Logical Properties of Warrant

Here, I talk about the epistemologists’ technical notion of “warrant” and some controversies about it.*

[*Based on: “Logical Properties of Warrant,” Philosophical Studies 122 (2005): 171-82.]

1. The Notion of Warrant

Alvin Plantinga introduced the epistemologists’ technical use of “warrant”, to refer to the property that a true belief must have (besides being a true belief) in order to qualify as knowledge.

E.g., suppose you think knowledge = justified, true belief. In that case, you think warrant = justification.

But no one thinks that anymore. Suppose you think knowledge = justified, true belief with no (non-misleading) defeaters. In that case, you think warrant = having justification with no (non-misleading) defeaters.

Etc.

Here a more formal interpretation: Warrant is the relation, W, such that, necessarily, S knows that P iff S believes that P, P is true, and W(s,p).

Aside: Please don’t abuse this word.

Btw, “warrant” is one of the most annoyingly used words by epistemologists. Ever since Plantinga introduced that usage, epistemologists started throwing the word “warrant” around all over the place. In particular, they started replacing “justification” with “warrant” in their discussions (i.e., everything about the discussion will be written exactly as if they’re talking about justification, except that the word “warrant” appears in place of “justification”), thereby causing confusion as to whether they are using Plantinga’s technical sense, or the ordinary English sense (which is pretty close to “justification”).

Example: talking in a way that presupposes that there are degrees of warrant. Justification comes in degrees, but this does not mean that warrant (in Plantinga’s sense) comes in degrees. E.g., there aren’t degrees of “having no false beliefs in its evidential ancestry” or degrees of “having no defeaters”.

So, if you’re a student or epistemologist, please don’t throw “warrant” in when you are talking about justification.

That said, I’m actually going to discuss warrant in the technical sense here. If you have trouble sleeping, you may want to take a printout of this post to bed with you.

2. Warrant Is Not Unique

Here was one thing I noticed about the literature on warrant: epistemologists assumed (and probably still do, since they’re not paying enough attention to me) that there was a unique property satisfying the definition of warrant, i.e., a unique thing that, when conjoined with true belief, yields knowledge.

That’s not true. If any property satisfies the warrant role, then it’s guaranteed that other properties do as well. I.e., if Ksp = (Bsp & Tp & Wsp) for some relation W, then there will also be a different relation, W', such that Ksp = (Bsp & Tp & W'sp).

(Read: If S’s knowing P is equivalent to S’s believing P and P’s being true and S’s standing in W to P, then there is a distinct relation, W', such that S’s knowing P is also equivalent to S’s believing P and P’s being true and S’s standing in W' to P.)

Example

Call the following the Simple Defeasibility Analysis:

S knows that P iff:

i) S believes that P,

ii) P is true,

iii) S is justified in believing that P, and

iv) there are no defeaters for S’s justification for P.

Now consider the following, Alternative Defeasibility Analysis:

S knows that P iff:

i) S believes that P,

ii) P is true,

iii) S is justified in believing that P, and

iv’) there are no defeaters for S’s justification for P that are compatible with P.

Now, notice, first, that the Simple Defeasibility Analysis is, overall, logically equivalent to the Alternative Defeasibility Analysis. These aren’t meaningfully different theories; if one is correct, they are both correct. To see this, notice

a) If (iv) holds then obviously (iv’) holds, and

b) Given (ii), if (iv’) holds, then (iv) holds. (The truth of (ii) guarantees that there are no defeaters that are incompatible with P, and the truth of (iv’) means there are no defeaters that are compatible with P, so overall there are no defeaters.)

Notice, second, that the account of “warrant” in the two theories differs: in the Simple Defeasibility Analysis, warrant is the conjunction of (iii) and (iv) (i.e., warrant = being justified in the absence of defeaters). In the Alternative Defeasibility Analysis, warrant is the conjunction of (iii) and (iv’), which is not equivalent to the conjunction of (iii) and (iv).

So if either version of Defeasibility Analysis is correct, then there are two, non-equivalent properties that could be called “warrant”.

Generalization

For a trivial, general proof, assume that Ksp = Bsp & Tp & Wsp. So W satisfies the definition of “warrant”.

