Defeating Luzzi's dilemma: on knowledge from falsehood, Gettierized belief, and defeasibility

Abstract

Branden Fitelson (2010) proposes a strengthened version of knowledge from falsehood, according to which one may not have known that p had one not falsely believed that q. However, Federico Luzzi (2019) challenges Fitelson’s proposal. He believes that Fitelson’s account is unsuccessful because it depends on the unjustified assumption about the impossibility of knowledge from Gettierized belief. For Luzzi, Fitelson faces a dilemma: he must either accept knowledge from Gettierization and abandon his own theory about inferential knowledge from robustly false belief, or accept that knowledge from Gettierization is different from his account and deny knowledge from falsehood. He can’t have both. The goal of this paper is to dissolve that dilemma. The essay proceeds as follows. I explain Fitelson’s account and Luzzi’s objection against it. In the final section, I argue that a defeasibility theory of knowledge can help Fitelson defend himself against Luzzi’s objection and, therefore, dissolve the dilemma.

Keywords:
False belief; Gettierization; Inferential knowledge; Defeasibility

Introduction

An Aristotelian epistemological mainstream view regarding inferential knowledge is that only knowledge begets knowledge in both deductive and non-deductive reasoning.¹ This idea has been labeled by Federico Luzzi (2010, 2019) as ‘counter-closure,’ according to which if one competently infers p from q, and one knows that p, then one knows that q. Counterexamples have challenged this conception notwithstanding. For instance, some authors believe that one can inferentially know that p from an unknown premise q. Despite the prima facie plausibility of knowledge from non-knowledge hypothesis, I believe that the most pressing source of objection against counter-closure comes from the possibility of knowledge from falsehood.² Due to its intuitive force, Branden Fitelson (2010) argued that the possibility of knowledge from falsehood can be strengthened by a case where one knows that p only based on his competent inference from a robustly false premise q - that is, in counterfactual scenarios where the premise q were true, this true premise would not have been a proper basis for one to know that p. According to Fitelson (2010, p. 666), “[i]f the subject’s belief [q] had not been false, then the example would not have constituted a case of inferential knowledge”.³

Luzzi (2019) disagrees; he believes that Fitelson’s proposal is unsuccessful because it rests on an unjustified assumption that one cannot get knowledge from Gettierized belief . For Luzzi, Fitelson faces a dilemma: he must either accept knowledge from Gettierization and abandon his own theory about inferential knowledge from robustly false belief, or accept that knowledge from Gettierization is different from his account and deny knowledge from falsehood. He can’t have both.

I believe that there is a way for Fitelson to reply to this objection and dissolve this dilemma. Hence, this paper aims to develop a way to dissolve that dilemma. The essay runs as follows. I explain what Fitelson’s account is about and Luzzi’s objection against it. In the final section, I argue that a defeasibility theory of knowledge can help Fitelson defend himself against Luzzi’s objection and, therefore, dissolve the dilemma.

1. A stronger case of knowledge from falsehood by Branden Fitelson

One of the first misguided lessons we learned about the Gettier problem is that if a falsehood plays an (epistemic and causally) indispensable role in reasoning to know a conclusion p, then p cannot be known. That is an attractive view, which so many epistemologists endorse. To name a few, Gilbert Harman (1973, p. 120) asserts that “reasoning that essentially involves false conclusions, intermediate or final, cannot give one knowledge”. Michael Clark (1964) states that, in order to answer the Gettier problem, it is necessary condition that there are no false grounds for believing that p. That ‘no-false-ground intuition’ is so plausible that it is consistent with both the defeasibility theory of knowledge (Klein, 1981) and the truth-tracking theory of knowledge (Nozick, 1981).

Although having an intuitive appeal and being able to handle the original Gettier cases (and others structurally similar), the no-false-ground intuition cannot fully explain Gettierization (because, e.g., some Gettier cases are inferential without false premises, and some are perceptual Gettier cases)⁴. The strongest objection against it comes from Risto Hilpinen (1988), Ted Warfield (2005), Peter Klein (2008), Claudio de Almeida (2017, 2023), and Federico Luzzi (2014, 2019). They all believe that there can be knowledge from falsehood (KFF), according to which one can know that p on the basis of a false premise q from which they essentially infer p.^{5 6} Here are two such cases:

[Fancy Watch]: I have a 7 p.m .meeting and extreme confidence in the accuracy of my fancy watch. Having lost track of the time and wanting to arrive on time for the meeting, I look carefully at my watch. I reason: ‘It is exactly 2:58 p.m.; therefore I am not late for my 7 p.m. meeting’. Again I know my conclusion, but as it happens it’s exactly 2:56 p.m., not 2:58 p.m. (Warfield, 2005, p. 405)

[Handout]: Counting with some care the number of people present at my talk, I reason: ‘There are 53 people at my talk; therefore my 100 handout copies are sufficient’. My premise is false. There are 52 people in attendance - I double counted one person who changed seats during the count. And yet I know my conclusion. (Warfield, 2005, p. 407-408)

Warfield (2005, p. 408) claims that these cases are knowledge from falsehood cases if and only if both the following conditions are met:

• #1 the examples involve inferential knowledge of a conclusion.

• #2 the examples involve a false relevant premise.

The most contentious condition is #2. On a plausible reading of #2, being relevant might mean that the false belief q is both causally and evidentially essential for one to infer p from q. As de Almeida (2017, p. 294) puts it, “there would have been no inferential knowledge there if it were not for the causal and evidential roles [the false belief plays]”. Given its prima facie plausibility, I will assume that being relevant, in KFF cases, is equal to being both causally and evidentially essential for one to know p.

