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Gettier and the Problem of Induction
by Ean Maloney

Introduction
 Fifty-four years have passed since Edmund 
Gettier’s short treatise undercut philosophers’ 
complacent confidence in the justified true belief 
(JTB) definition of knowledge. Subsequent attempts 
to redeem, modify, or replace JTB have made 
progress towards these goals but are still inadequate. 
I propose that the reason for these deficiencies lies in 
an overestimation of the human capacity to possess 
propositional knowledge. Accordingly, a theory of 
knowledge not subject to Gettier problems must 
assume a more limited scope of knowledge than 
usually considered. Specifically, it is necessary to 
reconsider our implicit trust in the possibility and 
accessibility of inductive knowledge.

Gettier’s Dilemma
 Though I will present several scenarios for 
consideration in this paper, we ought to keep in 
mind the original two Gettier cases, or the Smith-
Jones-Brown (SJB) cases (Gettier, 1963). In Case I, 
Smith and Jones apply for the same job, and Smith 
believes the proposition:
 (1) Jones is the man who will get the job, and 

Jones has ten coins in his pocket.
This leads him to the conclusion:
 (2) The man who will get the job has ten coins in

his pocket. 
Gettier assures us that Smith’s evidence for believing 
(1) is sound, so Smith is justified in believing (1). 
However, as the example goes, Smith is hired instead 
of Jones, yet Smith has ten coins in his pocket as well. 
So, did Smith actually have knowledge of (2)? Gettier 
and many JTB revisionists answer negatively, but 
differ on the reasons for why Smith does not know 
(2).
 In Case II, Smith once again finds himself in 
an epistemic mire when he believes with “strong 
evidence” the proposition: 
 (3) Jones owns a Ford.
Smith then arbitrarily draws the conclusion:

 (4) Either Jones owns a Ford, or Brown is in
Barcelona.

Let us ignore the fact that the “either…or” formulation 
seems to neglect the possibility that Jones could own 
a Ford and Brown could be in Boston, as we could 
easily reformulate (4) to account for this. Gettier tells 
us that Smith is mistaken that Jones owns a Ford, but 
in fact Brown is in Barcelona. 
 The SJB cases reveal that the JTB model fails 
to account for “epistemic luck,” instances where a 
conclusion is true for purely coincidental reasons 
not initially considered by the subject (or at least 
not believed to exist). These reasons in the SJB 
Cases are, respectively, that Smith has ten coins in 
his pocket and that Brown is in Barcelona. Though 
the obvious option for amending the JTB model is 
to explicitly exclude epistemically lucky cases from 
being considered instances of knowledge, this seems 
a rather ad hoc approach.1 Thus, we might with more 
intellectual integrity look for more fundamental 
problems inherent to JTB. 

Necessary Conditions for Justification
 The truth and belief conditions of the JTB model 
seem prima facie conditions for knowledge and 
unable to be further differentiated. By definition, 
“knowledge” concerns propositions that correspond 
to reality, i.e., are true. Furthermore, “knowledge” 
denotes propositional material that a subject 
epistemically possesses and considers true, i.e., is 
believed. If one of the conditions of the model is 
controversial or needs to be further elaborated, it 
must be justification. What is required, then, is a 
movement from JTB to (J’)TB. I propose that the 
(J’) condition concerns the property of veracity. 
By veracity, I mean a “no-false grounds/premises” 
condition, an idea Goldman associates with Michael 

1The Stanford Encyclopedia of Philosophy article, “The 
Analysis of Knowledge,” creatively refers to this as 
“degettiering” (Ichikawa & Steup, 2016).
 



