is another, less dramatic but equally 
effective way. Let them speak. Let them say whatever they like to whomever they like, but 
stop that speech from counting as an action…” (Langton 1993, 299)

Illocutionary silencing is the refusal to admit a proposition’s illocutionary force, 
or that which is constituted by the words themselves.1 It nullifies the performative 
force of the words, disallowing the utterances from passing on their intended 
meaning, thus following from epistemic injustice’s emerging inequities. In the case 
of Williams, her attempt to describe this racist encounter was negated—her words 
stripped of their force in invoking a case of discrimination. Similarly, the inability to 
articulate a grammar for sexual harassment may count as a form of silencing insofar 
its conceptual deficit precludes the description of the experience. Furthermore, the 
reactions to circumlocutionary attempts to do so effectively impedes the victims’ 
ability to promulgate those experiences, and resultingly, commits the injustice 
(whether testimonial or hermeneutical) all the same.    

To conclude, epistemic injustice is the sort of injustice that emerges from differences 
in epistemic stature. For the remainder of this paper, I use this as the pedagogical 
framework to make sense of the injustice enacted by classical formal logic and its 
insistence on consistency. 

1 For more on this, see Austin’s How to Do Things With Words (1962)



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§II Ex Contradictione Quodlibet’s Epistemic Injustice 

In a keynote lecture delivered at the 8th Annual Philadelphia Trans-Health 
Conference in 2009, writer and trans-bi activist Julia Serano stated, “[t]here is simply 
no more effective way of hurting me than trans-invalidating me.” In what follows, 
I argue that the consequence of triviality from contradiction clears the path to such 
harms of invalidation through its enactment of epistemic injustice. 

But first, a brief note on the specifics of ex contradictione quodlibet. While the path 
from contradiction to triviality may differ, one such form famously derived by David 
Lewis takes the following structure: 

“Suppose  P and not-P

Then  P  by Simplification,

whence   P or Q  by Addition,

  not-P  by Simplification again,

and finally Q  by Disjunctive Syllogism.”

According to this argument, any statement Q follows from the premise of P and not 
P. Some may object to this proof in that entailment needs to do more work than 
simply truth-preservation: it also needs to retain some meaningful connection or 
relevance between the two propositional statements. Regardless of how one argues 
ex contradictione quodlibet, the central point remains: contradiction explodes into 
triviality. 

It is important to take note of what the definition and consequences of what it 
means to be trivial, the first of which being that triviality could be taken as entailing 
everything. This, however, draws from the principle of ex contradiction quodlibet, 
proving to be circular reasoning at best, and because of this, cannot be taken freely 
as the definition. Second, triviality is that which is uninteresting or insignificant. 
Essential to this definition is the assumed goal of logic and epistemology to uncover 
truths, or, at the very least, proximate truths about the world. There are certain 
propositions more interesting than others and the rejection of contradiction from ex 
contradictione quodlibet implies the undesirability of triviality. For the remainder of 
this paper, I adopt this latter definition. 



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Dianoia: The Undergraduate Philosophy Journal of Boston College

Having adopted this understanding of triviality as ‘that which is uninteresting or 
insignificant,’ it is now possible to move on to the discussion of inconsistency’s 
intertwinement with epistemic injustice—beginning with an example of gender 
queerness. Consider the following statement: 

(A) I am a girl. 

(B) I am not a girl. 

Let’s say that Alex utters these two statements in response to a question asking them 
to identify their gender. Alex identifies as genderqueer.2 To them, both (A) and (B) 
are true.3 Given how they identify, Alex is both a girl and not a girl.  

By formal logic’s adoption of ex contradictione quodlibet, however, Alex’s utterances 
make it such that each and every statement can follow. They are all trivial, and thus, 
devoid of importance. From this, epistemic injustice then enters into the picture. 
With their speech now made trivial, Alex’s credibility as a knower and their ability 
to make significant contributions to the conversation on genderqueerness is cast out, 
thereby constituting a case of testimonial injustice. It is also arguable that Alex also 
experiences hermeneutical injustice since the mutually exclusive gender binary does 
not provide the conceptual resource to capture Alex’s experience of gender, and on 
this count, their social experiences are effectively obscured. 