The contentiousness is because not all epistemologists agree that a false belief plays an indispensable evidential role in acquiring knowledge that p in KFF cases. Some of them believe that these cases are better described as knowledge despite falsehood because if the falsehood plays a role, it is at least only a causal role; the epistemizing support for having inferential knowledge that p comes from a true proxy premise - either a true proposition or a true belief.⁷ I will not argue for or against knowledge despite falsehood strategy;⁸ I will just follow Fitelson’s assumption that knowledge from falsehood is possible (which means that, in those cases, the false belief plays both an essential causal and evidential role for having knowledge that p through reasoning).

Fitelson (2010) claims that if Warfield’s diagnosis of KFF is correct, then we can construct a stronger case in an exciting way. Hence, Fitelson developed his own account of knowledge from falsehood, which we can call the knowledge from robust falsehood account (KFRF). This account adds the following necessary condition for inferential knowledge:

• #3 if q had not been false, the conclusion p would not have been known.

Adding #3 to Warfield's conditions makes it a requirement that the false premise be the causal and evidential basis for knowledge that p, even in close possible worlds - that’s why the premise is robustly false, that is, in close possible worlds, if the premise were true, it would not be an appropriate causal and evidential basis for knowledge that p in those worlds. Therefore, Fitelson (2010, p. 667) asserts that if the three conditions above are satisfied, we have “a case in which the inferential knowledge (that [p], on the basis of [q]) is counterfactually dependent on the falsity of the relevant premise [q]”. To support such an account of KFAF, consider the following case from Fitelson (2010, p. 667):

[Campanile Clock]: I have a 7pm meeting and extreme confidence in the accuracy of both my fancy watch and the Campanile clock. Having lost track of the time and wanting to arrive on time for the meeting, I look out of my office window (from which the Campanile clock is almost always visible). As luck would have it (owing, say, to the fluke occurrence of a delivery truck passing by my window), the Campanile clock is obscured from view at that instant (which is exactly 2:56pm). So, instead, one minute later, I look carefully at my watch, which (because my watch happens to be running one minute slow) reads exactly 2:56pm. I reason: ‘It is exactly 2:56pm [q] therefore [p] I am not late for my 7pm meeting’. Thus (supposing Warfield is right), I have inferential knowledge that [p], based on a relevant premise [q], which is a falsehood. Now for the twist. If my belief that [q] had been true, then (we can plausibly suppose) it would have been based on my reading (at exactly 2:56pm) of the Campanile clock, which would have read exactly 2:56. Unbeknownst to me, however, the Campanile clock has been (and would have been) stuck at 2:56 for some time.

When we look at the Campanile Clock, there are two inferential paths leading to conclusion p <I am not late for my 7 p.m. meeting>. The first inferential path is identical to the Fancy Watch scenario: in the actual world, the subject falsely believes that it’s exactly 2:56 p.m. and, based on his competent inference from it, believes that p. In the second inferential path, the subject is in a counterfactual scenario where there’s no truck obstructing the window’s view and he believes truly that it’s exactly 2:56 p.m. after looking carefully at the Campanile Clock. Based on that belief, he believes that p <I am not late for my 7 p.m. meeting>. According to Fitelson (2010, p. 667), even if the subject truly believes that p in that counterfactual scenario, his belief doesn’t amount to knowledge because the Campanile clock has been (and would have been) stopped. For the belief that it's exactly 2:56 p.m. is luckily true, the belief that p would not be known. However, in the actual world, as stated by the first inferential path, nothing goes wrong, epistemically speaking, with the subject. The false premise yields inferential knowledge that p, although if q had not been false (that is, had been true), the conclusion p would not have been known. Hence, the premise being false in an actual scenario is causally and evidentially essential for the subject to know p - the false premise that q would not play the epistemizing role if the premise were true. This account shows that one can have knowledge from a robustly false premise.

2. Federico Luzzi’s objection

2.1. First horn of the dilemma

For Luzzi (2019, p. 73-84), Fitelson’s Campanile Clock case doesn’t establish that one can know from a robustly false premise (condition #3 is not met). The reason why is because Fitelson assumes unjustifiably the impossibility of knowledge from Gettierized belief. If Gettierized premises can yield inferential knowledge, as Luzzi argues, then the second inferential path in Campanile Clock can be read as a Gettierized premise yielding inferential knowledge, which would show that condition #3 is false because if the premise had not been false (because it is Gettierized, ergo, it’s true by definition), the conclusion would still have been known. Hence, Fitelson’s KFRF account would be undermined.

The challenge for Luzzi is to offer a rationale for defending the possibility of knowledge from Gettierized belief (KFG). He faces this challenge by offering a supposedly KFG case and a principle that connects KFF and KFG phenomena. So consider the following case:

Agoraphobia: Unbeknownst to Ingrid, her only flatmate Humphrey is chronically averse to football: if the TV in the lounge displays any program showing or discussing football, Humphrey quietly walks to his room and hides his head under his pillow. Football aside, however, Humphrey quite likes watching TV, and the TV’s being on is a reliable indicator that Humphrey is in the lounge watching it. Sadly for Humphrey, the football World Cup has started recently, so virtually all TV time is devoted to showing or discussing recent and forthcoming matches. Also unbeknownst to Ingrid, Humphrey is agoraphobic, and hence would leave the house under very few circumstances; any circumstance in which he would leave the house (e.g., because of a raging fire in the house) is undoubtedly one in which Ingrid would be aware that he is leaving the house. Tonight, while Ingrid is in the conservatory, Humphrey sits down in the lounge and turns on the TV. Luckily, the time Humphrey turns on the TV coincides with the beginning of the only one minute stretch of the day when no football-related program is showing on any channel. So Humphrey remains seated for the next minute. Thirty seconds after he turns on the TV, Ingrid forms the belief that Humphrey is in the lounge by relying (whether implicitly or explicitly) on this inductive argument: ‘(A) The TV is on and I didn’t turn it on. (B) When this happens, Humphrey is almost always in the lounge. So ([q]) Humphrey is in the lounge’. Ingrid then relies on this premise in the following deductive inference: ([q]) Humphrey is in the lounge. ([r]) (If Humphrey is in the lounge, then Humphrey is in the house). Therefore: ([p]) Humphrey is in the house. Furthermore, Ingrid believes (p) by no other epistemic route. (Luzzi, 2019, p. 35-36).

Looking at Agoraphobia, the belief-conclusion p is essentially based on a Gettierized belief-premise. The belief that q <Humphrey is in the lounge>, even though true and justified, is not knowledge because it is fortuitously true. When Ingrid forms that belief, she does that in the only minute when that belief would be true. Her belief would not have been true at any other minute she ended up with that belief. So, it’s not just that she was lucky in having evidence she had; rather, her true belief was luckily true because of her environmental situation. Hence, Ingrid finds herself in an inhospitable epistemic environment and her belief could easily have gone wrong - such that even if she arrives at the truth, her belief that Humphrey is in the lounge is true only due to the unfriendly nature of the environment.^{9 10}

Looking at the epistemic status of belief-conclusion, why should one think that that belief is known? Plausibly, the belief that p is known because it is competently inferred from q (a justified true belief that does not amount to knowledge). Moreover, Ingrid’s belief is not luckily true.

Among the most popular constraints to account for epistemic luck, sensitivity-based truth-tracking and safety-based accounts come to the fore, and Ingrid’s belief meets both these modal conditions.¹¹ According to Nozick (1981), if one knows that p, then the one’s belief that p is sensitive: if p were not true in the closest possible world, one would not have believed, in that world, that p. In the closest possible world where p is false, Ingrid would not believe that p because she would have known that a catastrophic event has happened (such as a raging fire in the house). Humphrey would leave the house, as the case suggests, because of extremely rare circumstances, and a fire would be one of these.

Safety-based accounts are slightly different. They look at what would be true if the subject were to believe it in the most nearby possible worlds. Following Pritchard (2016), if one knows that p, then that true belief that p is safe: in nearby possible worlds where S believes that p, S ends up with a true belief that p. In nearby possible worlds where Ingrid believes that p, her true belief that p could not easily have been mistaken in these worlds. Given Humphrey’s condition of agoraphobia, the worlds where he isn’t at home are so far-fetched because, by hypothesis, they are worlds where he isn’t affected by agoraphobia. Hence, in these worlds, Ingrid’s belief that p could not easily have been false. Because her belief satisfies both sensitivity and safety conditions, as Luzzi argues (2019, p. 36), it’s plausible that her belief that Humphrey is in the house is known because it’s inferred from a Gettierized belief.

Even if Agoraphobia is methodologically useful for evaluating Fitelson’s KFRF account, the most important assumption for Luzzi’s objection is the ‘Link Principle’:

Link: if one accepts KFF, then one ought to accept that knowledge of a conclusion can also inferentially arise from a Gettiered premise. (Luzzi, 2019, p. 71)

This principle states that for every explanation for KFF, you must account for KFG with it. If one explains KFF with modal conditions for knowledge, such as safety or sensitivity, then one ought to explain KFG with this apparatus. If one also explains KFF with a defeasibility condition for knowledge, then one ought to explain KFG with this tool. To sum up, take your favorite epistemological explanation: if it can account for KFF, it ought to account for KFG as well. As Luzzi claims (2019, p. 71, fn. 29) “[...] Link is plausible on one way (amongst potentially several ways) of diagnosing KFF”.

To see why Link is appealing for Luzzi, consider the safety-based account for KFF. In Fancy Watch scenario, in most nearby possible worlds where the subject believes that she is not late for her 7 p.m. meeting based on valid inference from her false belief that it’s exactly 2:58 p.m., her true belief could not easily have been false in these worlds. It would be awkward to be late for her 7 p.m. meeting after (falsely) believing that it is exactly 2:58 p.m. because the watch is slightly inaccurate (which would at least lead the subject to arrive earlier rather than later for her meeting). As I have shown in previous paragraphs, one can also explain KFG using safety-based accounts.

Inasmuch as both explanations for KFF and KFG come together, Luzzi (2019, p. 71) states that “it seems highly plausible that at least some Gettiered premises are single-handedly capable of providing paths to the truth of the conclusion that are just as stable as (or even more stable than) those provided by the false premise [in KFF cases]”. That seems to suggest that if a false belief yields inferential knowledge in the actual world by providing a stable path to the truth (as Warfield has suggested (2005, p. 408)), then a false belief could yield inferential knowledge in nearby possible worlds. This sounds plausible because Gettierized beliefs could easily have been false on most nearby possible worlds if one explains Gettierization on modal constraints. That is why the Gettierized beliefs do not amount to knowledge in the actual world. Hence, as Luzzi (2019, p. 71) claims

commitment to KFF involves endorsing the view that knowledge of [p] can survive the actual falsehood of the premise [q] it is inferentially based on. If this is accepted, then the view that in principle knowledge of [p] can survive the mere nearby possible falsehood of [q] seems hard to deny. How could one plausibly maintain that knowledge of [p] is sometimes resilient to the actual falsehood of [q], but that it is never resilient to its mere nearby possible falsehood?

