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What is the problem of awareness growth and how should an epistemologist respond to it?

©2022 Essay 10 Seiten

Zusammenfassung

This essay argues that there cannot exist a formal framework that consistently obtains intuitively correct results for all cases of awareness growth. This is because intuitions determine the rationally correct outcome of any case of awareness growth. Since it is reasonable for intuitions to vary between rational agents, it is feasible to obtain different intuitively correct results with two rational agents in an identical case of awareness growth. This impedes the existence of a framework that consistently obtains intuitively correct results for all cases of awareness growth.

First, I present the classical Bayesian framework and explain how the problem of awareness growth arises. Second, I present Bradley’s account of Reverse Bayesianism as a credence-revision rule and show that it fails to provide intuitively correct results for mixed cases of awareness growth, which disqualifies it as a general framework for all cases of awareness growth. Third, I demonstrate that intuitions determine the rationally correct outcome of any case of awareness growth and show that it is feasible to rationally obtain different intuitively correct outcomes when considering the exact same case of awareness growth with two rational agents.

Last, I conclude that it is impossible for a framework that consistently obtains the intuitively correct outcome to exist and suggest that credence-revision following awareness growth should occur on a case-by-case basis without any constraints other than the rationality assumption of the rational agent.

Leseprobe

What is the problem of awareness growth, and how should an epistemologist respond to it?

This essay argues that there cannot exist a formal framework that consistently obtains intuitively correct results for all cases of awareness growth. This is because intuitions determine the rationally correct outcome of any case of awareness growth. Since it is reasonable for intuitions to vary between rational agents, it is feasible to obtain different intuitively correct results with two rational agents in an identical case of awareness growth. This impedes the existence of a framework that consistently obtains intuitively correct results for all cases of awareness growth.

First, I present the classical Bayesian framework and explain how the problem of awareness growth arises. Second, I present Bradley’s account of Reverse Bayesianism as a credence-revision rule and show that it fails to provide intuitively correct results for mixed cases of awareness growth, which disqualifies it as a general framework for all cases of awareness growth. Third, I demonstrate that intuitions determine the rationally correct outcome of any case of awareness growth and show that it is feasible to rationally obtain different intuitively correct outcomes when considering the exact same case of awareness growth with two rational agents. Last, I conclude that it is impossible for a framework that consistently obtains the intuitively correct outcome to exist and suggest that credence-revision following awareness growth should occur on a case-by-case basis without any constraints other than the rationality assumption of the rational agent.

The classical Bayesian model and how the problem of awareness growth arises

The classical Bayesian model is considered the standard framework to represent an agent’s credences and thus their epistemic state. It models the epistemic state in a probability set consisting of different possible worlds, which can be allocated to different propositions. The probabilities assigned to these propositions are called credences. This model assumes the agent being rational who is aware of all possible propositions in their probability set. According to the Bayesian framework, the only way to update an agent’s credences is by gaining evidence for or against a certain proposition, and to conditionalize all propositions in the probability set on that newly gained evidence.

Awareness growth describes the situation when a new proposition occurs to the agent without being initiated by new evidence. Thereby, the agent’s probability space increases by one or more propositions they were unaware of before. Awareness growth poses a problem to the classical Bayesian framework because the necessary change in credences following the awareness growth cannot be modelled by conditionalization since the agent did not receive any new evidence. Therefore, the classical Bayesian framework cannot handle cases of awareness growth.

