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.
But once you have multiple warrant properties you can arrange them in a logical strength lattice. In particular, if W1 and W2 are both warrant properties, then Wd = W1 v W2 is also a warrant property.
a) Ksp = Bsp & p & W1sp
b) Ksp = Bsp & p & W2sp
c) Bsp & p & (W1sp v W2sp) = (Bsp & p & W1sp) v (Bsp & p & W2sp) = Ksp v Ksp = Ksp.
Given that warrant is a property that a true belief "must have" in order to be knowledge, the warrant-propertiness of Wd would seem to imply that neither W1 nor W2 is, in fact, a warrant! After all, the true belief/knowledge could satisfy W1 instead of W2 (so the true belief does not need to satisfy W2 in order to be knowledge, and thus W2 is not warrant). And similarly for W1.
Of course if W1 -> W2, then anything that must satisfy W1 must also satisfy W2. In that case, W2 might be a warrant property -- satisfying W1 is not an alternative to satisfying W2, but only a particular way of satisfying W2. For example, (iv) -> (iv'), so it's not the case that (iv) "must be" true in order to make Ksp from Bsp; we can get away with just (iv') -- we can safely ignore defeaters of Jsp that are not compatible with p. So if (iv') is a warrant property, then (iv) is NOT a property that a true belief "must have" in order to be knowledge -- it does not satisfy Platinga's definition of warrant.
Follow the logic thru, and it seems like warrant must the the logically weakest property that turns belief into knowledge. That is, there is, contrary to your claim here, a unique warrant property.
Mark, the way I'm understanding these, W1 and W2 are going to be logically equivalent *given* (p & Bsp) (although they are not equivalent tout court). Everyone agrees that in order to have K, you have to have p & Bsp, so it's also going to be true that to have knowledge, you have to have both W1 and W2.
So all of the things that I'm calling "warrant properties" are going to be things that you have to have in order to have knowledge.
OK, I think I understand that. If W1 and W2 are both warrant properties, there may well exist s and p such that W1sp <> W2sp, but for all s and p, (Bsp & p) -> (W1sp = W2sp). Since all knowledge "must have" Bsp & p, thus all knowledge "must have" both W1 and W2. I was looking at "must have" as a regulation rather than as a regularity!
But I think my argument still shows that there is a unique weakest warrant property, being the disjunction of all warrant properties. (Hmmm. Or possibly just the least upper bound of all warrant properties. I'm not sure how we feel about infinite disjunctions -- especially if the infinite set being disjoined is uncountable....)
Anyway, I'm sure epistemologists would be interested in knowing what properties that LUB has. Based on the constructions you gave for W' and W", it seems like maybe the LUB would not entail truth and would not be closed under entailment. Have you given the question any consideration?
Yes, there is a weakest warrant property and also a strongest one; see comment by technosentience.
Yes, it seems like the weakest one would violate closure and not entail truth. However, the weakest warrant property doesn't obviously have any better claim to being called "warrant" than the strongest warrant property, or some other warrant property. Intuitively, properties like (p -> Bp -> Kp) are less natural candidates for "the" warrant property, if we wanted to pick out one canonical warrant property.
Oct 16, 2022·edited Oct 16, 2022Liked by Michael Huemer
I haven't read the epistemological papers talking about this, but couldn't one reason we want to talk of warrant at all is to ask questions about the value of knowledge?
For example, we could ask: "If knowledge is true, warranted belief, then does the value of that belief come from its truth, its warrant, or both? If both, is the value additive or is it an organic unity? What about truth, warrant, or their combination makes knowledge valuable?"
So, one of the goals of talking about warrant could potentially be not only to indicate what, when added to truth, makes a belief knowledge, but also what might make knowledge valuable. If that is or should be one of the goals, then a lot of your alternative warrant properties clearly fail in this regard.
For example, if your example is correct, what matters isn't that there is justification which isn't defeated by defeaters compatible with P, what matters (if knowledge has any value at all beyond true belief) would presumably just be that the justification remains undefeated period.
The upshot would seem to be that your critique fails: we could ask whether there is one unique property which both makes true belief into knowledge and makes that knowledge valuable, whether this property guarantees truth, and whether this property is closed under entailment.
I would think that it's good to lack defeaters of either kind. It's good to lack defeaters that are compatible with P, and it's also good to lack defeaters that are incompatible with P.