We should note that accepting KFG does not commit one to accept KFF. Because Gettierized beliefs are true in the actual world, KFG’s advocates could claim that the premise being true in the actual world is a necessary condition for inferential knowledge, although it could be false in the closest possible worlds. In this reading, KFF cases would not meet one constraint for inferential knowledge - for the belief-premise is false in the actual world. What Luzzi is claiming is that being committed to KFF is a reason for being committed to KFG.

Where does Link Principle lead us regarding Fitelson’s KFCF account? If the Link principle were true, Fitelson ought to accept KFG because of his commitment to KFF. Can he consistently accept KFG? For Luzzi (2019, p. 74-76), this question leads to undesirable theoretical consequences for Fitelson, because in the second inferential path from the Campanile Clock condition #3 is not met. When the subject forms the Gettierized belief by looking at the stopped clock and competently infers from it that she is not late for her 7 p.m. meeting, she does know it. On a safety-based account, there is no nearby possible world where the subject forms a false belief that she is late for her 7 p.m. meeting based on his Gettierized belief that it’s exactly 2:56 p.m. How can a world in which she is late for her 7 p.m. meeting, even though she truly believes it's exaclty 2:56 p.m., be a close one? On the sensitivity-based account, in the closest possible world where the subject is late, she would not believe that she is not late. For instance, if it were 6:30 p.m. and she had to cross the entire city to be at her meeting, it would be irrational for her to believe that she is not late. Hence, even though the belief-premise in the Campanile Clock has not been false, the belief-conclusion would still have been known. Therefore, if the possibility of knowledge from Gettierized belief is true, then the subject in the Campanile Clock would have known that p by taking the second inferential path.

Furthermore, the epistemic standing of her belief-conclusion that p in the second inferential path is qualitatively similar to Ingrid’s belief-conclusion in the Agoraphobia case. In every deductive scenario from knowledge from non-knowledge, such as KFF and KFG, all belief-conclusion p is logically weaker than the belief-premise q (if the reasoning is valid from non-equivalent propositions). Given that, an epistemic weakness on the belief-premise q doesn’t imply epistemic weakness on the belief-conclusion p. So, Luzzi claims (2019, p. 74-75), even though the belief-premise q in the Campanile Clock is unsafe, insensitive, and its justification is neutralized by undefeated counterevidence, the belief-conclusion p still has a better epistemic standing whatsoever. It is modally stable, and its justification is not defeated by undefeated counterevidence.¹² All these epistemic qualities are (supposedly) shared with Ingrid’s belief-conclusion that Humphrey is in the house. Therefore, if one thinks that Agoraphobia is a case of knowledge from Gettierized belief, one should also think that the second inferential path in Campanile Clock is likewise a case of knowledge from Gettierized belief.

Here is the key point: given that Fitelson accepts KFF, he ought to accept KFG (as stated by Link Principle). However, if one can know through reasoning from a Gettierized belief, the second inferential path in the Campanile Clock could be seen as Gettierized belief yielding inferential knowledge. It undermines Fitelson’s KFAF account because it shows that condition #3 is false: if q had not been false (that is, had been true), the conclusion p would have been known. Inferential knowledge that p would not be lost in the actual world even though the belief-premise q were true. Therefore, we can formulate the first horn of the dilemma as follows: Fitelson must accept the existence of knowledge from Gettierization and abandon his theory about inferential knowledge from robustly false belief.

2.2. Second horn of the dilemma

Fitelson can resist that conclusion accepting that one can know that p through Gettierized belief while arguing that the second inferential path in the Campanile Clock is unknown. He can do that by looking carefully at what we have learned from Gettier problem literature and analyzing if some necessary condition for knowledge is not met. Here, we are looking specifically at indefeasibility condition, appropriate causal connection condition and modal conditions for knowledge, such as safety and sensitivity. For this strategy to explain the objection away, it must both account for why the subject’s belief-conclusion that p is not known in the Campanile Clock and not exclude Ingrid’s knowledge that p.

As we have already seen, modal conditions for knowledge can’t come to the rescue. In Campanile Clock, both sensitivity and safety conditions are met in the same way as they are in Agoraphobia. Maybe could the defeasibility condition help? Luzzi (2019, p. 77) believes it couldn’t. For him, in both scenarios, there is counterevidence that undermines one’s inferential knowledge that p, but the counterevidence effect would be neutralized by some new information the subject may have acquired, thereby restoring one’s justification and knowledge. I will come back to this in the next section.

If the appropriate causal connection is a necessary condition for knowledge, can it help Fitelson? One “naïve” understanding of this condition states that one knows p only if there is an appropriate causal connection between the belief that p and fact p.¹³ This condition suggests that the causal history of a belief is a salient factor for knowledge that p. If belief-conclusion that p competently inferred from beliefs-premises lacks the proper causal standing, then one’s beliefs-premises will not be caused by appropriate facts either. That’s why Gettier original cases are not knowledge.

This condition is not met in Campanile Clock though. The subject forms the belief q that it is exactly 2:56 p.m because she is looking at a stopped clock. Plausibly, stopped clocks are not a proper causal basis for knowing what time it is. This explains why that belief is not knowledge: it’s not caused by the appropriate fact p. Because the belief-premise is not adequately caused, the belief-conclusion based solely on it will not be properly caused either. Ergo, the belief-conclusion p that the subject isn’t late for her 7 p.m. meeting is not appropriately caused by the relevant fact. What explains the belief being true is the stopped clock, not the fact that she isn’t late for her meeting. Moreover, the appropriate causal condition explains why Ingrid knows that Humphrey is in the house. Her belief that Humphrey is in the lounge is correctly connected to the relevant fact because she has auditory evidence from the TV turning on that indicates this fact. Therefore, in the second inferential path, Fitelson could argue that the belief-conclusion p is not known due to its faulty causal standing and accept that Ingrid knows that p from her Gettierized belief.

