Ignorance, Knowledge, and Two Epistemic Intuitions

Abstract

One of the most venerable and enduring intuitions in epistemology concerns the relationship between true belief and knowledge. Famously articulated by Socrates, it holds that true belief does not suffice for knowledge. I discuss a matching intuition about ignorance according to which true belief does not suffice for the absence of ignorance. I argue that the latter intuition undercuts the New View of Ignorance (according to which ignorance is the absence of true belief) and supports the Standard View of Ignorance (according to which ignorance is the absence of knowledge).

Socrates: “I too speak rather in ignorance; I only conjecture. And yet that knowledge differs from true opinion is no matter of conjecture with me. There are not many things which I profess to know, but this is most certainly one of them.”

--Meno (98b) in (Plato 1957)

1 Introduction

A central and enduring question in epistemology concerns the relationship between true belief and knowledge. An important related question about ignorance is increasingly attracting much more attention than it has historically.¹ It concerns the relationship between true belief and ignorance.²

I discuss both of these relationships in this paper. I do so with an offensive and defensive objective. My offensive objective is to critique a relative newcomer in the literature on ignorance, namely the New View of Ignorance according to which ignorance is the absence of true belief.³ My defensive objective is to defend a much more traditional view in this literature, namely the Standard View of Ignorance according to which ignorance is the absence of knowledge.⁴ I aim to achieve these objectives with a novel argument that links an important intuition about ignorance to a venerable and widely-shared intuition about knowledge.⁵

2 Some Preliminaries

Contemporary epistemologists widely agree that true belief is necessary but not sufficient for knowledge. We may put this point in terms of the following two theses:

Knowledge Necessity Thesis: True belief is necessary for knowledge (i.e., knowledge entails true belief).

Knowledge Sufficiency Thesis: True belief is sufficient for knowledge (i.e., true belief entails knowledge).

Contemporary epistemologists widely accept the Knowledge Necessity Thesis, but also widely reject the Knowledge Sufficiency Thesis. Given its widespread acceptance and for ease of reference, we may call the “Standard View of Knowledge” the conjunction of the Knowledge Necessity Thesis with the denial of the Knowledge Sufficiency Thesis. Given the widespread rejection of the latter thesis, the following thesis has found little traction in epistemology:

Knowledge/True Belief Equivalence Thesis: True belief is necessary and sufficient for knowledge (i.e., knowledge entails and is entailed by true belief).

This lack of traction can be explained—at least in significant part—by the appeal of a venerable and widely-held epistemic intuition that supports the Standard View of Knowledge. In honor of Socrates, we may call it the “Socratic Knowledge Intuition.” It holds that it is not the case that true belief suffices for knowledge.⁶ In other words:

Socratic Knowledge Intuition: True belief does not suffice for knowledge (i.e., true belief does not entail knowledge).

Given this intuition, there is a gap—call it the “Knowledge Gap”—between true belief and knowledge. Much, though not all, epistemological work has been concerned with how to bridge this gap. If the Socratic Knowledge Intuition is correct, (mere) true belief is not knowledge.⁷

Interestingly, the latter intuition is paralleled by a matching intuition about ignorance—we may call it the “Matching Ignorance Intuition.”⁸ It holds that it is not that case that (mere) true belief suffices for the absence of ignorance. In other words:

Matching Ignorance Intuition: True belief does not suffice for non-ignorance (i.e., true belief does not entail non-ignorance).

Given this intuition, there is a gap—call it the “Ignorance Gap”—between true belief and ignorance such that true belief is compatible with ignorance.⁹ As we will see, the Matching Ignorance Intuition parallels the Socratic Knowledge Intuition, for similar cases exemplify both.

3 Two Views of Ignorance

Because it holds that ignorance is the absence of true belief, accepting the New View of Ignorance requires accepting the following related thesis:

Ignorance/Absence of True Belief Equivalence Thesis: Ignorance is equivalent to the absence of true belief (i.e., ignorance entails and is entailed by the absence of true belief).

By contrast, because it holds that ignorance is the absence of knowledge, accepting the Standard View of Ignorance requires accepting the following related thesis:

Ignorance/Absence of Knowledge Equivalence Thesis: Ignorance is equivalent to the absence of knowledge (i.e., ignorance entails and is entailed by the absence of knowledge).

The Standard and New Views of Ignorance are in agreement about:

Ignorance/Absence of True Belief Sufficiency Thesis: The absence of true belief entails ignorance.

They differ, however, on:

Ignorance/Absence of True Belief Necessity Thesis: Ignorance entails the absence of true belief.

The New View of Ignorance affirms the latter whereas the Standard View of Ignorance rejects it.

