Document Type : Research Paper
Authors
1 PhD Student of Logic with a Philosophical Approach, University of Isfahan, Isfahan, Iran
2 Associate Professor of Philosophy, University of Isfahan, Isfahan, Iran
Abstract
Extended Abstract
Introduction
The problem of the normativity of logic is one of the fundamental debates in contemporary philosophy of logic, examining the relationship between the “formal laws of logic” and “epistemic norms.” This theory seeks to attribute a role to logic that extends beyond the mere evaluation of the validity of arguments, presenting it as a normative tool for regulating belief and properly guiding thought. Such a conception transforms logic from an abstract science into a practical guide for epistemic life. Nevertheless, the unquestioning acceptance of the normativity of logic faces numerous psychological and epistemic challenges. Philosophers therefore attempt to determine how a balance might be achieved between the “logical ought” and human “epistemic capacity.” If logic is regarded as strictly normative, the human mind is confronted with a vast array of logical consequences that it lacks the capacity to process; conversely, if the link between logic and norms is severed, rationality and the coherence of thought are compromised. This research aims to find a middle ground to address this dilemma.
Research Question(s)
Is it possible to provide a formulation of the normativity of logic that is both consistent with common-sense intuitions and resilient against fundamental critiques (particularly those advanced by Harman)?
Can a diachronic interpretation of logical norms address Gilbert Harman’s critiques regarding everyday reasoning?
Literature Review
The normativity of logic, which roots can be traced to philosophers such as Immanuel Kant and particularly Gottlob Frege, has been reconstructed and further developed in the contemporary era by John MacFarlane. The perspective held by Frege and MacFarlane is grounded in the conviction that logic must prescribe binding normative rules for thought. By contrast, Gilbert Harman, through his critique of the principles of implication and contradiction, argues that these principles have limited utility in everyday life and that there is no definitive link between formal logic and ordinary reasoning.
In response to these critiques, John MacFarlane attempts to provide a more nuanced account of logical normativity by proposing a systematic framework known as ‘Bridge Principles.’ By introducing 36 distinct formulations based on three parameters, the type of deontic operator (obligation, permission, or having a reason), polarity (positive or negative norms), and scope (narrow, medium, or wide), he outlines a comprehensive set of possible norms. These formulations enable philosophers to specify precisely under what conditions a logical entailment obliges an agent to revise their beliefs.
The Preface Paradox demonstrates that an individual may hold a set of inconsistent initial beliefs without knowing which specific one is false. In such a situation, the abrupt or arbitrary discarding of beliefs is irrational. This paper proposes the ‘Gradual Belief Revision’ approach, which is grounded in a step-by-step review and the incremental identification of contradictions.
Methodology
This research employs a method of logical-philosophical analysis and systematic evaluation. In the first step, by utilizing 36 different formulations of normative principles derived from the relation , and by applying MacFarlane’s indices (deontic operator type, polarity, and scope), the landscape of possible norms was mapped. Subsequently, these norms were evaluated against five rational criteria: Maximal Demands, the Preface Paradox, the Strictness Criterion, the Priority Problem, and Logical Adversity.
Furthermore, to resolve the ‘Preface Paradox,’ the ‘Gradual Belief Revision’ approach was proposed and elucidated through practical analogies. After identifying the weaknesses in traditional norms (such as those based on strict requirement), the study, using an analytic-synthetic method, proposes a new model based on the distinction between ‘synchronic’ and ‘diachronic’ interpretations.
Discussion
In the evaluations conducted, many Wo+ and Wr- norms are rejected for various reasons. A focal point of the discussion is the ‘Preface Paradox’, which demonstrates that an individual may hold a set of conflicting initial beliefs without being able to correctly identify which specific belief is false. In such circumstances, the abrupt or arbitrary discarding of beliefs is irrational. In response to this problem, the paper proposes an approach based on the ‘gradualness of belief revision.’ According to this view, the process of making a belief network consistent should not rely on instantaneous elimination; rather, it should be grounded in continuous review, the incremental identification of contradictions, and step-by-step refinement. This approach is illustrated through an analogy of managing real-world issues (such as a factory manager dealing with undocumented employees).
In this article, while critically analyzing various normative formulations, the author examines the combination of Wr+ and Wo- norms. Here, Wr+ functions as a positive reason for believing in logical consequences, allowing for the defeasibility of reasons in the face of the stringent requirements of Wo+. Meanwhile, the Wo- norm is introduced as a norm governing the ‘closure’ of the belief network, requiring that whenever an individual believes in premises A and B, they must not disbelieve the consequence C.
Through this lens, the paper identifies two distinct interpretations of Wo-: Synchronic and Diachronic. The synchronic interpretation (Wo-s) asserts that an individual’s beliefs must be fully consistent with norms at a single moment; that is, you must ensure that at the very instant you believe A and B, you do not disbelieve C. However, this expectation is unrealistic in everyday life, as beliefs may encounter contradictions simultaneously. In contrast, the diachronic interpretation (Wo-d) emphasizes that adherence to norms must occur over time. That is, an individual should gradually avoid disbelieving logical consequences through continuous revision of their beliefs; you must ensure that throughout the time you hold beliefs A and B, you do not disbelieve C. This approach allows for the gradual identification and resolution of contradictions and is more aligned with intuition and daily experience.
Therefore, the diachronic interpretation of Wo- is proposed as a more logical and practical model compared to its synchronic counterpart. According to Wo-d, an individual must avoid disbelieving logical consequences over time through the gradual revision of their beliefs. This diachronic interpretation aligns with fallibilism, epistemic revision, and common-sense intuitions.
Conclusion
In conclusion, the paper demonstrates that the combination of Wo−d and Wr+ as two complementary norms not only compensates for the weakness of Wo− in facing logical adversity but also mitigates the limitations of Wr+ regarding its obligatory force. Furthermore, by establishing a balance between logical requirement and epistemic flexibility, this combination provides a deliberate framework for responding to Harman’s criticisms.
Additionally, considering the variation in circumstances, the relative importance of these two norms is deemed context-sensitive: the significance of Wr+ becomes more pronounced in contexts where an individual’s background beliefs are limited, whereas its role diminishes in contexts with a vast number of background beliefs. In contrast, Wo−d remains consistently important, while it is Wr+ that fluctuates in intensity depending on the context. This flexibility in prioritizing norms is itself an indication of the proposed model’s theoretical capacity to align with the real-world complexities of reasoning and believability.
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