Luzzi (2019, p. 79-80) claims that while this appropriate causal strategy is promising, it nevertheless leads to unbearable consequences for Fitelson. Look at the standard KFF cases, such as Fancy Watch and Handout. What is exactly the causal basis for the belief-conclusion that p in those cases? Its causal basis is the competent inference from a justified false belief. However, what is precisely the causal basis of one’s false belief? By definition, one’s false belief cannot be appropriately caused by the relevant fact because there is no such fact. Hence, all false beliefs cannot meet the appropriate causal constraint for knowledge.

Fitelson assumes that KFF is possible notwithstanding. This is a necessary condition for his KFAF account to be successful. Given that assumption and his would-be commitment to an appropriate causal condition, how can one know from a false belief if false beliefs are not causally linked to the facts? Why would a lack of appropriate causal standing be a knowledge-suppressing element in Campanile Clock while not in KFF cases? It seems arbitrary that the absence of appropriate causal history undermines only knowledge in Campanile Clock, and not also in KFF cases. The shortcoming is that if Fitelson accepts the appropriate causal condition for knowledge in order to explain why the subject does not know in Campanile Clock, it undermines the possibility of knowledge from falsehood.

Here is the takeway: Luzzi argues that if Fitelson accepts KFG and denies that the second inferential path in the Campanile Clock is not a case of knowledge because of the lack of appropriate causal connection, he must abandon his assumption about knowledge from falsehood - for there is no causal connection in KFF cases either. However, if Fitelson must abandon the possibility of knowledge from falsehood, it undermines his knowledge from robustly false belief account. Hence, we can formulate the second horn of the dilemma as follows: Fitelson must accept that knowledge from Gettierization is different from his account and also deny the existence of knowledge from falsehood.

2.3. The Dilemma Summary

If Link Principle is plausible, then if one accepts KFF, one ought to accept KFG. This leads Fitelson to a dilemma: if one can acquire knowledge from Gettierized belief, then he must abandon his account of knowledge from robustly false belief. If he argues that cases of knowledge from Gettierized belief are different from the case that motivates his theory because the appropriate causal condition is not met in the latter but is met in the former, he must deny his assumption about knowledge from falsehood. Hence, Fitelson must accept knowledge from Gettierization and abandon his theory about inferential knowledge from robustly false belief, or accept that knowledge from Gettierization is different from his account and deny knowledge from falsehood. Regardless, Fitelson’s account of knowledge from robust falsehoodwould be undermined.

3. A defeasibility defense

The objection put forward by Luzzi is an exciting one because it’s supported by the most plausible anti-Gettier conditions for knowledge and a general principle connecting knowledge from non-knowledge phenomena. Nonetheless, I believe Fitelson can explain Luzzi’s argument away by showing that in Campanile Clock the second inferential path cannot lead to inferential knowledge. Here is the plan for the remainder of this section: I will delve into main concepts from the defeasibility theory of knowledge, and I show that its use by Luzzi to explain Campanile Clock and Agoraphobia may be challenged.

You would probably agree if someone told you that knowledge is compatible with more knowledge. This intuition was first suggested by Hintikka (1962, p. 22) when he claims that “[i]f somebody says ‘I know that p’ in this strong sense of knowledge, he implicitly denies that any further information would have led him to alter his view...” The lesson we’ve learned from him is that ‘old’ knowledge must be compatible with ‘new’ knowledge.

Defeasibility theorists have taken this intuition and developed their theory as an anti-Gettier condition on knowledge.¹⁴ For them, one knows that p only if one’s justification for p bears up with the addition of more true propositions to one’s belief system, which is called ‘truth-resistant’ justification. For instance, if I know that I ran on Saturday morning, there’s no actual truth that undermines my justification for believing it - since justification necessary for knowing withstands the addition of more truth to the subject’s doxastic system.

When we look at the Gettier problem literature, we nevertheless get the opposite result. One’s Gettierized belief doesn’t amount to knowledge because its justification isn’t truth-resistant. Take any relevant actual truths and add them to the subject’s doxastic system, and you will realize that the justification for Gettierized belief doesn’t withstand any actual truth the subject may have learned. For instance, consider the famous case Sheep in the field, which was put forward by Chisholm (1989). The subject has a justified belief that there is a sheep in the field based on her perceptual experience of what looks like a sheep. And that belief is true because, hidden by a tree in the middle of the field, there is a sheep out of her vision. However, what the subject is actually seeing is a shaggy dog who looks exactly like a sheep. What would the defeasibility theorist say? The subject doesn’t know because her justification is not truth-resistant: if she learns that she’s seeing a shaggy dog instead of a sheep, her justification is defective as it cannot withstand this new actual truth. That is, that actual truth is a defeater which destroys her justification for believing that there is a sheep in the field. Because there is a defeater for her justification, that justification is not good enough for knowledge. As de Almeida & Fett (2016, p. 156) claim, “[t]he fundamental assumption is that truth-resistance is a necessary condition on knowledge-yielding justification”. Hence, the defeasibility theorist claims that one knows that p only if there’s no defeater for one’s justification.