Interestingly, the Standard View of Ignorance and the Standard View of Knowledge parallel each other in being supported by sister intuitions: the Matching Ignorance Intuition and the Socratic Knowledge Intuition respectively. The two views are also structurally similar in that accepting each requires rejection of a respective equivalence thesis: in the case of the Standard View of Knowledge, that knowledge is equivalent to true belief (the Knowledge/True Belief Equivalence Thesis); and, in the case of the Standard View of Ignorance, that ignorance is equivalent to the absence of true belief (the Ignorance/Absence of True Belief Equivalence Thesis).

Does the New View of Ignorance also bear a structural similarity to a view concerning the nature of knowledge? Indeed it does, namely to Sartwell’s Thesis according to which knowledge is (mere) true belief.¹⁰ Accepting Sartwell’s Thesis requires accepting the Knowledge/True Belief Equivalence Thesis; accepting the New View of Ignorance requires accepting the Ignorance/Absence of True Belief Equivalence Thesis.¹¹

A major reason Sartwell’s Thesis has not gained more traction in epistemology is that accepting it comes at quite a steep intuitive cost, namely that of rejecting the venerable and widely-shared Socratic Knowledge Intuition. In the next section, I argue that accepting the New View of Ignorance also comes at a similar steep intuitive cost, namely that of rejecting the Matching Ignorance Intuition.

4 The Steep Intuitive Cost of the New View of Ignorance

One of the most famous discussions of the Socratic Knowledge Intuition comes in the Theaetetus. At 187b4–8, Theaetetus proposes that knowledge is true belief (Plato 1961). This provokes Socrates to consider how false belief is possible, and after five failed attempts to answer the question, the discussion ends with Socrates returning to Theaetetus’s proposal. At 200d–201c, Socrates wields a counter-example against it: a jury can be persuaded to have a true belief as a result of the rhetorical skill of a jurist intent on getting a certain verdict on the basis of unsubstantiated hearsay, and such a true belief does not count as knowledge (Ibid.).

A case such as this, Socrates avers, exemplifies how (mere) true belief does not suffice for knowledge. We may add, moreover, that such a case can also be taken to exemplify how (mere) true belief does not suffice for non-ignorance; for instance, a jury’s (mere) true belief that p does not suffice for the jury’s not being ignorant that p. This accords with what the Matching Ignorance Intuition tells us, and it parallels the Socratic Knowledge Intuition in that the same cases exemplify both.

As further illustrations of this parallelism, consider the following true propositions:

• p₁: Female platypuses lay eggs.

• p₂: The Dutch are the largest per capita consumers of licorice in the world.

• p₃: Shakespeare’s epitaph contains a curse for grave robbers.

• p₄: (6 × 9) + (6 + 9) = 69

• p₅: No three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ

• for any integer value of n greater than 2.¹²

Now consider the following five cases:

Al irrationally believes that p₁ as a result of a strange schizophrenic hallucination. Because of the irrational basis on which he believes this, it seems quite counter-intuitive to claim that he knows that p₁, and also quite intuitive to claim that he is ignorant that p₁ despite the truth of his belief.

Betty, who loathes licorice, believes that p₂, and her belief results from a hasty generalization based on her petulant anti-Dutch prejudice. It seems quite counter-intuitive to claim that she knows that p₂, and also quite intuitive to claim that she is ignorant that p₂ despite the truth of her belief, because of the unjustified way she believes it.

Charles gullibly believes that p₃ based on reading a highly unreliable source such as the National Enquirer, a notoriously untrustworthy American tabloid. Once again, it seems quite counter-intuitive to claim that he knows that p₃ and quite intuitive to claim that he is ignorant that p₃ despite the truth of his belief, because of the highly unreliable way he came to believe it.

Danielle believes that p₄ because, while on the operating table for brain surgery, a surgeon accidentally stimulates her prefrontal cortex in a way that happens to give rise to this belief. Yet again, it seems quite counter-intuitive to claim that she knows that p₄ and quite intuitive to claim that she is ignorant that p₄ despite the truth of her belief, because of the accidental way she came to believe it.

Ernest believes that p₅ as a result of committing a mathematical blunder and his over-confidence about not needing to check his work. Once again, it seems quite counter-intuitive to claim that he knows that p₅ and quite intuitive to claim that he is ignorant that p₅ despite the truth of his belief, because of the way his belief arose from a blunder and over-confidence.