Now let W’sp = (p → Wsp). Then W’ is obviously non-equivalent to W. But (Bsp & Tp & Wsp) is nevertheless equivalent to (Bsp & Tp & W’sp). So W’ also satisfies the definition of “warrant”.

Because of this, we should either say there is no such thing as warrant (if we insist that it be unique), or that there are multiple, non-equivalent warrant properties.

Let’s take the latter, less radical option, so we can still have something to talk about.

3. Warrant Does and Does Not Entail Truth

At the time I wrote the paper (circa 2005), there was a debate in the literature about whether warrant (whatever it is) must entail truth. But this is a fruitless debate, because it is guaranteed that some warrant properties entail truth, while others do not.

To see this:

(i) Assume what W is a warrant property that entails truth (i.e., Ksp = [Bsp & Tp & Wsp] and Wsp entails Tp). Now consider this other warrant property: W'sp = (p → Wsp). W' is also a warrant property (as discussed above), and W'sp obviously does not entail p (if p is false, W'sp is automatically true). So, if there is a warrant property that entails truth, then there is also one that doesn’t.

(ii) Now assume that W is a warrant property that doesn’t entail truth (i.e., Ksp = [Bsp & Tp & Wsp] and Wsp doesn’t entail Tp). Now consider this other warrant property:

W"sp = (p & Wsp). W" is also a warrant property (if conjoined to true belief, it yields knowledge), and W"sp obviously entails that p is true. So, if there is a warrant property that doesn’t entail truth, then there is also one that does.

4. Is Warrant Closed Under Entailment?

There’s a debate in epistemology about whether “knowledge is closed under entailment”. This means something like: if you know P, and P entails Q, then you know Q.

We could similarly wonder whether warrant is closed under entailment, i.e., whether if P is warranted, and P entails Q, Q must also be warranted.

We could also wonder about the relation between knowledge closure and warrant closure. At least one philosopher thought that if knowledge is closed under entailment, then warrant must also be. That turns out to be a mistake.

If knowledge is closed under entailment, then some warrant properties are closed under entailment, while others are not.

Assume that knowledge is closed under entailment.

(i) Now assume W is a warrant property that satisfies closure, so Ksp = [Bsp & Tp & Wsp] and whenever (Wsp & p entails q), then Wsq.

Then consider the alternative warrant property, W', where W'sp = (p → Wsp). W' violates closure. To see this, let q be any true proposition that lacks W' (there must be some, since, by all accounts truth doesn’t entail warrant). And let p be any false proposition that entails q (again, there must be some such).

Then (p → Wp) holds, since p is false, so p satisfies W'. By hypothesis, q violates W'. So we have a counterexample to closure for W'.

Hence, if there is a warrant property that satisfies closure, then there is another one that doesn’t.

(ii) Now assume, instead, that W is a warrant property that violates closure. Now just let W'sp = (Wsp and S stands in W to every logical consequence of p). W' obviously satisfies closure. Also, given our assumption that knowledge is closed under entailment, the two analyses

Ksp = [Bsp & Tp & Wsp]

Ksp = [Bsp & Tp & W'sp]

are equivalent. So W' is also a warrant property.

Hence, if there is a warrant property that violates closure, then there is another one that satisfies it.

Combining (i) and (ii): if knowledge satisfies closure, then there are warrant properties that violate closure and others that satisfy it.

If knowledge is not closed under entailment (for interesting reasons), then no warrant properties are closed under entailment.

Epistemologists don’t care about case where belief violates closure; in other words, we tend to restrict the domain of cases considered to those in which the subject in fact believes a particular logical consequence of p. So we stipulate that belief is closed under entailment in the cases of interest.

Truth is trivially closed under entailment.

So if knowledge fails to be closed under entailment (in the cases of interest), it has to be because warrant fails closure.

5. Conclusion

• Stop talking about “warrant” as a unique property. There are multiple warrant properties.

• Also stop debating whether warrant entails truth. Some warrant properties do and others do not.

• If knowledge violates closure, then so does warrant. If knowledge satisfies closure, then some warrant properties also satisfy it while others do not.