The defeasibility theory of knowledge reaches maturity when Peter Klein (1981) distinguishes between genuine and misleading defeat. This distinction is motivated by the famous case of the demented Mrs. Grabit put forward by Lehrer and Paxson (1969), which showed that defeasibility condition on knowledge is too strong.¹⁵ Although their objection could have jeopardized defeasibility accounts of knowledge, it ultimately failed. Peter Klein argues that Lehrer and Paxson miss the target as some defeating effects depend only on truths, while others depend on falsehoods. That is, a distinction between genuine and misleading defeat should be taken into account for a full picture of defeasibility theory.

The misleading defeat notion underlies the thought that not every actual truth defeats one’s justification because its defeating effect depends on a falsehood justified by that truth. Namely, when one’s justification for p is defeated by a misleading defeater, its justificatory status is ultimately neutralized by an actual truth because this truth justifies a false proposition, which defeats one’s justification when they are combined with justifiers for p that one might have. This defeat is illusory, so to speak, because of its dependency on falsehood. In other words, if one’s justification for p is then misleadingly defeated, its defeating status ultimately depends on a falsehood being the would-be effective defeater. The good news is that misleading defeat effect on one’s justification can be canceled out by a restorer or a ‘defeater-eater’. It is an actual truth which is not a reason for p and neutralizes the illusory damage caused by a falsehood. To sum up, when one justification for p has misleading defeaters, it does not reflect that that justification isn’t knowledge-yielding justification - since it remains truth-resistant justification.

An example may help to properly understand the definition. Suppose you know that p based on your good justifiers for p. If someone is an unreliable person and says that q (which is incompatible with p), should the actual truth of this saying so defeat your justification for p? Plausibly not. The actual truth <that person says that q> is a reason for one to accept q, which is, by hypothesis, a false proposition. Whether that truth defeats your justification for p, it’s an illusory or pseudo-defeat because it justifies a falsehood. If you have learned the truth about that person’s unreliability, your justification based on your good justifiers would be restored since that truth neutralizes misleading defeat effect on your justification. Your justification then withstands the addition of truth, showing its truth-resistant property.

Genuine defeat, on the other hand, is easy to spot. One’s justification for p is genuinely defeated when her justifiers for p do not withstand the addition of actual truth (and any other actual truth justified by that truth). When we consider the Gettier cases, in all those cases, the defeat is genuine, because the Gettierized subject cannot rationally maintain her justifiers for p and the genuine defeaters. Because the genuinely defeated justification is no truth-resistant justification, no truth would cancel the defeating effect caused by genuine defeaters and restore one’s justification. You could still find some truths we don’t see as genuine defeaters, because they are neither restorers nor genuine defeaters. They could be independent reasons for justifiably believing that p. If you have learned that there’s a sheep out of your vision in the middle of the field, this actual truth wouldn’t restore your perceptual justification based on your perceptual experience from a shaggy dog. Instead, you’d have a completely new reason for p. Hence, the lesson we should learn from Peter Klein (1981) can be summarized as follows: one knows that p only if there’s no genuine defeater for one’s justification for p - that is, all defeaters for one justification for p are misleading defeaters.

What does Luzzi’s dilemma stand for in Fitelson’s view? Luzzi (2019, p. 76-77) claims that defeasibility theory cannot come to the rescue because, in both cases, Campanile Clock and Agoraphobia, there are restorers for one’s justification, which means that their justification is truth-resistant justification. I strongly disagree with Luzzi. Fitelson can and should take a defeasibility condition of knowledge for dealing with Luzzi’s dilemma. That could explain why both Agoraphobia and the second inferential path in Campanile Clock are not knowledge cases, while it wouldn’t undermine Fitelson's commitment to knowledge from falsehood.

Look carefully at what Luzzi claims:

[In Agoraphobia] while the fact that the programmes this time of year focus usually on football acts as a defeater for her belief in [q <Humphrey is in the lounge>], in the case of her belief in [p <Humphrey is in the house>] it is defeated by the defeater-defeater that Humprey is agoraphobic. So the reasons for deeming [q] not known lapse in the case of [p]. (Luzzi, 2019, p. 37)

One could say of [the second inferential path in Campanile Clock] that there is a defeater, such as the Campanile has stopped, which undermines justification (and thereby knowledge) of the premise it is exactly 2:56 p.m. And it could be claimed that the presence of this defeater also serves to ultimately undermine knowledge of the conclusion I am not late for my 7 p.m. meeting. However, it is not clear that this strategy [...] adequately distinguishes [the second inferential path] of Campanile Clock from Agoraphobia. For it seems that the Gettiered premise-belief in the latter case (Humphrey is in the lounge) is also affected by a defeater (e.g., The World Cup is taking place and Humphrey goes to his bedroom when he sees football on TV), and, by analogy, one would have to explain, in line with the commitment to deeming the inference in Agoraphobia as yielding knowledge, why this does not similarly undermine knowledge of the conclusion.

One response might be to claim that there is a ‘knowledge-rescuing’ truth which, if added to the subject’s stock of beliefs, would restore her knowledge of the conclusion Humphrey is in the house: for example, the truth Humphrey is agoraphobic. If Ingrid were to believe this, she could justifiably retain her belief in the conclusion. However, the same could be said for [the second inferential path] of Campanile Clock. If the subject believed the truth the Campanile stopped approximately 12 x n hours ago, for some natural number n (and it is not nighttime), her justification and knowledge of her conclusion could be restored. (Luzzi, 2019, p. 76-77)

The one-million-dollar question is: is the subject’s justification in both cases affected by misleading defeaters? Luzzi thinks it is because some truths would restore one’s justification for the belief that p. In both cases, an actual truth restores one’s original justification, which explains why one knows that p. That’s why Luzzi states that defeasibility condition on knowledge cannot help Fitelson in distinguishing Agoraphobia and the second inferential path in Campanile Clock. In both scenarios, the subject acquires inferential knowledge from Gettierized belief, and the defeasibility theories warrant this verdict.