Gettier and the Problem of Induction

Aisthesis      Volume 8,  201736

Clark (1967, p. 358).2 If we could have empirical 
knowledge, a causality condition would arise as 
well. Goldman famously proposes a “causal theory 
of knowing,” which holds that for a proposition to 
be considered knowledge, a “causal connection” 
must exist between what makes the proposition in 
question true and a subject’s belief in that proposition 
(1967, p. 358). However, causality is not a necessary 
condition for deductive or a priori knowledge, as 
these beliefs cannot rightly be said to be ultimately 
caused by anything other than their a priori status.
      Especially in light of Levin’s paper (2006), which 
identifies false premises even in examples claimed 
to be “non-false,” the veracity condition seems 
highly useful in resolving Gettier-type problems. 
Causality remains an important factor in analyzing 
empirical knowledge, however, because of the close 
link between causality and induction based on sense 
data. For example, the belief that a cup of coffee 
sits on my desk is based on my seeing it, which is 
presumably caused by the presence of the cup in my 
field of vision. In other words—and as considered 
by Goldman—a causal connection exists between 
objective facts and sense data, which is the grounds 
for empirical belief (1967). Although causality can 
be represented as a special instance of the veracity 
condition—we can consider the former as a set of 
propositions about causal relations, perception, and 
belief3—it seems much simpler to consider the two 
conditions separately for many cases. 
 Both Goldman’s and Clark’s assessments can 
be viewed as diagnoses of what goes wrong in the 
SJB cases to prevent Smith from having knowledge. 
Though Goldman (1967) and Clark (1963) interpret 
their conditions as being in addition to the three 
proposed by JTB (thus making the working model 
JTB+X), I argue that they should be considered 
specific components of justification.4 Both SJB 

2 Goldman at least seems to consider justification to mean 
that the move from premise to conclusion is warranted or 
reasonable. Also see Clark’s “Knowledge and Grounds: A 
Comment on Mr. Gettier’s Paper.” 
3 We might hold the propositions “X causes Y, therefore 
when X, then Y” and “When P(X), then X,” where P(X) 
represents that a subject perceives X.
⁴ Clark states that his condition goes beyond “no-false 
grounds,” but I believe that the simplification is adequate 
for my purposes (1963, pp. 46-47).

cases can be explained in terms of causality and/or 
veracity. 
      SJB-1 fails to be causally coherent because the fact 
that Smith has ten coins in his pocket does not cause 
him to believe (2). It fails the veracity condition 
because (1) is false; Jones will not get the job. SJB-2 
fails in similar ways because Brown’s location is not 
causally linked to Smith’s believing (4), and because 
(3) is a false premise.5 
      
Strange Knowledge and the Problem of Induction
 Though adding veracity to JTB improves the 
model immensely, a fundamental problem remains: 
the problem of strange knowledge. What strange 
knowledge shows is the weakness of “knowing” 
by induction. An instance of strange knowledge 
can be seen in the following example, call it SK-1.6 
Erin wakes up one morning and, looking out the 
window, sees that the ground is covered in snow. She 
infers that it snowed last night—an inference that 
Goldman would call “highly warranted” (1967, p. 
361). However, though it did in fact snow last night, 
the snow all melted before she woke that morning. 
The reason for the snow on the ground is actually 
that her husband, Gary, who owns a chain of snow 
cone shops, had decided to dispose of a truckload of 
extra crushed ice by dumping it on their front lawn 
between the time the snow melted and when his wife 
woke up. Though Erin’s conclusion that it snowed 
the previous night is true, she cannot be said to have 
knowledge of this, since, like in the Gettier cases, her 
inference is true purely by luck. Yet, imagine that the 
snow had not melted and Gary had not dumped a 
truckload of powdered ice on their lawn. In that case, 
if she had drawn the same conclusion, many would 
say that she had knowledge that it had snowed the 
previous night. Is it not strange that from the same 
sense data—the presence of powdery ice crystals on 
the lawn—and the same inference—that if the lawn 
is covered with powdery ice, it must have snowed 
recently—there can be one case in which Erin is said 
to have knowledge and one in which she is not? 

⁵ The only of these conclusions explicitly addressed is 
Goldman’s interpretation of SJB-2 (1967). 
⁶ Based on an example given by Goldman (1967, pp. 361-
62). 