You could say that it is best to lack any defeaters whatsoever. True, but lacking incompatible defeaters is already entailed by the truth condition, so one might think it's a little redundant. The value of warrant should be only part of the value of knowledge; in particular, it doesn't have to redundantly include the value of truth.
Oh, I see. That's interesting. I didn't realize that the value of warrant could potentially be split parallel to the split of the work done between W and W' (i.e. such that W includes the work or value entailed by truth while W' excludes it).
I'm not sure that would work with every theory of the value of knowledge, though, and in particular organic unity theories. For example, if you think that the value of knowledge lies in "grasping the truth" (this is a metaphor, and I don't really know how to spell out the metaphor), then you might say that the value of such "grasping the truth" cannot be split between the value entailed by truth (e.g. there being no defeater incompatible with truth) and that entailed by "grasping" (e.g. there being no defeater compatible with truth). Nonetheless, the "grasping" (i.e. the warrant) could play a substantial explanatory (but non-additive) role in making "grasping the truth" valuable.
Then again, maybe there will be another parallel split between the substantial explanatory (but non-additive) roles for W and W', with W (perhaps redundantly) including some of the explanatory work truth does in making "grasping the truth" valuable while W' excludes that work.
Oct 15, 2022·edited Oct 16, 2022Liked by Michael Huemer
Colloquially, knowledge is understood as a true belief, with or without justification, so the question of justifying the need for ‘justification’ (of a true belief) is of itself an important one.
I will try to expand on the term ‘justification’ and relate to ‘warrant’.
Knowledge that P
= knowledge that ‘belief that P’ is true
= having a sufficient reason that ‘belief that P’ is true.
The truth value of <knowledge that ‘belief that P’ is true> consists not just in the observer-independent truth of P, but in the (higher order) knowledge ‘that’ P is true. Another way, in order to say, truthfully, that we know something, we must know that we know it with certainty, and this implies knowledge of the ‘truthmaker’ for our certainty. The criterion of certainty may be satisfied in different ways, for example, we may have certainty that P, or, certainty that the probability that P is (Xmin to Xmax)%, but ‘P’ is a different type of fact from ‘probability that P’; equivocation between these two types gives rise to a common error, a category mistake: the false belief that we may ‘know’ something even without certainty.
I understand this is consistent with the ‘no defeaters’ requirement, provided that the absence of knowledge that there are ‘no hidden defeaters’ is of itself a defeater (of knowledge that P). I also understand that your use of ‘warrant’ implies compatibility of W and W’, but in order to accomplish compatibility under the ‘no hidden defeaters’ condition there must be universality/objectivity of justification (sufficient reason), so either W=W’ or one of these is incorrect.
If (ii) could be false, then (iv’) is incorrect. As a matter of epistemic principle, (ii) can be false, therefore (iv’) is incorrect; the possibility of defeaters that are incompatible with P must be included, because it is possible for (iii)&(iv’) not to “warrant” even if there are no ‘P compatible’ defeaters.
I'm a fallibilist, i.e., I accept knowledge without certainty. This may sound wrong, but I basically think you have to give up the 'certainty' condition to account for >99% of the things we normally call "knowledge". I.e., we might be inclined to *say*, "knowledge requires certainty", but we don't actually use the word that way.
I would also deny the condition that knowing p implies knowing that you know p, because this leads to an infinite regress.
I would not call anything uncertain ‘knowledge’ but a ‘practical assumption’; a fallabilist accepts that he could be wrong, but is willing to try because doing nothing is not an option. The reason for my insistence on ‘certainty’ as a condition of ‘knowing’ is that Knowledge is always used in a normative sense, it is used as an argument, as a reason to sanction others, so it has ethical (and, less obviously, ontological) implications. For example, “I know that I am right, therefore you are wrong and there is no need for further deliberation, so you must comply, or else”, which is an implicit commitment to violence as the ultimate arbiter of facts.
On a purely logical level, if you do not know that P with certainty then what exactly do you know? You only know that P is probably true, but not certain to be true, and this is a different object/claim than ‘P is true’, so to evade the distinction would amount to a practical violation of the law of identity.
Regarding the charge of infinite regress, this was indeed a clumsy expression on my part. I should have said: “we must know it with certainty”. All I can defend here is that knowledge that P implies the awareness that it is ‘I’ who knows (but self-awareness is not an additional item of knowledge, because it is not falsifiable).
> Now let W’sp = (p → Wsp). Then W’ is obviously non-equivalent to W.