Luzzi is correct when he claims that defeasibility condition cannot account for a distinction between Agoraphobia and the second inferential path in Campanile Clock. Nevertheless, the conclusions he draws may be challenged. In both cases, the Gettierized belief cannot yield inferential knowledge because its justification is defeated beyond restoration. That is, the defeating effect is based on genuine defeaters, and therefore, no actual truth would neutralize that defeat. Take Campanile Clock, for instance. If the subject had learned that the Campanile has stopped, her inferential justification for the belief-premise q <it’s exactly 2:56 p.m.>, and consequently, belief-conclusion p <she’s not late for her 7 p.m. meeting> would be undermined - because one cannot rationally maintain the belief that the Campanile Clock has stopped and, at the same time, basing one’s belief about time on a stopped clock. Had the subject learned the actual truth that Campanile had stopped 12 hours ago and it’s not nighttime, she would be justified in believe that it’s exactly 2:56 p.m. and, consequently, that she’s not late for her 7 p.m. meeting - not because her perpetual justification has been restored, but because she acquires news and independent reasons for justifiably believe that p. And plausibly, what brings to the fore the intuition that the would-be restorer in this case can justify the belief that p is the actual truth <it’s not nighttime>, since the Campanile has stopped, it’s an unreliable basis to form any beliefs about time. Therefore, in the second inferential path in Campanile Clock, the Gettierized belief is not a good knowledge-yielding justification to ground one’s knowledge because it’s not truth-resistant justification.

Similarly, in Agoraphobia, if Ingrid had believed that Humphrey is chronically averse to football and virtually all TV time is devoted to the football World Cup, she would not be justified in believing that Humphrey is the lounge based on her auditory experience of the TV turned on - because since he loathes football and virtually all programmes are about football, the TV being turned on is not a good reason for believing that Humphrey is in the lounge. Also, she cannot distinguish, based on that auditory experience, between the minutes when football is or isn’t being discussed on TV. Ergo, had Ingrid learned these truths, she would have been unjustified in believing that Humphrey is in the lounge and that he is in the house as well. Once a genuine defeater defeats the justification for the belief-premise, so it’s the justification for the belief-conclusion inferred from that premise. She would nevertheless be justified in her belief-conclusion if she learns that Humphrey is agoraphobic, but that justification would be an entirely new reason for believing that he’s in the house; a totally independent reason from her auditory experience of the TV being turned on. Hence, no “knowledge-rescuing” truth restores Ingrid’s knowledge, as Luzzi suggested. What there really is a truth that offers a new reason for justified belief.

What I offer here for Fitelson is a way out of the dilemma. As soon as he accepts defeasibility condition on knowledge, he can explain away Luzzi’s dilemma by rejecting the possibility of acquiring knowledge from Gettierized belief - since in both Agoraphobia and Campanile Clock the subject would not have known the conclusion p if the premise q had been true (ergo, condition #3 on Fitelson KFAF account would not be undermined). He can also rationally maintain his commitment to the possibility of acquiring knowledge from falsehood. Even though the 1981-Kleinian defeasibility theory of knowing cannot account for the knowledge from falsehood phenomenon, as Klein (2008) wisely recognizes, there still are plausible defeasibility theories on the market that seem to be capable of explaining KFF - such as the fallibilist defeasibility theory of knowledge put forward by Claudio de Almeida (2017, 2023). Ergo, Fitelson could accept the fallibilist defeasibility spelled out for KFF without compromising his knowledge from robustly false belief account.¹⁶

Moreover, a fallibilist defeasibility condition for knowledge offers greater explanatory power than the corresponding appropriate causal condition on knowledge. As we’ve already seen, (fallibilist) defeasibility theorists can account for KFF, while appropriate causal condition advocates cannot. Furthermore, Gettierization is better explained by defeasibilist than appropriate causal theorists. The appropriate causal condition clearly fails when considering the famous Fake Barn case (Goldman, 1976). The subject has an appropriate causal basis with the fact that makes target-proposition true, however, it seems unreasonable to claim that he knows. On the contrary, defeasibility condition is not met in this situation. Had one believed that she is in a misleading environment with virtually all the barns being replaced by fake barns, she would not be justified in believing that what she sees is a barn. She wouldn’t then know that the object in front of her is a barn. Therefore, besides seeming to offer a better explanation for KFF, defeasibility theory also offers a better explanation of Gettierization. That is an additional reason for Fitelson to prefer defeasibility theory over appropriate causal theory for dealing with Luzzi’s dilemma.

Conclusion

The possibility of acquiring inferential knowledge from falsehood is a challenge we must deal with because it threatens both the Aristotelian orthodoxy on knowledge-yielding inferences and the plausibility of popular theories of knowing, in their standard versions. Fitelson goes one step further by arguing for the possibility of acquiring knowledge from robustly falsehood: if the premise q had not been false, and one infers p from q, then the conclusion p would not have been known.