Gettier and the Problem of Induction

Aisthesis      Volume 8,  201737

      Another example, call it SK-2.7 Ellen goes in to 
work one morning and sees keys for new cars on 
the desks of her friends Greg and Grover. She infers 
that Greg and Grover have both recently bought 
new cars. Greg and Grover have indeed bought 
new cars recently, but Grover’s new car is still at his 
house. He had driven his old car to work and has a 
different reason for his new key. He had lost his old 
car key, and the one Ellen saw on his desk is merely a 
replacement key, albeit one identical to a new car key. 
Is it not strange to say that Ellen can have knowledge 
from inferring that Greg has a new car, but not from 
inferring that Grover does? The same sense data and 
the same inference is again present in both cases. 
      Goldman would claim via his causal theory that 
in SK-1, Erin does have knowledge in the instance 
where the snow does not melt and does not in the 
instance where it melts (1967). Furthermore, in 
case SK-2, the veracity condition allows for Ellen to 
have knowledge of Greg’s owning a new car, but not 
Grover’s based on the following premise: If G has a 
new car key, G has a new car. This premise is true in 
Greg’s case, but not in Grover’s.8 But in this lies the 
strangeness. It seems very odd to base knowledge on 
a premise that is only sometimes true. 
 In both SK-1 and SK-2, subjects reach their 
conclusions via an inductive premise. They are, 
respectively:
 (SK-1) If there is snow on the ground, then it has

snowed recently.
 (SK-2) If someone has a new car key, then they 

have a new car.
Both these premises are shown by the examples to be 
less than infallible. They really ought to be stated as:
 (SK-1’) Probably, if there is snow on the ground, 

then it has snowed recently.
 (SK-2’) Probably, if someone has a new car key, 

then they have a new car.
Levin, however, points out a variety of problems that 
remain, foremost among them that a “Probably X” 
statement does not seem to be something that can 
be believed at all, since it does not have a truth value 
if construed as something like “Maybe X;” however, 

⁷ Based on an example given by Levin (2006, pp. 384-
85). 
⁸ Levin considers the implications of a similar proposition 
(2006, p. 385). 

both Levin and I believe that “Probably X” is most 
usefully stated as something like, “In most cases X” 
(2006, p. 388). Construed as such, both (SK-1’) and 
(SK-2’) are usually good grounds for justification. 
However, we lack a way to determine whether they 
can provide sound justification in any particular 
situation. If we accept that these—and in fact all—
inferences are essentially probabilistic, then in any 
real-world scenario involving empirical knowledge, 
the strongest claim we can reasonably make is one of 
the following:
 (5a) S knows probably X.
   OR
 (5b) S probably knows X.
Probably true or probably justified belief seems 
like a weak sort of knowledge, yet I can imagine no 
empirical cases that do not reduce to it. The only 
reason theoretical cases might is that we accept a 
priori whether a subject’s conclusion is true or false 
based on what the creator of the case tells us. 
 A second concern about strange knowledge cases 
concerns the concept of knowing as a consciousness 
state. The problem is that the strange knowledge 
cases have been interpreted in ways that make the 
conditions for this consciousness state dependent 
on external facts. Though knowledge must depend 
on the truth of a given proposition, it cannot be 
grounded in any more specific external conditions. 
To clarify this point, I provide the following case: 
Consider a traveler who sees a lake that may or 
may not be a mirage. If we want to know whether 
the traveler has knowledge of the existence of a lake, 
we might break down the case into the external 
and internal components. No problem exists in the 
external elements; either the lake exists or it does not, 
regardless of what the traveler thinks. Independently 
of external conditions, the traveler has a definite 
sight perception. He really does see something. 
Whether this perception corresponds to reality is 
still at question, but the traveler can be certain of 
the existence and quality of the perception itself. 
The weakness seems to be somewhere in the middle, 
in the conversion of information from the external 
to internal domains. I will examine this conversion 
process in more detail later, but it is not hard to see 
that it proceeds via the production of sense data. 
Thus, the challenge in analyzing knowledge arises 
when sense data is introduced as grounds.



Gettier and the Problem of Induction

Aisthesis      Volume 8,  201738

 What we have reached at this point is the 
Humean problem of induction. As he famously 
wrote, when it comes to “matters of fact”—which I 
have referred to as empirical—we generally must be 
ignorant (Hume, 2016, p. 214). No matter how likely 
it is that the Sun will rise tomorrow, even if we are 
99.9999999999999% sure, we cannot know that it 
will. We are always subject to perceptual error, lack 
of relevant data, deception, and hidden variables, of 
which we are very often unaware. Simply put, it is 
very hard to know what we do not know. Because 
of this, drawing a correct conclusion in SK-1, SK-
2, and any other inductive scenario will always be 
subject to some sort of epistemic luck. If our sense 
data corresponds to reality and the conclusions we 
draw from it correspond to reality, it is indeed lucky 
that we were not subject to a perceptual error, lack of 
data, deception, or hidden variables. This is especially 
clear with regards to SK-2, where it seems purely by 
chance that Erin can be right in one conclusion and 
wrong in the other.