Reverse Bayesianism as a response to awareness growth and its shortcomings

Reverse Bayesianism aims to provide a credence updating rule for the problem of awareness growth which is motivated by the classical Bayesian conservatism in changing credences as little as possible. Bradley, who endorses Reverse Bayesianism, identifies two different types of awareness growth: awareness growth by refinement and by expansion (Bradley, 2017, p.257). Awareness growth by refinement occurs when the agent becomes aware of an option that divides an existing proposition into more fine-grained propositions. Here, Bradley suggests keeping the same credences for the coarse-grained propositions (the old propositions) and only assign new credences to the fine-grained propositions such that it keeps the relation of the old propositions as before. Awareness growth by expansion occurs when the agent becomes aware of a proposition disjoint from all other existing propositions in their probability set. Motivated by having minimal change from the old credences and satisfying the constraint that the probability space must sum up to 1, Bradley suggests assigning a credence to the new proposition, and assign the remaining space to the old propositions, which must stay in the same relations to each other as before. To illustrate, this would mean that if I initially have credences of P(A)=0.3 and P(B)=0.7, and I become aware of P(C), I can assign P(C) any credence (e.g., 0.4) and would have to assign the remaining 0.61 such that the relation between P(A) and P(B) would remain the same. In this case, my credences would be P(A)=0.182, P(B)=0.423 and P(C)=0.4 after awareness growth.

In the following, I present a mixed case of awareness growth4 which shows that applying Reverse Bayesianism leads to results which are intuitively wrong (Mahtani, 2021, pp.8984-8985).

Landlord/Tenant-example

Bob shares his flat with his landlord. Imagine you are in his flat and you hear someone in the shower. You want to know who the person in the shower is. Since you do not have any indication of who it is, you assign credences to the propositions according to the table below. Suddenly, it occurs to you that the singer could be another tenant who is not Bob without gaining any new evidence. Applying Reverse Bayesianism to this case of awareness growth requires holding the relation between Landlord and Tenant constant. Since nothing has changed on the coarse-grained level of this case, Reverse Bayesianism demands to assign P(Landlord)=0.5 and P(Tenant)=0.5. Next, Reverse Bayesianism requires holding the relation between Landlord and Bob constant. Since P(Landlord)=0.5, P(Bob) must be P(Bob)=0.5 as well. Consequently, we need to assign P(Other)=05. However, intuitively and following rationality we want to assign the credences as in the table below:

Abbildung in dieser Leseprobe nicht enthalten

The results obtained using Reverse Bayesianism are different from the results our intuition suggests.6 Since Reverse Bayesianism de facto impedes awareness growth in this mixed case, and since it is reasonable to expect mixed cases to be covered by a framework that aims to explain all cases of awareness growth for rational agents, we can conclude that Reverse Bayesianism is not a strong enough concept to provide the correct results for all cases of awareness growth (Mahtani, 2021, p.8986).

As an attempt to safe Reverse Bayesianism, Steele and Stefánsson identify a condition for cases of awareness growth which ensures that Reverse Bayesianism provides the intuitively correct results for cases that satisfy this condition7 (Steele & Stefánsson, 2021). While this seems to be an interesting way to categorize cases, it does not aim to develop a credence-revision framework that works for all cases of awareness growth. As this essay aims to scrutinize the possibility of a framework that works for all cases of awareness growth, I will not pursue this idea any further.

[...]


1 1-0.4=0.6

2 P(A)=0.6*0.3=0.18

3 P(B)=0.6*0.7=0.42

4 A mixed case of awareness growth is a case in which awareness grows by expansion and refinement

5 P(Other)=P(Tenant)-P(Bob)

6 Landlord stands for the proposition that the landlord is the singer. The same logic applies to Tenant, Bob and Other

7 Mahtani shows that this condition/restriction does not hold for all cases. She uses a formally identical example to the Landlord/Tenant-example and demonstrates that restricted Bayesianism also leads to intuitively wrong results (Mahtani, 2021, pp.8986-8991). However, as this is not integral to my paper, I refrain from an in-depth analysis of this part.

Details

Seiten
10
Jahr
2022
ISBN (PDF)
9783346705617
Sprache
Englisch
Institution / Hochschule
London School of Economics
Erscheinungsdatum
2022 (August)
Note
First Class Honours
Schlagworte
what
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Titel: What is the problem of awareness growth and how should an epistemologist respond to it?