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2Логические исследования 2024. Т. 30. № 2. С. 72-88 УДК 16
Logical Investigations 2024, Vol. 30, No. 2, pp. 72-88 DOI: 10.21146/2074-1472-2024-30-2-72-88
Философия и логика
Philosophy and Logic
Masqud Alyand
Rethinking logical disagreements: a critique of verbalism and a normative constraints approach
Masoud Alvand
University of Isfahan,
Daneshgah St., Isfahan, 8174673441, Iran.
E-mail: [email protected]
Abstract: Logical pluralism posits that various conceptions of logic can coexist, suggesting that all acceptable judgments about the validity of an argument are valid without rivalry. This view implies that disagreements between logical theories are merely verbal. Contrary to Kouri Kissel's proposal of metalinguistic negotiation as an explanation for logical disagreements, this article challenges the notion that such disputes are purely verbal. Employing inference to the best explanation, the author argues in favor of normative restrictions on belief in premises and conclusions as a more compelling explanation for logical disagreements.
Keywords: logical pluralism, metalinguistic negotiation, logical disagreement, normativity of logic, inference to the best explanation
For citation: Alvand M. "Rethinking logical disagreements: a critique of verbalism and a normative constraints approach", Logicheskie Issledovaniya / Logical Investigations, 2024, Vol. 30, No. 2, pp. 72-88. DOI: 10.21146/2074-1472-2024-30-2-72-88
1. Introduction
Logical systems, serving as theories of the logical consequences relation, often diverge in their views on the nature or instances of this relation, or sometimes both. Consequently, different logical theories can exhibit disagreements regarding the validity of arguments. A well-known illustration of such rivalry exists in the disagreement between intuitionistic logic and relevant logic(s) with classical logic.
Classical logicians generally define a valid argument as one that preserves truth:
The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X [Tarski, 1983, p. 417].
© Alvand M., 2024
This definition implies that sentence X logically follow from the set of sentences K if and only if, in any model where the set K is true, sentence X is also true. Consequently, being truth-preserving becomes a sufficient condition for argument validity. However, relevant logicians adopt a more stringent stance, considering truth preservation as necessary but not solely sufficient for inference validity. According to them, implication paradoxes arise from this specific understanding of logical validity. To avoid these paradoxes, relevant logicians argue that the conclusion must not only preserve truth but also be related to the premises, ensuring that the conclusion logically follows from the given premises:
The present approach, however, directly replaces the Classical Account with the Relevant Account, and extracts the notion of relevance from the new criterion for validity. For if the conclusion really does follow from the premises, then they must be (logically) relevant to it [Read, 1988, p. 4].
Hence, the relevant logician introduces an alternative conception of logical validity, diverging from the classical understanding. This deviation arises from a disagreement with the classical perspective on the nature of logical validity, driven by the aim to preclude arguments that, in their view, lack validity. Consequently, a prominent illustration of the rivalry between different logical systems surfaces in the ongoing debate between relevant logicians and classical logicians regarding the very essence of logical validity.
Furthermore, when we substitute Kripke models with the models in Tarski's definition of logical validity, an intuitionistic logician perceives truth-preservation in these models as a sufficient condition for logical validity. However, a divergence emerges when comparing their stances with classical logicians, especially on instances such as the Double Negation rule. Within the realm of intuitionistic logic, Michael Dummett stands out for his robust advocacy, elucidating the distinctions between intuitionistic and classical logic. In one of his seminal articles championing intuitionistic logic against its classical counterpart, he articulates his position:
The question with which I am here concerned is: What plausible rationale can there be for repudiating, within mathematical reasoning, the canons of classical logic in favour of those of intuitionistic logic? <... > I am concerned only with the standpoint of the intuitionists themselves, namely that classical mathematics employs forms of reasoning which are not valid on any legitimate construal of mathematical statements [Dummett, 1978, p. 215].
Therefore, Dummett, acting in the capacity of an intuitionistic logician, endeavors to bolster his viewpoint on "validity" by critiquing classical notions
of validity. In doing so, he proposes his perspective as a potentially superior alternative to classical validity.
Despite the common intuition that logical theories are in competition, two obstacles challenge this perspective: the variability in meaning of logical constants across logical systems and the concept of logical pluralism. Both factors lead us to consider logical validity as a property tied to specific systems, with judgments of different logical systems about argument validity seemingly talking past each other. The aim of this article is to demonstrate that logical disagreements carry significance, and disputes among logicians are not merely verbal.
The article is structured as follows: In the second section, we provide a brief explanation of the two obstacles to rivalry in different logics. The third section delves into Kouri Kissel's solution for explaining logical disagreements. Through the concept of metalinguistic negotiation, Kouri Kissel attempts to illustrate that logical disagreements align with the pluralistic view of logic, suggesting that logicians are involved in reasoning on a metalinguistic level and critiquing each other's perspectives. Moving to the fourth section, we examine the challenges posed by this explanation of logical disagreements. Finally, in the fifth section, an alternative solution will be presented that aims to address these challenges without encountering the identified problems.