False Lemmas and Inductive Knowledge
 A further consideration against the possibility 
of inductive knowledge arises from the condition of 
veracity. In all cases of empirical, inductive, matter 
of fact, or sense data-based knowledge, one crucial 
assumption is made at some level. This premise takes 
two forms that are intrinsically linked:
 (6a) Premises derived from sense data are 

(always or in this case) true.
 (6b) If something is probably true, it is true.
I argue that both these assumptions count as false 
premises and that accepting them has caused many 
to vastly overestimate the range of beliefs that can 
be considered knowledge. Although this view may 
seem like an unwarranted descent into skepticism, 
both the consideration of “strange knowledge” cases 
and the fallacious nature of moving from “X seems to 
be” to “X is” show the necessity of such a conclusion. 
 Take any scenario of the following type. S 
perceives X (P(X)) and assumes,
 (P1) P(X)⇒X.
 (C1) ∴X obtains. 
This line of reasoning breaks down by assuming (6a) 
or (6b). First, in (P1) S assumes (6a). If S assumes that 
premises derived from sense data are always true, S 
certainly has adopted a false premise. No process of 

empirical perception possessed by human beings is 
free from all possibility of error. If S assumes that in 
this case (P1) must be true, S still must show how S 
knows his or her perceptive faculties are not deceived 
in this case, which I argue cannot be done with the 
certainty necessary for knowledge. This is consistent 
with Wykstra’s condition of reasonable epistemic 
access (CORNEA), which he states as,

On the basis on cognized situation s, human 
H is entitled to claim “It appears that p” only if 
it is reasonable for H to believe that, given her 
cognitive faculties and the use she has made of 
them, if p were not the case, s would likely be 
different than it is in some way discernible by 
her. (1984, p. 85)

According to CORNEA, in our context, S cannot 
claim “It appears that X,” unless S can reasonably 
believe that if X does not obtain, P(not X) will imply 
not X. Even then, license to claim, “It appears that 
X,” is different from being entitled to make the 
claim, “X obtains.” I argue that unless S can make 
the claim “X obtains,” S does not have knowledge 
of the proposition, “X obtains.” So let us consider a 
stricter sense of CORNEA pertaining to claims of 
knowledge. This condition, CORNEA+, consists of 
two parts:

(+1) We are entitled to the claim “S knows X” 
only if S is entitled to claim “X obtains.” 
(+2) S is entitled to claim “X obtains” only if it is 
the case that, if X does not obtain, then S would 
have knowledge of the proposition “X does not 
obtain.”

Admittedly, these conditions at first glance may seem 
to be circular, as the knowledge claim in (+2) is subject 
to condition (+1), which is subject to (+2). Put more 
simply, the essence of CORNEA+ is that, for S to 
know a proposition, it must be impossible for S to be 
mistaken about the truth value of that proposition. If 
this is not the case, we make knowledge probabilistic. 
We cannot allow ourselves to say, “There is a 90% 
(or 99%, or 99.999%) probability that S knows X; 
therefore, S knows X,” which is a derivative of (6b). 
This is the very claim implicitly made by anyone 
accepting inferential conclusions as knowledge.
 
What Knowing Looks Like 
 So what does our “knowledge producing” 
process look like given everything said above? I 
would represent it by what I call the functional 