Nitpicking, this is actually incorrect: for example, if Wsp itself is of the form (p -> Bsp -> Ksp), (p -> Wsp) is logically equivalent to Wsp (as (p -> (p -> X)) <-> (p -> X) for all X, even under necessity). But the construction from part 3 works for all cases, since those propositions imply different consequences.
In general, one can rearrange the definition Ksp = Bsp & p & Wsp as:
1) Ksp -> Wsp
2) Wsp -> (Bsp -> p -> Ksp)
Thus in some sense (Bsp -> p -> Ksp) is the minimum warrant property and Ksp is the maximum one, with others sandwiched between them in their logical strength.
Well, there is the example from the OP. On one account, W = the property of being justified in the absence of defeaters. W' = the property of being justified in the absence of (defeaters that are compatible with p).
Those are non-equivalent properties. W entails truth, whereas W' does not.
At the risk of sounding obtuse, what would a concrete example of each of those be in real life?
One of the places I lose the proof is how W’ could be different from W when the article also asserts in the prior section that the systems are logically equivalent. What would a defeater that is not compatible with p even mean? My naive expectation is that a defeater that is not compatible with p is not a defeater, and thus W’ is W, and then I lose it all.
My hope is that an illustrating concrete example of a form similar to “Susie knows that rain is wet (Ksp) because she believes it (Bsp) and it is true (Tp) and because there is no evidence otherwise (Wsp).” But perhaps with an example that shows the differences.
I’m sure the literature abounds. I’m just a layman.
So we could say Sue knows that rain is wet because she believes it, it's true, she's justified in believing it, and there are no defeaters for the proposition that rain is wet.
Or: because she believes it, it's true, she's justified in believing it, and there are no defeaters for the proposition that rain is wet that are compatible with rain being wet.
W and W' are equivalent only given (Bp & p). I.e., you can have W be different from W', yet (W & p & Bp) be equivalent to (W' & p & Bp). It's a general point about logic that you can have A /= B, but (A&C)=(B&C).
A defeater that's incompatible with p would be, say, ~p. If p is false, then ~p would be a true proposition that if added to your beliefs would make you not justified in believing p. So that's a defeater.
Very nice.
But once you have multiple warrant properties you can arrange them in a logical strength lattice. In particular, if W1 and W2 are both warrant properties, then Wd = W1 v W2 is also a warrant property.
a) Ksp = Bsp & p & W1sp
b) Ksp = Bsp & p & W2sp
c) Bsp & p & (W1sp v W2sp) = (Bsp & p & W1sp) v (Bsp & p & W2sp) = Ksp v Ksp = Ksp.
Given that warrant is a property that a true belief "must have" in order to be knowledge, the warrant-propertiness of Wd would seem to imply that neither W1 nor W2 is, in fact, a warrant! After all, the true belief/knowledge could satisfy W1 instead of W2 (so the true belief does not need to satisfy W2 in order to be knowledge, and thus W2 is not warrant). And similarly for W1.
Of course if W1 -> W2, then anything that must satisfy W1 must also satisfy W2. In that case, W2 might be a warrant property -- satisfying W1 is not an alternative to satisfying W2, but only a particular way of satisfying W2. For example, (iv) -> (iv'), so it's not the case that (iv) "must be" true in order to make Ksp from Bsp; we can get away with just (iv') -- we can safely ignore defeaters of Jsp that are not compatible with p. So if (iv') is a warrant property, then (iv) is NOT a property that a true belief "must have" in order to be knowledge -- it does not satisfy Platinga's definition of warrant.
Follow the logic thru, and it seems like warrant must the the logically weakest property that turns belief into knowledge. That is, there is, contrary to your claim here, a unique warrant property.
Right?
Mark, the way I'm understanding these, W1 and W2 are going to be logically equivalent *given* (p & Bsp) (although they are not equivalent tout court). Everyone agrees that in order to have K, you have to have p & Bsp, so it's also going to be true that to have knowledge, you have to have both W1 and W2.
So all of the things that I'm calling "warrant properties" are going to be things that you have to have in order to have knowledge.
OK, I think I understand that. If W1 and W2 are both warrant properties, there may well exist s and p such that W1sp <> W2sp, but for all s and p, (Bsp & p) -> (W1sp = W2sp). Since all knowledge "must have" Bsp & p, thus all knowledge "must have" both W1 and W2. I was looking at "must have" as a regulation rather than as a regularity!
