The project explores a view of the mind according to which it is fragmented. With belief as the exemplary mental state, the working hypothesis of fragmentation includes four claims:


  1. The total belief set of a single person’s mind is fragmented into separate belief systems.
  2. Each belief system is consistent and, we propose, a multiple-premise deductive closure principle holds for obvious consequences within each system.[1]
  3. The belief systems of a single agent work somewhat independently: they may not be consistent with each other and the agent may not believe the consequences of his belief fragments taken together.
  4. Different belief systems of a single agent guide the agent’s actions in different contexts.

Although something like Fragmentation can be found in the work of Cherniak, Egan, Elga, Lewis, Rayo, and Stalnaker, few today endorse Fragmentation. The orthodox, often implicit, view – underlying formal and non-formal inquiries – is that the mind is unified:


Agents have a unified representation of the world, a single system of beliefs[2], organized by two principles:

  1. Consistency: The total set of an agent’s beliefs is consistent.[3]
  2. Closure: The total set of an agent’s beliefs is deductively closed. That is, agents believe the deductive consequences of their beliefs.

In the literature, Unity is sometimes endorsed with significant qualifications. It is often endorsed not as a descriptive claim about what finite cognitive agents are like but as a normative claim about what a rational overall belief state is like. Nevertheless, it is endorsed.

Despite widespread reliance on Unity, its picture of the mind faces serious challenges. We focus on a number of problems – some for the descriptive and some for the normative version of Unity – where the fragmentation view promises to offer a superior alternative.

A) It is patently obvious that as a descriptive claim, Unity is a gross mischaracterization of people’s beliefs and of related cognitive abilities. Human agents constantly fall short of keeping their beliefs consistent and drawing all the logical consequences from their beliefs. Take for instance the following three categories of cases that illustrate common failures of Consistency and Closure:

  1. Ordinary cases of inconsistent beliefs. Paul believes that China is the world’s second-largest national economy. Paul also believes that China is not a member of the G8. Yet Paul believes that the G8 consists of the governments of the eight largest economies in the world.
  2. Cases of failure to “put the pieces together.” Eva believes that everyone with a yearly income above 40.000 Euros should give 10% of their income to charity. Eva also believes that she earns 50.000 Euros a year. But she fails to believe that she should give 10% of her income to charity.
  3. Cases of cognitive dissonance. Anna, a feminist academic, asserts sincerely and with conviction that men and women are equally competent in all scientific fields. Nevertheless, she is systematically sexist in most of her automatic behaviour, unreflective judgments and subjective experiences. Anna is aware of her biases and tries to control them, but she is unable to eliminate them.

Cases of type (1) and (3) exhibit violations of Consistency, cases of type (2) exhibit violations of Closure. One goal of the project is to explore whether a single view of fragmentation can explain human belief and agency in all such cases. For illustration, the bare outline of the explanation of inconsistent beliefs looks like this: Inconsistent beliefs belong to distinct fragments of belief, which are accessed, and guide action, under different circumstances or for different purposes, so that the inconsistency is not noticed. Similarly for cases of Closure failure: an agent may hold the belief that P in one fragment, and the belief that if P then Q in another, so that in neither fragment it deductively follows that Q. Thus the agent may fail to draw the conclusion that Q.

B) As normative claims about the rationality of belief (and other attitudes), Unity’s assumptions of Consistency and Closure also face major difficulties. Here are three of the most prominent ones:

  1. The Problem of Deduction. Real-life agents are not in general consistent and do not draw all the deductive inferences from their beliefs. This is known as the problem of deduction for many theories of belief content and standard epistemic and doxastic logics that adopt Unity as a simplifying or idealizing assumption. Importantly, the problem also has a normative dimension: It is far from clear that ideally rational human agents with finite cognitive capacity should have a single coherent and deductively closed corpus of beliefs.
  2. Preface Paradox. It is rational for a book author to believe all the statements she makes in the book. At the same time, it is rational for her to admit her fallibility, i.e. to admit that at least one of these beliefs is false. Thus, it is rational for her to have inconsistent beliefs: a set of beliefs and the belief that at least one of them is false. This paradox provides reason to reject Consistency (and Closure): it can be ideally rational to hold inconsistent beliefs. Since we should admit our fallibility regarding almost any subject matter, having inconsistent beliefs seems to be a fundamental feature of rationality.
  3. Frege’s puzzle. Marie rationally believes that Hesperus is the brightest object in the evening sky. Marie also rationally believes that Phosphorus is not the brightest object in the evening sky. Since Hesperus is Phosphorus, Marie holds inconsistent beliefs – at least on a very popular view about belief content. Thus Marie would count as irrational. However, Marie seems fully rational in her beliefs; she just lacks the knowledge that Hesperus is Phosphorus. We surmise that it is Unity – the assumption of a single, unified and consistent set of beliefs – that gives rise to Frege’s puzzle, and that the puzzle can be solved on a fragmentation view of the mind.


[1]     A belief is a deductive consequence of a set of beliefs in case it follows from the set by the laws of deductive logic.
[2]      By a “system of beliefs”, we mean a set of beliefs that is organized by the two principles of Consistency and Closure (or suitably weaker versions). This notion of a system does not imply that systems are individuated by kinds of cognitive processes.
[3]     A set of full beliefs is consistent iff it contains no two beliefs whose contents cannot be true together. We will, for the most part, explore full belief; where a graded notion of belief is relevant, consistency is understood as follows: A set of graded beliefs is probabilistically consistent iff it obeys the laws of probability.



  1. 1
    Phase 1: Groundwork – the fragmentation hypothesis

    Phase 1 has two objectives: to categorize the existing fragmentation views and to develop the project’s account on fragmentation.

    The project proposes a distinction between horizontal and vertical fragmentation strategies that could be employed in the attempt of explaining cases of type (1), (2) and (3) above. Vertical strategies are those that appeal to the distinction between belief and other kinds of mental states. Usually, vertical strategies do not give up Unity for belief. Horizontal strategies are those that appeal to divisions within the same kind of mental state. Our categorization includes only horizontal views regarding belief.

    The development of the project’s fragmentation view encompasses philosophical and empirical research on the mind. We submit that exploring cognitive capacities related to the belief system provides us with unique tools to substantiate a fragmentation view of beliefs. The project focuses on one cognitive capacity that is somewhat unexplored in the philosophical studies on fragmentation, namely memory. Our working hypothesis is that Fragmentation is substantiated by the existence of different memory systems.

    The project explores different types of memories (i.e. working memory versus long-term memory), their respective criteria of individuation (i.e. capacity and duration) and factors related to the way information is organized in memory (e.g. categorization and learning context) in order to formulate individuation criteria of belief fragments. The project holds that memory types do not individuate belief fragments within the subject’s belief system. However, the former can help identifying the latter. Our presupposition is that the way beliefs are organized in different belief fragments is revealed by the different circumstances in which those beliefs are activated in working memory. In the case of Paul’s beliefs (case 1), for example, their separated activation is indicative of the fact that the two belief fragments belong to different belief fragments in Paul’s long-term memory.

    Apart from the early works by Cherniak (1981, 1983), there is little work done on the relationship between fragmentation and memory despite the clear connection between the two. The most popular empirical grounds for fragmentation seem to appeal either to the modularity hypothesis or to the dual-processing theories. However, neither of such hypotheses seem to illuminate all the central cases of this project. The project focuses only on the positive proposal linking fragmentation and memory.

  2. 2
    Phase 2: The problem of deduction, rationality, and the preface paradox

    The problem of deduction, also known as the problem of logical omniscience, is standardly understood to lie in the divergence between the idealizing assumptions of the theory and the facts in the intended domain of application. Real agents’ total beliefs are not always consistent, and they are not deductively closed. This is a key problem for possible-worlds approaches to propositional attitude content and also for mainstream formal theories of belief.

    The fragmentation strategy, most notably developed by Robert Stalnaker (1984) for possible-worlds content, aspires to solve the problem by giving up Closure as a condition on an agent’s total set of beliefs. Within any of an agent’s belief fragments, a weakened Closure principle is maintained. An agent may fail to believe Q despite believing P and If P then Q when: (i) P and If P then Q belong to separate belief fragments (in neither of which Q is a deductive consequence) and (ii) the agent fails to integrate, or connect, the fragments. The fragmentation strategy also explains why agents may learn something new by engaging in deductive reasoning: by (partially) integrating two or more fragments of belief, they come to have new beliefs – those beliefs that are consequences of the new, integrated fragment but were not consequences in either fragment before integration (see Stalnaker 1984 and Rayo 2013).