Gettier and the Problem of Induction

Aisthesis      Volume 8,  201739

model of knowing. This model is functional because 
it uses the notation of functions and equations to 
represent epistemic operations, and because, as in a 
function, we would like one “input” to correspond 
to only one possible knowledge “output.” It would be 
inconsistent with our intuitions about knowledge if a 
basic scenario—e.g., there is a barn—could produce 
multiple exclusive knowledge interpretations—there 
is a barn; there is a gas station. One unit of real, 
knowable data should only correspond to one unit of 
known data. 
 If a subject U could know empirical facts, it 
would be represented as follows. Let us assume that 
the empirical fact in question is,
 [7] There is a red apple on the table.
This can be represented by the proposition,
 (7) There is a red apple on the table.
The process by which [7] is converted into 
knowledge, assuming it can be, occurs in two steps. 
First, by the use of the senses, U converts [7] into 
sense data. In this case, there are three pieces of sense 
data: the existence of the apple, the color of the apple, 
and the position of the apple. Next, U assembles the 
sense data into an epistemic state of belief, i.e., a 
proposition. This is represented as follows:
 (S1) P[7]={7}.
 (S2) I{7}=(7).
The various brackets represent different states in 
which information can exist. The square brackets 
represent facts, the squiggly brackets represent sense 
data, and the parentheses represent propositions. 
The two “epistemic functions” involved are sense 
perception (P[X]) and interpretation of sense data 
(I{X}). Thus in (S1), U converts facts into sense 
data, and in (S2) converts that sense data into a 
proposition. For U to have knowledge of [7], all 
information present in [7] must be contained in (7). 
More explicitly, the process can be represented as,
 (S1’) P[apple; red; on table]={apple; red; on 

table}
 (S2’) I{apple; red; on table}=(There is a red apple 

on the table.)
However, neither of the epistemic operations in the 
process above are infallible; each carries with it a 
certain probability that it preserves the information 
in [7] when it is converted from one form to another. 
These probabilities can be expressed by the coefficient 
kn, where 0≤kn≤1. If kn=0, all the information is not 

preserved; if kn=1, all the information is preserved. 
Intermediate values correspond to a probability 
between 0 and 1 that all the information is preserved. 
When multiple conversions occur, as above, the 
coefficients from each conversion compound 
multiplicatively. Considering this, the process above 
becomes,
 (S1’’) P[7]={kP{7}}.
 (S2’’) I{kP{7}}=(kPkI(7)). 
For [7] to be equivalent to (kPkI(7)), both coefficients 
must equal 1. But, neither human perceptive nor 
interpretive faculties are infallible, so U is not entitled 
to claim knowledge of [7]. Thus, U cannot know 
(7). Some might point out that there is a difference 
between being entitled to claim knowledge of 
something and knowing it, and that the latter could 
occur without the former. To the contrary, as long as 
U cannot be certain of (7), (7) lacks full justification 
as a belief, and therefore cannot be known by U. To 
claim otherwise requires the introduction of at least 
one of the false premises (6a) and (6b). It cannot 
be definitively shown that (6a), the reliability of 
sense data or interpretation, holds. Even if it did, we 
could at best only claim probable knowledge, since 
a variety of factors could prevent knowledge even if 
the senses do not err (as in example SK-2). Either 
way, in the end a subject can, at best, probably know 
a proposition, but, to assume (6b), that “probably X 
obtains” implies “X obtains,” is fallacious.9

 On the other hand, a deductive proposition, for 
example,
 (8) 4+5=9
would go through like this for a subject S:
 (D1) P(8)=(8)
 (D2) J(8)=T
Because in this example, information is not converted 
from one form to the other, there are no error 
coefficients. S simply perceives or “calls to mind” 
the proposition (8), which puts S in a consciousness 
state. Then S applies a judgement function, J(8), 
and judges the proposition to be true. This can be 
represented more explicitly as,
 (D1’) P(4+5=9)=(4+5=9)
 (D2’a) J(4+5=9)=(9=9)
 (D2’b) J(9=9)=T
I will take it for granted that my readers agree with 
S’s conclusion.

⁹ X would be something like, “S knows Y.” 



Gettier and the Problem of Induction

Aisthesis      Volume 8,  201740

Weak Justification
 At this point, I will address a possible objection, 
namely, that infallibility is not widely considered 
a necessary condition for justification. Indeed, 
I am arguing for a stronger form of justification 
than usually considered. What I have proposed 
is a set of conditions in which a justified belief 
will always constitute knowledge (given that it is 
true). In contrast, Gettier presents the subjects of 
his SJB scenarios as having justified beliefs even 
though they do not constitute knowledge (1963). 
Additionally, though Goldman seems to sometimes 
equate justification with causality, he considers 
certain beliefs to meet that condition and constitute 
knowledge, which I would not.10 I argue that what 
Gettier and Goldman consider justification is not. At 
most, it is a weak form of justification that at best 
can allow for a weak form of knowledge, “probably” 
knowledge. And so, I would interpret the first SJB 
case as such.11

(i.) Smith is told by the CEO of the company at 
which he and Jones have applied that Jones will 
be hired. (Weak/no justification, since Smith 
could have misheard the CEO or the CEO could 
be lying or mistaken.)
(ii.) Smith concludes that Jones will be hired. 
(Probably/no knowledge, since based on weak 
or no justification.)
(iii.) Smith knows that Jones has ten coins in his 
pocket. (Accepted as given.)
(iv.) Smith concludes that the man who will be 
hired has ten coins in his pocket. (Probably/no 
knowledge, since based on weak/no knowledge.) 