But I think my argument still shows that there is a unique weakest warrant property, being the disjunction of all warrant properties. (Hmmm. Or possibly just the least upper bound of all warrant properties. I'm not sure how we feel about infinite disjunctions -- especially if the infinite set being disjoined is uncountable....)
Anyway, I'm sure epistemologists would be interested in knowing what properties that LUB has. Based on the constructions you gave for W' and W", it seems like maybe the LUB would not entail truth and would not be closed under entailment. Have you given the question any consideration?
Yes, there is a weakest warrant property and also a strongest one; see comment by technosentience.
Yes, it seems like the weakest one would violate closure and not entail truth. However, the weakest warrant property doesn't obviously have any better claim to being called "warrant" than the strongest warrant property, or some other warrant property. Intuitively, properties like (p -> Bp -> Kp) are less natural candidates for "the" warrant property, if we wanted to pick out one canonical warrant property.
I haven't read the epistemological papers talking about this, but couldn't one reason we want to talk of warrant at all is to ask questions about the value of knowledge?
For example, we could ask: "If knowledge is true, warranted belief, then does the value of that belief come from its truth, its warrant, or both? If both, is the value additive or is it an organic unity? What about truth, warrant, or their combination makes knowledge valuable?"
So, one of the goals of talking about warrant could potentially be not only to indicate what, when added to truth, makes a belief knowledge, but also what might make knowledge valuable. If that is or should be one of the goals, then a lot of your alternative warrant properties clearly fail in this regard.
For example, if your example is correct, what matters isn't that there is justification which isn't defeated by defeaters compatible with P, what matters (if knowledge has any value at all beyond true belief) would presumably just be that the justification remains undefeated period.
The upshot would seem to be that your critique fails: we could ask whether there is one unique property which both makes true belief into knowledge and makes that knowledge valuable, whether this property guarantees truth, and whether this property is closed under entailment.
I would think that it's good to lack defeaters of either kind. It's good to lack defeaters that are compatible with P, and it's also good to lack defeaters that are incompatible with P.
You could say that it is best to lack any defeaters whatsoever. True, but lacking incompatible defeaters is already entailed by the truth condition, so one might think it's a little redundant. The value of warrant should be only part of the value of knowledge; in particular, it doesn't have to redundantly include the value of truth.
Oh, I see. That's interesting. I didn't realize that the value of warrant could potentially be split parallel to the split of the work done between W and W' (i.e. such that W includes the work or value entailed by truth while W' excludes it).
I'm not sure that would work with every theory of the value of knowledge, though, and in particular organic unity theories. For example, if you think that the value of knowledge lies in "grasping the truth" (this is a metaphor, and I don't really know how to spell out the metaphor), then you might say that the value of such "grasping the truth" cannot be split between the value entailed by truth (e.g. there being no defeater incompatible with truth) and that entailed by "grasping" (e.g. there being no defeater compatible with truth). Nonetheless, the "grasping" (i.e. the warrant) could play a substantial explanatory (but non-additive) role in making "grasping the truth" valuable.
Then again, maybe there will be another parallel split between the substantial explanatory (but non-additive) roles for W and W', with W (perhaps redundantly) including some of the explanatory work truth does in making "grasping the truth" valuable while W' excludes that work.
Colloquially, knowledge is understood as a true belief, with or without justification, so the question of justifying the need for ‘justification’ (of a true belief) is of itself an important one.
I will try to expand on the term ‘justification’ and relate to ‘warrant’.
Knowledge that P
= knowledge that ‘belief that P’ is true
= having a sufficient reason that ‘belief that P’ is true.
The truth value of <knowledge that ‘belief that P’ is true> consists not just in the observer-independent truth of P, but in the (higher order) knowledge ‘that’ P is true. Another way, in order to say, truthfully, that we know something, we must know that we know it with certainty, and this implies knowledge of the ‘truthmaker’ for our certainty. The criterion of certainty may be satisfied in different ways, for example, we may have certainty that P, or, certainty that the probability that P is (Xmin to Xmax)%, but ‘P’ is a different type of fact from ‘probability that P’; equivocation between these two types gives rise to a common error, a category mistake: the false belief that we may ‘know’ something even without certainty.
I understand this is consistent with the ‘no defeaters’ requirement, provided that the absence of knowledge that there are ‘no hidden defeaters’ is of itself a defeater (of knowledge that P). I also understand that your use of ‘warrant’ implies compatibility of W and W’, but in order to accomplish compatibility under the ‘no hidden defeaters’ condition there must be universality/objectivity of justification (sufficient reason), so either W=W’ or one of these is incorrect.