The path to illocutionary silencing is not far off. In this case, Alex’s illocutionary act is 
the very proclamation of their gender identity as a girl and not a girl. In keeping with 
ex contradictione quodlibet and its aversion towards triviality, only one of these two 
statements can be true, which of course has the negative consequence of disallowing 
their entire illocutionary force. By having their proclamation fall upon deaf ears, 
Alex experiences both testimonial and hermeneutical injustice, and thus, becomes 
silenced. 

Despite however much the act of silencing in itself is negative, the scope of these 
harms extends even further with repercussions for both social justice and political 
freedom. Concerning social justice, when one silences the speech of the powerless, 
they favor a specific form of discourse—that of the powerful. This perpetuates 
the further marginalization of the powerless through the determination of what 
sort of gender proves significant, which nullifies Alex’s own words as unimportant 
given their contradiction. On this account, epistemic injustice is a manifestation 

2 This is understood in the sense that their gender identities are maintained by some combination of masculinity 
and femininity, or neither.

3 For the remainder of this paper, I will assume Alex identifies themselves using the pronouns “they/them/theirs.” 
It may change, of course, and this is by no means an assumption that all genderqueer people need use such 
pronouns.



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of social injustice stemming from the rendering of the powerless as the speechless.  
Furthermore, taken as a collective, the experiences of all those who identify as 
genderqueer are similarly silenced, paving the way for injustice to affect an entire 
social class of people like Alex. 

Concerning political freedom, Fricker makes this a point in referencing Phillip Petit’s 
contestability criterion. He states that a functioning deliberative democracy needs 
to meet the three conditions for contestation, which include: a “potential basis for 
contestation,” a “channel or void available by which decisions may be contested,” 
and a “suitable forum in existence for hearing contestations.”4 Being illocutionary 
silenced, however, disables speakers from contestation. Because Alex’s identity was 
not taken as it was intended in meaning, the immediate jump to the consequence 
of triviality as stipulated by ex contradictione quodlibet strips Alex of their ability 
to contest this conclusion. From this, they are excluded from securing a certain 
threshold of political freedom, which Petit stipulates as necessary for a deliberative 
democracy. 

What does this mean for technology?

Returning to my original motivation, the basis of this paper resides in the substantial 
overlap between formal logic and the logic underlying computer science and artificial 
intelligence. It is this overlap and the permeation of technology into nearly every 
crevice of our lives that lends an urgency to my demand to attempt a rectification, 
or at the very least, acknowledgment of the inflicted epistemic injustice of ex 
contradictione quodlibet. In particular, by accepting formal logic as prior to other 
epistemic sources, as technology so often does, its stance on contradiction—that 
triviality necessarily follows—then holds the power to dictate our understanding of 
the world. By taking the principle as an authority on truth, the ontological may end 
up following the logical. Our social constructions of the world would be determined 
by a framework strictly adhering to a dichotomous binary, such that it creates a world 
where genderqueerness would not exist a priori. 

In taking into account how the field makes sense of this, it is important to note that 
recent developments in the field have increasingly shifted from rule-based algorithms 
to statistical models; in particular, vector semantics have exploded in popularity 
in building computational models of language.5 This largely consists in word 
association: for example, the definition of the word “bank” is determined depending 
upon whether the sentence contains words alluding to the likes of “money” or “river.” 
Following this, that the bulk of the two formalized propositions of (A) and (B) are 

4 Pettit, 186-187. 
5 For a brief overview on how vector semantics works, see the following: https://medium.com/@ram.analytics1/an-

introductory-notes-on-vector-semantics-tf-idf-model-and-a-toy-implementation-9046198bf7d and https://web.
stanford.edu/~jurafsky/li15/lec3.vector.pdf



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Dianoia: The Undergraduate Philosophy Journal of Boston College

identical indicates that they are on the same broad topic of someone being something. 
Much like the case with many other prepositions and conjunctions, the “not” is not 
always captured in building the meaning of the proposition.6 

While negation systems have not become all-around powerful enough to build the 
meaning of the proposition on their own, the scope of this paper applies to cases on 
the margins of error where the negation of “not” is able to be captured (the choice of 
which made on account of the fact that the field is headed in that direction). Yet, as 
I have argued, accommodation of negation in a formal setting leads to instances of 
epistemic injustice.   