In all five of these cases, (a) the believer’s true belief does not suffice for knowledge (as indicated by the Socratic Knowledge Intuition); (b) the believer’s true belief does not suffice for his or her being non-ignorant (as indicated by the Matching Ignorance Intuition); (c) the Socratic Knowledge Intuition and the Matching Ignorance Intuition are exemplified by these same cases.¹³

In illustrating the steep intuitive cost of the New View, I have envisaged examples where a true belief is irrational, or unjustified, unreliably formed, or accidentally acquired, or based on a blunder and over-confidence. We can also make this point, however, with examples other than mine. DeNicola (2017), for instance, provides telling examples involving the removal of ignorance that implicitly invoke this intuition.¹⁴

5 Diagnosis

I have argued above that the Matching Ignorance Intuition undercuts the New View and supports the Standard View of ignorance. What would lead defenders of the New View to take a position at odds with this intuition? This calls for some diagnosis.

We may begin by noting that, in all the cases given above in this paper, someone believes a true proposition and is not ignorant of the proposition in question. Indeed, someone who believes that p (where p is true) but who lacks knowledge that p is not ignorant of p. In arguing that ignorance is not the absence of knowledge that p, Van Woudenberg (2009, pp. 373–374), for instance, avers that someone who lacks knowledge that p (as in Gettier-type cases) is not ignorant of p. Peels (2017b, p. 167) makes a similar claim. Consider his example of Jim, a track diver from Miami who.

believes contrary to all evidence that he is going to be the next president of the United States. He thus comes to believe the proposition q that the next president of the United States currently lives in Miami. As is turns out, the next president is Ms. Jones, a female congress member living in Miami whom Jim has never heard of. In this case Jim truly believes, but does not know that q. Is he ignorant of q? On the New View, he is not. There are all sorts of truths in the neighborhood that, on the New View he is ignorant of and it is hard mentally to isolate q from all those other truths, truths such as Ms. Jones is going to be the next president, Ms. Jones live in Miami, and The next president is currently a congress member. Adherents of the New View sometimes suggest that we may be inclined to think that Jim is ignorant of q because we know that he is ignorant of other propositions. If we focus on q, however, the idea is that it seems that Jim is not ignorant of q (p. 167, italics in original).

It is true that, in each case I give above, the believer is not ignorant of the true proposition in question. This is also true in Peels’s case of Jim. In fact, in each of these cases the believer would not have the belief in question were s/he ignorant of the true proposition in question, for believing that p requires non-ignorance of some proposition p.

But so what? The key issue here is not whether (i) a true belief that p (or q or what have you) entails non-ignorance of p, but rather whether (ii) a true belief that p entails non-ignorance that p. The Matching Ignorance Intuition and the Standard View of Ignorance are perfectly compatible with (i); it is (ii) with which they are not compatible. To reject them on the basis of (i) is to commit an ignoratio elenchi. Just because one is not ignorant of a true proposition p, it does not follow that one is not ignorant that p.¹⁵ While ignorance of p entails ignorance that p, the latter does not entail the former.

To see why this is so, take any true proposition, say p₁ as an example, and take any propositional attitude toward it such as entertaining that p₁, doubting that p₁, anticipating that p₁, hoping that p₁, desiring that p₁, fearing that p₁, believing that p₁, or knowing that p₁. If someone S is ignorant of p₁, then S cannot have any of these propositional attitudes toward p₁. But just because S is not ignorant of p₁, it hardly follows that S is not ignorant that p₁. For instance, if (say) S entertains that p₁ or doubts that p₁, then S is not ignorant of p₁, but it does not follow from this that S is not ignorant that p₁, mutatis mutandis for any true proposition. Thus it is clear that non-ignorance of a proposition p does not suffice for non-ignorance that p.

A defender of the New View might reject the Matching Ignorance Intuition on the ground that someone who believes a true proposition that p is not ignorant of the fact that p. Peels (2010, p. 60; 2012, p. 745), for instance, avers that someone who believes that p but fails to know that p is not ignorant of the fact that p. To see why this response does not give us a good reason to reject the Matching Ignorance Intuition, let’s consider more closely what is meant by “fact” since this term has two important philosophically-relevant senses worth disambiguating. In one sense, a fact is a true proposition; in the other sense, a fact is a state of affairs (a truth-maker) in virtue of which a proposition is true.

If we take “fact” in the sense of a true proposition, this response amounts to simply reasserting the New View and begging the question against the Matching Ignorance Intuition, for it simply reasserts that someone who believes a true proposition p is not ignorant that p.

If we take “fact” in the sense of a truth-maker, then the response is manifestly implausible in virtue of it being manifestly implausible that the believers in the examples above are not ignorant of the truth-makers in question.¹⁶ The response fails on both these philosophically-relevant senses of “fact.”