1.1. Meaning variance of logical constants
The diversity in meanings assigned to logical constants across various logical systems raises the question of whether logical disagreements might be considered meaningless. As an illustration, consider the possible world semantics of negation in classical logic and Routley's semantics1 for it in relevant logic respectively:
~ A is tru in w iff A is false in w ~ A is true in w iff A is not false in w*
The assertion that altering the truth condition of a logical constant suffices to change its meaning implies that theories attributing different truth conditions to negation ascribe distinct meanings to it. Consequently, when these theories diverge on the question of argument validity, their disagreement is deemed verbal. The meaning variance of logical constants, according to Quine, leads to the belief that paraconsistent logicians and classical logicians are not engaged in a common discourse; their discussions revolve around different issues:
1 In this interpretation, each world, w, comes with a mate, w*, its star world, such that ~ A is true at w if A is false, not at w, but at w*. See [Priest, 2008, p. 151].
My view of this dialogue is that neither party knows what he is talking about. They think they are talking about negation, 'not'; but surely the notation ceased to be recognizable as negation when they took to regarding some conjunctions of the form 'p . ~ p' as true, and stopped regarding such sentences as implying all others. Here, evidently, is the deviant logician's predicament: When he tries to deny the doctrine he only changes the subject [Quine, 1970, p. 81].
Quine's perspective on non-classical logic as opposed to classical logic is encapsulated in the slogan: changing logic is changing the subject. According to this viewpoint, a classical logician discusses one thing, while a non-classical logician discusses something else. Therefore, disagreements between non-classical and classical logicians are deemed meaningless.
1.2. Logical pluralism
Logical pluralism posits that there is more than one right logic, but it can be viewed in various ways. Carnap, for instance, contends that the question of the right logic is meaningless. In his view, we are free to choose a linguistic framework governed by specific rules, and no philosophical argument is necessary to justify this choice. Simply stating one's syntactic rules clearly is sufficient [Carnap, 1937, p. 51-52].
Shapiro offers a different view, asserting that the rightness of a logic depends on its structure and application context. For example, he argues that the axioms of constructive analysis in mathematics and classical analysis in mathematics are compatible with intuitionistic and classical logics, respectively. Each set of axioms produces various structures, and according to Shapiro, each structure requires a different logic for correctness within that specific context [Caret, Kouri Kissel, 2020, p. 4].
Beall and Restall, drawing inspiration from Tarski's definition of logical validity, contend that "validity" does not carry the same meaning across all logical systems. According to them, each logical system requires a different meaning of "logical validity":
(GTT): An argument is valid^ if and only if, in every caseK in which the premises are true, so is the conclusion [Beall, 2006, p. 29].
Thus, Cases adopts different meanings in various logics, leading to distinct meanings of validity in these logics. If "Case" is regarded as a consistent and complete world, it results in "classical validity". If considered as an inconsistent and incomplete world, it yields "relevant validity". Finally, defining it as a structure gives rise to "intuitionistic validity" [Ibid., p. 31-32].
Therefore, logical pluralism suggests that multiple logics can adequately capture logical consequence relations if a logical system is viewed as a theory
of such relations. For instance, Beall and Restall prioritize the question of argument validity in any logical system, asserting that all (acceptable) logical systems provide correct answers to this question. Consequently, they argue that logical disagreements regarding "validity" are meaningless2:
These two accounts of consequence are different but, with respect to the chief question of Logic (what arguments are valid?), they are not rivals. There is no sense in calling the two accounts rivals with respect to whether such and so argument is valid. Qua answers to Logic's chief question, the two accounts do not compete [Beall, 2006, p. 44].
Logical pluralism posits that all logical theories are right, rendering them incapable of being rivals. Additionally, the meaning variance of logical constants prevents a direct comparison between these theories. Despite these challenges, logicians openly engage in disputes with opposing logical theories, advocating for their respective perspectives. Two possible approaches to understanding these disagreements are to dismiss them as purely verbal disputes or to seek an explanation. In the following section, we will explore Kouri Kissel's proposed solution to this intricate problem.
2. Metalinguistic negotiation explanation
for logical disagreement
As a pluralist, Kouri Kissel contends that logical pluralism initially appears inconsistent with the prospect of meaningful dialogue between different logical theories. However, she recognizes this inconsistency as undesirable and endeavors to present a solution [Kouri Kissel, 2019, p. 1]. While she specifically advocates a particular form of logical pluralism, her proposed solution can be viewed as a defense of the broader possibility of dialogue between logical theories, irrespective of the specific conception of logical pluralism embraced.