§III The Solution: Paraconsistent Logic 

To the above, I believe that paraconsistent logic is a strong contestant as a positive 
solution to the formal infliction of epistemic injustice, its defining characteristic being 
its rejection of ex contradictione quodlibet. Since its inception, a number of influential 
strands have emerged. For example, among the first was Stanislaw Jaśkowski’s 
discussive logic, where truthfulness is determined by the totality of assertions posited 
by a single subject. Graham Priest’s “Logic of Paradox” introduced a three-valued 
logic, the third being both true and false, and Newton Da Costa presented logics of 
formal inconsistency (isolating the instances of inconsistency), which has since been 
expanded upon by many others, such as Walter Carnielli and Marcelo Coniglio. For 
the remainder of this section, despite citing several of these logics as solutions to the 
problems of epistemic injustice, I would like to remain indifferent on which of these 
specifically proves most favorable. 

To reiterate, the problem with ex contradictione quodlibet is that it assumes Alex’s 
utterances, technically contradictions in formal logic, do not matter. Priest, however, 
maintained that inconsistent theories did not necessarily lead to triviality, citing 
Bohr’s theory of the atom. Alex’s utterances of (A) and (B) are not inconsistent, but 
from the standpoint of the listener, it would absurd to argue that this then makes 
their statements insignificant—if anything, it is the conjunction of the two that 
makes their speech especially relevant.  

One might object here, pointing to the goal of logic to approximate the truth. 
What I have presented may appear as circular in that Alex’s gender identification 
indicates a non-trivial, but inconsistent theory. Yet, the existence of a non-trivial, but 
inconsistent theory is also what allows Alex to identify the way that they do. To this, 

6 For applied progress in the field, see: Mehrabi, Saeed et al. “DEEPEN: A negation detection system for clinical 
text incorporating dependency relation into NegEx,” Journal of Biomedical Informatics 54 (2015): 213-219 and 
Wu, Stephen et al. “Negation’s Not Solved: Generalizability Versus Optimizability in Clinical Natuarl Language 
Processing,” PLOS One (2014), accessed from https://journals.plos.org/plosone/article?id=10.1371/journal.
pone.0112774



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I take on the assumption that gender identity is something that is self-promulgated 
rather than externally imposed, well within the right of an individual to proclaim 
as theirs as it fosters a knowing self-consciousness capable of validating their own 
experience.7 

Counter to classical first-order logic, paraconsistent logic can accommodate the 
contradiction to uphold the significance of Alex’s words. For example, the many-
valued logics Priest proposed gives space to inconsistent and non-trivial theories. The 
truth-value of “both true and false” creates a third dimension of truth-evaluation 
that keeps the relation from exploding into triviality. The consequences of this for 
Alex are substantial: by not having their words trivialized, their words are therefore 
legitimized. The admission of inconsistency erases the inherent bias within the 
traditionally binary logical system that obscures their social experience. This, in turn, 
deflects the harms of illocutionary silencing and the formal inflictions of testimonial 
and hermeneutical injustice. 

Still, one might consider another potential interpretation of the apparent paradox 
posed by Alex’s utterances of (A) and (B)—namely, what if this is just a matter of 
language? The epistemic injustice would not be located in the words themselves, but 
in linguistic conflation. In the case of Alex, one might argue that their utterances of 
(A) and (B) reflect a variation in the sense of the term “girl” itself, with one being 
biological and the other social. 

While this may be so, the concern assumes a direct causality where thought is prior 
to language, and hence, the knowledge of two distinguishable senses proves sufficient 
enough to cast aside this juxtaposition, This, however much it would reconcile the 
problem, cannot be freely granted. Work in philosophy, linguistics and psychology 
demonstrates the profound influence of language on thought, whereby some like 
Donald Davidson, for example, claimed that belief states emerged from public 
linguistic interaction such that thought and language work in tandem. Psychologist 
Lera Boroditsky argues further that grammatical gender strongly sways the descriptive 
attributes of an object,8 which when taken with Davidson’s thesis, strongly suggests 
that linguistic resources may affect our cognitive understandings. The same can be 
said of formal resources: as mentioned earlier, the priority of formal logic may lead to 
an embedding of the binary into our cognitive framework. 

In fact, the linguistic aspect might compound the problem of epistemic injustice 
in formalized language, not even admitting a difference in the biological and the 
social senses. By way of the formal properties of the term “girl,” the biological sense 

7 This derives from strands of the Kantian tradition emphasizing self-knowledge and self-conception.
8 See: Boroditsky, Lera, “How Does our Language Shape the Way We Think?” accessed from https://www.edge.org/

conversation/how-does-our-language-shape-the-way-we-think



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is inherently conflated with the social, which may result in further iterations of the 
harm (if not also a further narrowing of the hermeneutical resources). 