In sum, one can be led to reject the Matching Ignorance Intuition (and by extension the Standard View of Ignorance) by conflating non-ignorance of a (true) proposition p with non-ignorance that p, and/or by conflating non-ignorance of a fact understood as a true proposition with non-ignorance of a fact as a truth-maker. We have good reason, however, to avoid such conflations.

6 Conclusion: Why the Standard View Is Preferable to the New View

We have seen above how the New View founders on the Matching Ignorance Intuition. The Standard View of Ignorance, by contrast, not only harmonizes with, but finds support in this intuition. Hence, insofar as we share this epistemic intuition—one that parallels the Socratic Knowledge Intuition, one of the oldest and most venerable epistemic intuitions—we have reason to prefer the Standard View of Ignorance to the New View. Similar to how Sartwell’s Thesis proves too wide in counting any true belief whatsoever as knowledge that p, the New View also proves too wide in counting any true belief whatsoever as non-ignorance that p. However new it may be, the New View of Ignorance is vitiated by an intuition that parallels an old Socratic intuition about knowledge.¹⁷

Appendix

If conjoined with Sartwell’s Thesis, the New View entails the Standard View, and therefore the former does not offer an alternative to the latter. This can be proved as follows (where p is some true proposition, Kp is knowledge that p, and Bp is belief that p):

• 1. Kp ↔ Bp Implication of Sartwell ' s Thesis

• 2. ${\displaystyle \begin{array}{cc}\mathrm{I}p\leftrightarrow \sim \mathrm{B}p& \mathrm{Implication}\ \mathrm{of}\ \mathrm{New}\ \mathrm{View}\ \mathrm{of}\ \mathrm{Ignorance}\end{array}}$

• 3. ${\displaystyle \begin{array}{cc}\left(\mathrm{K}p\to \mathrm{B}p\right)\&\left(\mathrm{B}p\to \mathrm{K}p\right)& \mathrm{From}\ 1,\mathrm{Equivalence}\end{array}}$

• 4. ${\displaystyle \begin{array}{cc}\mathrm{K}p\to \mathrm{B}p& \mathrm{From}\ 3,\mathrm{Simplification}\end{array}}$

• 5. ${\displaystyle \begin{array}{cc}\mathrm{B}p\to \mathrm{Kp}& \mathrm{From}\ 3,\mathrm{Simplification}\end{array}}$

• 6. ${\displaystyle \begin{array}{cc}\left(\mathrm{I}p\to \sim \mathrm{B}p\right)\&\left(\sim \mathrm{B}p\to \mathrm{I}p\right)& \mathrm{From}\ 2,\mathrm{Equivalence}\end{array}}$

• 7. ${\displaystyle \begin{array}{cc}\mathrm{I}p\to \sim \mathrm{B}p& \mathrm{From}\ 6,\mathrm{Simplification}\end{array}}$

• 8. ${\displaystyle \begin{array}{cc}\sim Bp\to \mathrm{I}p& \mathrm{From}\ 6,\mathrm{Simplification}\end{array}}$

• 9. ${\displaystyle \begin{array}{cc}\sim \mathrm{B}p\to \sim \mathrm{K}p& \mathrm{From}\ 4,\mathrm{Contraposition}\end{array}}$

• 10. ${\displaystyle \begin{array}{cc}\mathrm{I}p\to \sim \mathrm{K}p& \mathrm{From}\ 7\ \mathrm{and}\ 9,\mathrm{Hypothetical}\ \mathrm{Syllogism}\end{array}}$

• 11. ${\displaystyle \begin{array}{cc}\sim \mathrm{K}p\to \sim \mathrm{B}p& \mathrm{From}\ 5,\mathrm{Contraposition}\end{array}}$

• 12. ${\displaystyle \begin{array}{cc}\sim \mathrm{K}p\to \mathrm{I}p& \mathrm{From}\ 8\ \mathrm{and}\ 11,\mathrm{Hypothetical}\ \mathrm{Syllogism}\end{array}}$

• 13. ${\displaystyle \begin{array}{cc}\left(\mathrm{I}p\to \sim \mathrm{K}p\right)\&\left(\sim \mathrm{K}p\to \mathrm{I}p\right)& \mathrm{From}\ 10\ \mathrm{and}\ 12,\mathrm{Addition}\end{array}}$

• 14. ${\displaystyle \begin{array}{cc}\mathrm{I}p\leftrightarrow \sim \mathrm{K}p& \mathrm{From}\ 13,\mathrm{Equivalence}\end{array}}$

The conclusion of this argument—namely, Ip ↔ ~ Kp—takes ignorance to be, in effect, equivalent to the absence of knowledge.