However, Luzzi argues that if one accepts KFF, one ought to accept the possibility of acquiring knowledge from Gettierized belief. The reasonableness of this Link Principle jeopardizes the success of Fitelson KFAF account - had the premise not been false (because it’s Gettierized), the conclusion would still have been known though. Fitelson is then faced with a dilemma: if one can know from Gettierized belief, then he must abandon his account of knowledge from robustly false belief. If he argues that cases of knowledge from Gettierized beliefare different from the case that motivates his theory because the appropriate causal condition is not met in the latter but in the former, he must deny his assumption about knowledge from falsehood. Either way, his account would be undermined.

In the last section, I argued that a defeasibility condition on knowledge, properly understood, can dissolve the dilemma. Because there is genuine defeat beyond restoration for one justification for p in both Agoraphobia and the second inferential path in Campanile Clock, the subjects cannot know that p based on a Gettierized belief. Hence, what I offer for Fitelson is a way out of the dilemma: as soon as one accepts a (fallibilist) defeasibility condition, one can explain away the misleading evidence from the possibility of having KFG while accepting both the possibility of acquiring KFF and KFCF. Moreover, the defeasibility condition provides a better account of Gettierization than the appropriate causal condition does.

What we should learn from that discussion is that Fitelson’s KFRF account is more plausible than one would have expected it to be. It not just strengthens the possibility of knowledge from falsehood, but it might be an explanation for why critics of KFF may be mistaken - a true proxy premise may not be good enough for yielding inferential knowledge, in the same way as the Gettierized belief is not a good epistemic standing for one to acquire knowledge that p. More than that, the good news is that thinking about KFF, KFRF, and KFG can illuminate the general kind of knowledge from non-knowledge. As Luzzi states (2019, p. 83), “[the research program on KFF, KFRF and KFG] recognizes the more general phenomenon of knowledge from non-knowledge as a primary target of inquiry”. Luzzi may be correct on this, but regardless of whether he is, the KFG hypothesis would still lie outside the scope of inquiry into knowledge from non-knowledge if defeasibility theory accounts for it.

Acknowledgments

I am grateful to Claudio de Almeida, Gregory Gaboardi, Gustavo Oliva, João Fett, LP Cichoski, Vinicius Felipe Posselt, and Matteo Baggio for their careful reading of the paper and their insightful suggestions. I also wish to thank the two anonymous referees for their valuable feedback and constructive comments. Finally, I would like to thank the Brazilian funding agency CNPq (141066/2021-0) for the doctoral scholarship, which funded my research on this topic.

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• 1
  See Borges (2019) for a discussion of acceptance of this idea throughout the history of epistemology.
• 2
  Other instances of knowledge from non-knowledge are at least (i) knowledge from Gettierized belief (Luzzi, 2019; Olivier, 2022), (ii) knowledge from unjustified belief (Murphy, 2017), and (iii) knowledge from unbelieved proposition (Murphy, 2013).
• 3
  All the emphases on citations in this essay are on the original.
• 4
  See de Almeida & Fett (2015) and Chisholm (1989).
• 5
  We must be careful here. For Klein (2008) (and maybe for Hilpinen (1988)), falsehoods indispensable for knowing p through reasoning are only causally indispensable. As Klein calls them, they are useful falsehoods because they play an essential causal role in acquiring inferential knowledge that p. They aren’t evidentially essential because useful falsehoods imply a true proposition, which is the real epistemizing element to inferentially knowing p. For the other authors, the falsehoods play an indispensable causally and evidentially role in knowing p.
• 6
  See de Almeida and Fett (2019) for a history of the topic.
• 7
  Some advocates for knowledge despite falsehood are Montminy (2014), Ball & Blome-Tillmann (2014), and Borges (2017, 2020).
• 8
  For objections against knowledge despite falsehood strategy, see Fitelson (2017), Buford & Cloos (2018), Luzzi (2019), and Alves (2024).
• 9
  This explanation lies on the thought that knowledge is compatible with evidential but not with veritic epistemic luck. The former explains luckily evidence possession, while the latter explains luckily true belief formation. See Pritchard (2005) and Pritchard, Millar, and Haddock (2010) for further discussion.
• 10
  An interesting property of her belief is shared with the subject from Fake Barns (Goldman, 1976): both beliefs are subject to environmental epistemic luck because both Ingrid and Henry are in an unfriendly epistemic environment.
• 11
  See Zagzebski’s double-luck account (1994) for an alternative view for evaluating epistemic luck.
• 12
  We will look at the defeasibility condition in the next section.
• 13
  This is slightly different from Goldman’s (1967) Causal Theory of Knowing, which claims that a belief that p having an appropriate causal connection with fact p is both a necessary and sufficient condition for one to know that p.
• 14
  Some epistemologists who have made leading contributions to the development of defeasibility theory of knowledge are Keith Lehrer (1965), Peter Klein (1981, 2008), Marshall Swain (1974, 1981), Risto Hilpinen (1988), John Pollock (1986), Claudio de Almeida and J.R Fett (2016), and Claudio de Almeida (2017, 2023).
• 15
  You can see a fully explanation of the demented Mrs. Grabit case in Klein (1981), de Almeida & Fett (2016), and Alves (2021).
• 16
  One may plausibly ask: can one accept a defeasibility account for KFF and KFG? In other words, is Link Principle true? The quick answer is no. Unfortunately, there’s no room here to develop a full explanation here.
• Article info
  CDD: 121.
• Funding:
  This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [Grant Number 141066/2021-0], via the doctoral scholarship.
• Research Data Availability:
  All research data are available within the main text of the article.

Data availability

All research data are available within the main text of the article.

Publication Dates

• Publication in this collection
  20 Oct 2025
• Date of issue
  2025

History

• Received
  11 Feb 2025
• Reviewed
  14 July 2025
• Accepted
  05 Aug 2025