To this, paraconsistent logic may again play the role of a remedy. Admission of (A) 
and (B) as contradictory, but non-trivial, allows for both the biological and social 
senses to hold true. The use of adaptive logics, for example, which offers severance 
to contact, accounts for internal inconsistency within a single subject. By adapting 
to different situations, the word “girl” takes on different meanings according to 
contextual clues and background knowledge, such as Alex’s intentions and the very 
idea of gender queerness. By this, it allows for both senses to be true, but also admits 
the term in the same sense with respect to the context of an expanded knowledge of 
genderqueerness. 

I have made the claim that paraconsistent logic offers a fruitful response to the 
challenges posed to formal logic by inconsistent, but non-trivial theories and 
linguistics. But it is possible to take the argument even further: not only does 
paraconsistent logic do such work, but it also proves necessary in order to properly 
convey meaning in formalized language. All of this is to say that the logic itself must 
not dictate meaning, but rather that, meaning must lead to its formalization. The 
fact that inconsistency permeates our world must be reflected in formalized language. 
Applications of paraconsistent logic are growing in data and knowledge bases (Grant 
2000), isolating inconsistent material so as to simultaneously admit the two nodes 
of inconsistency. However, interest in such must be acted upon for the purpose of 
retaining meaning and preventing epistemic injustice. 

One last point to be made on my argument: formal logic as it applies to natural 
language fails normatively, but not necessarily, formally. From the standpoint of 
logical argumentation, classical first-order logic does indeed succeed. Furthermore, it 
must also be noted that it does not inflict epistemic injustice in all cases: when I utter 
(A) and (B), one is necessarily true and the other necessarily false on the basis of how 
I identify my gender identity. Classical formal logic succeeds in my case. However, its 
failure to represent Alex’s social experience according to that by which they identity 
indicates that we ought not to take it as an omniscient authority over truth.

The argument I have set forth here is not meant to discredit the standing of formal 
logic in its entirety, but rather, to elucidate its futility under certain contexts. The 
claim is meant to provide a normative approach to opening the door to logical 
pluralism. First-order logic need not be discredited in its totality, but its scope should 
be limited in its application and its position ceded to other logical systems (viz. as 
paraconsistent logic). 



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Concluding Remarks

In this essay, I have shown that paraconsistent logic serves as a positive solution to 
the epistemic injustice and associated harms inflicted by classical formal logic in its 
insistence on ex contradictione quodlibet. In particular, because formal logic stipulates 
a mutually exclusive true-false dichotomy, application of it effectively invalidates 
speech and information. In cases of genderqueerness, this leads to serious threats in 
our abilities as epistemic agents as well as in the broader picture of social justice and 
political freedom. That paraconsistent logic may be a promising logic proves so on 
account of its acceptance of inconsistency without the consequence of triviality, and 
its ability to represent the actual character of propositional meaning in a formalized 
language. As the future of AI is intrinsically bound to formal logic, the consequences 
of epistemic injustice will only become more evident and tangible lest we adopt 
some form of paraconsistent logic and adhere to logical pluralism. Accordingly, our 
fundamental view of formal logic must be tweaked and reevaluated in light of the 
normative and moral concerns presented previously. ◆

BIBLIOGRAPHY

Austin, John L. How to Do Things with Words, Oxford: Oxford University Press, 1962. 

Dotson, Kristie, “Tracking Epistemic Violence, Tracking Practices of Silencing,” 
Hypatia 26, no. 2 (2011): 236-257. 

Fricker, Miranda, Epistemic Injustice: Power and the Ethics of Knowing, Oxford: Oxford 
University Press, 2007. 

-- “Epistemic justice as a condition of political freedom?” Synthese 190, no. 7 (2013): 
1317-1332. 

Hornsby, Jennifer and Langton, Rae, “Free Speech and Illocution,” Legal Theory 4 
(1998): 21-37. 

Langton, Rae, “Speech Acts and Unspeakable Acts,” Philosophy and Public Affairs 4, 
no. 22 (1993): 293-330. 

Mizraji, Educardo, “Vector Logic: A Natural Algebraic Representation of the 
Fundamental Logical Gates,” Journal of Logic and Computation 18, no. 1 (2008): 
97-121. 

Norvig, Peter and Russell, Stuart J., Artificial Intelligence: A Modern Approach, Upper 
Saddle River: Pearson Inc., 2009.