If (ii) could be false, then (iv’) is incorrect. As a matter of epistemic principle, (ii) can be false, therefore (iv’) is incorrect; the possibility of defeaters that are incompatible with P must be included, because it is possible for (iii)&(iv’) not to “warrant” even if there are no ‘P compatible’ defeaters.
Does this sound right?
I'm a fallibilist, i.e., I accept knowledge without certainty. This may sound wrong, but I basically think you have to give up the 'certainty' condition to account for >99% of the things we normally call "knowledge". I.e., we might be inclined to *say*, "knowledge requires certainty", but we don't actually use the word that way.
I would also deny the condition that knowing p implies knowing that you know p, because this leads to an infinite regress.
I would not call anything uncertain ‘knowledge’ but a ‘practical assumption’; a fallabilist accepts that he could be wrong, but is willing to try because doing nothing is not an option. The reason for my insistence on ‘certainty’ as a condition of ‘knowing’ is that Knowledge is always used in a normative sense, it is used as an argument, as a reason to sanction others, so it has ethical (and, less obviously, ontological) implications. For example, “I know that I am right, therefore you are wrong and there is no need for further deliberation, so you must comply, or else”, which is an implicit commitment to violence as the ultimate arbiter of facts.
On a purely logical level, if you do not know that P with certainty then what exactly do you know? You only know that P is probably true, but not certain to be true, and this is a different object/claim than ‘P is true’, so to evade the distinction would amount to a practical violation of the law of identity.
Regarding the charge of infinite regress, this was indeed a clumsy expression on my part. I should have said: “we must know it with certainty”. All I can defend here is that knowledge that P implies the awareness that it is ‘I’ who knows (but self-awareness is not an additional item of knowledge, because it is not falsifiable).
> Now let W’sp = (p → Wsp). Then W’ is obviously non-equivalent to W.
Nitpicking, this is actually incorrect: for example, if Wsp itself is of the form (p -> Bsp -> Ksp), (p -> Wsp) is logically equivalent to Wsp (as (p -> (p -> X)) <-> (p -> X) for all X, even under necessity). But the construction from part 3 works for all cases, since those propositions imply different consequences.
In general, one can rearrange the definition Ksp = Bsp & p & Wsp as:
1) Ksp -> Wsp
2) Wsp -> (Bsp -> p -> Ksp)
Thus in some sense (Bsp -> p -> Ksp) is the minimum warrant property and Ksp is the maximum one, with others sandwiched between them in their logical strength.
Yep, that's right.
I’m not terribly familiar with either formal epistemology or formal logic.
Is there a real world English example that illustrates W, W’, and W’’ and shows their non-equivalence?
And one in which it entails the truth and one in which it doesn’t?
Where would I look for such examples?
Well, there is the example from the OP. On one account, W = the property of being justified in the absence of defeaters. W' = the property of being justified in the absence of (defeaters that are compatible with p).
Those are non-equivalent properties. W entails truth, whereas W' does not.
At the risk of sounding obtuse, what would a concrete example of each of those be in real life?
One of the places I lose the proof is how W’ could be different from W when the article also asserts in the prior section that the systems are logically equivalent. What would a defeater that is not compatible with p even mean? My naive expectation is that a defeater that is not compatible with p is not a defeater, and thus W’ is W, and then I lose it all.
My hope is that an illustrating concrete example of a form similar to “Susie knows that rain is wet (Ksp) because she believes it (Bsp) and it is true (Tp) and because there is no evidence otherwise (Wsp).” But perhaps with an example that shows the differences.
I’m sure the literature abounds. I’m just a layman.
So we could say Sue knows that rain is wet because she believes it, it's true, she's justified in believing it, and there are no defeaters for the proposition that rain is wet.
Or: because she believes it, it's true, she's justified in believing it, and there are no defeaters for the proposition that rain is wet that are compatible with rain being wet.
W and W' are equivalent only given (Bp & p). I.e., you can have W be different from W', yet (W & p & Bp) be equivalent to (W' & p & Bp). It's a general point about logic that you can have A /= B, but (A&C)=(B&C).
A defeater that's incompatible with p would be, say, ~p. If p is false, then ~p would be a true proposition that if added to your beliefs would make you not justified in believing p. So that's a defeater.