Thus, the paradigm I have proposed avoids the 
Gettier problem because it does not claim that Smith 
has knowledge of (iv.). 

What Can We Know?
Though my solution would greatly reduce the range 
of knowledge, it does not make us completely blind. 
Though we cannot have direct knowledge of the 
external world, we can have a sort of meta-knowledge 
about it. Though I would object to reasoning such as,
 (9) I see a flower; therefore, there is a flower. 

10 See Goldman, 1967, p. 361. 
11 Gettier suggests a justification similar to that in (i.). 

We might still say:
 (10) If I see a flower, then I see a flower.
Yes, (10) is in fact a tautology, but it is still knowable. 
It is true because it takes the form,
 (10’) If X, then X,
which must be true. (10) meets the justification 
condition because it relies on no false premises. The 
only premise (10) requires, (10’), is true.
      We might also have knowledge by virtue of some 
pragmatic assumptions, such as,
 (11) Premises derived from sense data are 

usually/probably true.
Notice that this is different than (6a) in that it makes 
a far weaker claim. (9) allows for us to make such 
statements as,
 (12) If (11) is true, then, if I see a flower, then 

there usually/probably is a flower.
Or rather, in terms of a perception operator,
 (12’) If P(X) probably equals X, then, if P(X), 

then probably X.
 There also exist certain subjectively perceptible 
states like pain, happiness, sorrow, etc., which a 
subject cannot help but know that he or she is 
experiencing. Clark expresses doubt as to whether 
this “incorrigible” knowledge should be considered 
knowledge at all (1963, pp. 47-48). Goldman 
refers to self-knowledge of this type as a “limiting 
or degenerate case of knowledge” (1967, p. 371). 
However, I would argue to the contrary. We might 
rephrase (8’) and take the following course:
 (13) If S feels X, then S feels X. 
 (14) If S feels angry, then S feels angry.
At some level, having the “feeling” of an emotional 
state seems identical to being in that emotional state, 
so we might conclude,
 (15) If S feels angry, then S is angry.
This holds for a variety of subjective states. 

Conclusions
 The complexities in knowledge elucidated 
by Gettier reveal fundamental weaknesses in 
any attempted analysis that seeks to preserve the 
inductive variety. Human experience of the outside 
world through sense-data is fundamentally limited, 
and so no premises derived from that sense-data 
are necessarily true. Thus, sense data premises 
rest on inductive grounds and do not represent 
strong grounds for knowledge. The only viable 



Gettier and the Problem of Induction

Aisthesis      Volume 8,  2017

candidates for knowledge, then, are premises that 
can be shown deductively to be true. Furthermore, 
because inductive knowledge cannot be reduced 
to a deductive line of reasoning—it would need to 
include fallacies (6a) or (6b)—claims to knowledge 
via inductive premises are insubstantial. 

References
Clark, M. (1963). Knowledge and grounds: A 

comment on Mr. Gettier’s paper. Analysis, 24(2), 
46-48. 

      
Gettier, E. L. (1963). Is justified true belief knowledge? 

Analysis, 23(6), 121-123. 
      
Goldman, A. I. (1967). A causal theory of knowing. 

The Journal of Philosophy, 64(12), 357-372. 
      
Ichikawa, J. J., & Steup, M. (2016). The analysis of 

knowledge. In The Stanford Encyclopedia 
of Philosophy. Retrieved from http://www.
plato.stanford.edu/archives/win2016/entries/
knowledge-analysis.

Levin, M. (2006). Gettier cases without false lemmas? 
Erkenntnis, 64, 381-392. doi:10.1007/s10670-
005-5470-2 

      
Wykstra, S. J. (1984). The Humean obstacle to 

evidential arguments from suffering: On 
avoiding the evils of “appearance.” International 
Journal for Philosophy of Religion, 16(2), 73-93. 

41