    The goal of Phase 2 is to further develop this kind of solution to the problem of deduction, based on the findings in Phase 1.

    On the normative side, taking Unity’s Closure and Consistency as ideals also leads to problems, such as the preface paradox. The fragmentation strategy explored in the second part of this phase takes its cue from Kyburg (1961), who proposes to solve the paradox by denying the principle of “agglomeration”, (B(P) & B(Q)) → B(P&Q). Similarly, fragmentation gives up Closure with respect to the totality of an agent’s beliefs. The fragmentation solution says that while one’s beliefs in the book’s statements belong to one fragment, beliefs arising from reflection on one’s fallibility by default belong to another fragment. Crucially, rationality on the fragmentation picture does not require that all our fragments be unified under all circumstances. This goes a long way towards explaining why it is not always irrational to hold beliefs that are inconsistent. In addition, the fragmentation strategy brings an important explanatory asset to the debate. It promises to explain why we have the impression of paradox: once we consider the book beliefs and the beliefs arising from reflection together (in a single fragment), we apply Closure and notice the inconsistency.

    The solution based on Fragmentation implies that it may be more rational not to integrate fragments than to integrate them (pace Davidson 1986, Greco 2013). This raises one of the most important questions for fragmentation strategies: Under what circunstances is it rational to be fragmented, i.e., when is it rational not to have one’s fragments unified?

  3. 3
    Phase 3: Cognitive Dissonance and Belief-Control

    The third phase of the project centers on cases of type 3. The objective is to examine the explanatory power of Fragmentation when applied to cases of cognitive dissonance.

    One central question in the philosophical debate about cognitive dissonance concerns the description of the dissonant person’s psychology: What types of mental state underlie Anna’s dissonance? Vertical strategies say that Anna is dissonant because her belief system is in conflict with the output of a different cognitive system. A horizontal approach says, on the other hand, that beliefs are the mental states underlying both her assertion and her behaviour: the dissonance appears because they belong to different belief fragments.

    In this phase, we will examine different approaches to dissonance cases, and will compare them with our horizontal fragmentation hypothesis based on memory. According to our hypothesis Anna’s beliefs belong to different belief fragments within her long-term memory. The fact that her beliefs follow different patterns of activation (endorsed linguistic responses versus spontaneous reactions) may be indicative of different belief fragments. However, cases of type (3) differ from cases of types (1) and (2) since Anna is unable to put the two beliefs together and thereby eliminate one of those. We will address the following research questions:

    • In which ways is the memory-centred fragmentation hypothesis superior to other available approaches?
    • What is the scope of horizontal fragmentation strategies? Are there important differences among key cases of cognitive dissonance such that horizontal fragmentation is a good explanation of some but not others?
    • Given horizontal fragmentation, why does the agent lack rational control over one of her beliefs in a dissonance case? Does explaining dissonance cases require explaining this kind of apparent failure of agency?
  4. 4
    Phase 4: Frege’s puzzle and the semantics of belief ascriptions

    The last phase is dedicated to exploring the prospects of the idea of horizontal fragmentation for a solution to Frege-style Hesperus-Phosphorus puzzles. The standard lesson from such puzzles is either that one’s theory of content must be revised (Fregeanism) or that something like different vehicles of belief, or ways of believing the same content, must be introduced (Neo-Russellianism). Both approaches face notorious problems. The project explores the diagnosis that it is the assumption of Unity itself that gives rise to the puzzle. We investigate the prospects of a solution to Frege’s puzzle based on Fragmentation, which avoids the traditional problems and receives independent confirmation from cognitive phenomena studied in the other phases.



The current project succeeds the project “Information and the Fragmented Mind: Rationality and Cognitive Dissonance”, which ran from September 2014 to March 2015 under sponsorship by the Land Steiermark, Wissenschaft und Forschung. A description can be found here.