The principle of attribution and retraction


The principle of attribution and retraction

Recently Ozy was explaining the concept of attribution and retraction in relations to belief and knowledge and I wanted to expound upon that a bit and perhaps simplify what was being said. First, I think it is necessary to establish the difference between “belief” and “knowledge”. Belief is one holding that a particular statement or proposition is true. If I say “It is raining outside” I’m accepting that the proposition p=it is raining outside is a true proposition, or in other words, I’m assuming a psychological state of belief that the proposition is true. I believe p is true can therefore be expressed as Bp where “B” is the predicate of the proposition meaning Bp= I believe p is true. “Belief” in this context is the “propositional attitude” we have towards the proposition (a mental position on the proposition: Eg., I “believe” x is true, I “know” x is true, I “fear” x, I “love” x ect.). So if I say “It is raining outside” I am making a belief claim that “I believe it is raining outside”. To remove ambiguity, we could more verbosely state it as “I believe the state of the affairs of the universe is such that it is true that it is raining outside.”

Beliefs as a propositional attitude:

Beliefs do not require certainty, so that in order to say that the proposition is true I do not have to “know” p is true nor that it is, in fact, raining outside in order to hold a belief that it is raining outside. Beliefs can be wrong. So let’s say I go outside at 1:00 PM and get soaked by a torrential down pouring of rain. If given “p=it is raining outside” as a proposition to evaluate my “attitude” would be that I believe p is true. If at 2:00 PM the rain stops without me being unaware of this change of state of affairs of the universe, and Sally asks me, “Steve is it raining outside?” And I respond “Yes, It’s raining outside”. I still believe that p is true, even though that belief is wrong. Another hour passes, and at 3:00 PM it starts raining again and Sally again asks me if it is raining, and I respond “Yes, it is still raining.” Another hour passes, and I walk outside and the raining has stopped which at this time my belief about p would change so that I would believe that the proposition “p=it is raining outside” is NOT true. Meaning I now hold to B~p or “I believe NOT p” which is the same as “I believe p is not true” or “I believe p is false”.

p=it is raining outside
1:00 PM I held to Bp (My propositional attitude about p was that I believed p was true, and my belief was correct)
2:00 PM I held to Bp (My belief was erroneous)
3:00 PM I held to Bp (my belief was correct)
4:00 PM I held to B~p (my belief was correct)

At all four times I held a belief about p. Even though at 2:00 PM my belief was erroneous, I did still hold the belief. There is no retraction of me not believing then. Changing my belief about p from 3:00 PM to 4:00 PM also doesn’t mean I am retracting that I never believed Bp at 3:00 PM  just because a 4:00 PM I then held to B~p. We don’t say because my belief was wrong at 2:00 PM that I never believed p was true as at that time I did have a belief that p was true.

Theories of knowledge:

Knowledge however is a bit different. Knowledge, unlike beliefs, can never be not true. We can mistakenly think we have knowledge, but knowledge itself is usually understood to be that which meets a tripartite set of conditions:

  1. p is true
  2. s believes p (s is the subject such as “I believe p”
  3. s is justified to believe p (Justified True Belief) or s believes p was produced by a reliable cognitive process (Reliablilism).

Justified True Belief and Reliable Produced True believe are two examples of theories of knowledge and there are few different ones, but all require p to be true. These theories are what we think is required to refer to something as “knowledge”. I will be writing a separate blog post on theories of knowledge, but for the sake of this post assume (3) is met by a reliable cognitive process.

Since one of the conditions for knowledge is that p is true (1), then it would be a contradiction to say knowledge can be false. Knowledge is a higher confidence of certainty, but unlike belief can not be false, and we can mistakenly think we had knowledge…but knowledge itself is always true. Similarity to believe we are not required to have epistemic certainty that p is true. We only need to meet the tripartite conditions to have knowledge. Since (2) is “s believes p” then when ever we know something, we also believe it. This is often stated as “knowledge entails belief”, since if we know it we must meet (2) condition and believe it.

Knowledge as a propositional attitude:

So let’s say instead of belief our propositional attitude on p at 1:00 PM was “I know p is true”, as well as 2:00, 3:00, and 4:00.

p=it is raining outside
1:00 PM I held to Kp (My propositional attitude about p was that I know p was correct)
2:00 PM I held to Kp (but my belief was incorrect, and I was mistaken about my knowledge.)
3:00 PM I held to Kp (my belief was correct, and I had knowledge)
4:00 PM I held to K~p (my belief was correct, and I had knowledge)

At 2:00 PM my belief was wrong, but here we there is a retraction of the knowledge. At 2:00 PM in hindsight I can now recognize the belief was wrong since p was not true and it failed to meet (1), therefore I never had knowledge at 2:00 PM. The knowledge was never not true, as knowledge must always be true (1)…but I was mistaken in that my belief that I had knowledge.

Between 3:00 PM and 4:00 PM my belief about p changed. Because of the change of conditions about the state of affairs of the universe I revised my belief on p from Bp to B~p and according my knowledge propositional attitude changed from Kp to K~p. So at 3:00 I believed it was raining, and at 4:00 PM I believed it was not raining. I still had beliefs at both times. Since at both times the tripartite conditions were met I also had knowledge at both times. So at 1:00 PM, 3:00 PM and 4:00 PM I believed and had knowledge it was raining, but at 2:00 PM I had belief it was raining, but I did not have knowledge it was (it is retracted).


Beliefs can change, and they can be wrong. Knowledge can never be not true, but we can be wrong about our position that we had knowledge.

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