Kouri Kissel's approach to logical pluralism falls within the realm of domain-specific logical pluralism, where "domain" refers to a specific field of discussion, such as mathematics or quantum mechanics, around which people engage in arguments. In this view, the rightness of a logic is contingent upon the goals
2 Other conceptions of logical pluralism also aim to alleviate logical disagreements concerning the nature or instances of validity (or both). For instance, Carnap's conventional pluralism, which permits any choice for a language framework bound by certain rules, and pluralism that grounds the correctness of logic in its structure and field of application similarly do not view different logics as rivals. These perspectives consider logical disagreements to be meaningless and assert that the judgment of any acceptable logical system about validity is correct. Consequently, Steinberger concludes that logical pluralism doesn't resolve logical disagreements but rather dissolves them and pluralists have been the heroes in ending these pointless disputes [Steinberger, 2019, p. 3].
of participants in the argumentative conversation and the specific domain in question [Kouri Kissel, 2019, p. 3]. Consequently, the selection of the right logic and connectives hinges on their alignment with the deductive aims of participants and its ability to guide deductive practices appropriately [Ibid., p. 3-4].
As an example, consider a classical logician and an intuitionistic logician who employ two distinct logics, not for different domains, but for the same domain. The classical logician applies classical logic to analyze mathematics, while the intuitionistic logician utilizes intuitionistic logic for the same purpose. Due to the different meanings of logical constants in these two logics, the two logicians do not use the same language when discussing the analysis of mathematics. Consequently, their disputes about the validity of mathematical arguments are deemed verbal because they employ different meanings for logical terms. However, Kouri Kissel asserts that despite this challenge, the logicians do not dismiss their discussions:
But this may not always be the case: there may still be a disagreement in place about who is doing analysis in the best way even after the practitioners realize that they are using different logical rules and connectives. In effect, merely verbal disputes are resolved once the different meaning/usage of the term in question is recognized, while these cross-language disputes may not be so easily sorted [Ibid., p. 5].
Indeed, according to Kouri Kissel, in Carnap's approach to pluralism, the disagreement between two logicians is considered verbal. In this understanding of pluralism, when two logicians adopt different linguistic frameworks, the meanings of logical terms are determined by the rules of their respective linguistic frameworks, resulting in different meanings [Ibid., p. 4]. Consequently, their conversation, particularly in the context of mathematical argument analysis, appears to be rendered impossible due to the divergence in the meanings of logical terms.
Beall and Restall, guided by (GTT), acknowledge different meanings for the term "validity" itself, despite maintaining a shared understanding of logical constants. Consequently, when engaging in disputes over the validity of mathematical arguments, classical and intuitionistic logicians may find themselves talking past each other, as their distinct meanings of "validity" lead to a lack of mutual understanding.
According to Kouri Kissel, logicians, even after acknowledging the use of different meanings of "validity", persist in debating the validity of mathematical arguments and engage in genuine discussions. To clarify this ongoing dispute, she introduces the concept of metalinguistic negotiation, defined as "disagreements about the proper deployment of linguistic representations" [Ibid., p. 6]
citing [Plunkett, Sundell, 2013, p. 3]. Metalinguistic negotiation involves two crucial characteristics: firstly, participants use words metalinguistically to discuss their correct use. What is critical in this negotiation is that the words under discussion are not merely mentioned but actively used. Secondly, metalinguistic negotiations are held to answer the question of what is the correct meaning of a word in a specific context and which word should be employed in it [Kouri Kissel, 2019, pp. 6-7].
In an illustrative example provided by Kouri Kissel, a metalinguistic negotiation unfolds between two individuals in a room who disagree about whether the room is cold. One attempts to raise the temperature by asserting, "The room is cold", while the other disputes this claim. The crux of their disagreement lies in differing definitions of "coldness": the first person considers the room cold when the temperature is below 70 degrees Celsius, while the second person holds that "coldness" applies when the temperature is below 65 degrees Celsius. Despite the verbal disagreement and the realization that they attribute different meanings to "coldness", the dispute does not end. Instead, each participant endeavors to persuade the other by presenting arguments to either maintain or alter the room temperature. This persistence in discussion, even after recognizing the differing meanings, exemplifies a metalinguistic negotiation in action:
This is a hallmark of metalinguistic negotiation. Each is using the term "cold" metalinguistically to demonstrate what they think the proper meaning/usage should be — in this sense, the debate has a normative characteristic about how "cold" ought to be used, and whether they ought to attempt to change the temperature in the office. In this case, they each use "cold" metalinguistically to make a claim about the proper extension of the term [Ibid., p. 6].
Indeed, in the given example, the roommates engage in a metalinguistic negotiation, which operates at a higher level than the object language. The disagreement revolves around the meaning that should be ascribed to the word "cold" in their conversation, with each participant advocating for their interpretation. Their efforts are directed at convincing one another regarding the correct meaning or usage of the term "cold" in the context of their goal, which is either maintaining or changing the room temperature. This aligns with the key characteristics of metalinguistic negotiations, where individuals, while using a particular word (such as "cold"), dispute its intended meaning and strive to establish the accurate meaning or usage.
Kouri Kissel's perspective on metalinguistic negotiation offers an explanation for why the disagreement between different logicians is genuine rather than merely verbal. Consider classical and intuitionistic logicians as an example. The classical logician asserts that the excluded middle is a theorem,
while the intuitionistic logician disputes this, maintaining that it is not. This discrepancy arises from differences in the meanings of logical constants in their respective logical systems or the disagreement over the term "theorem".
While Kouri Kissel acknowledges the challenge of precisely determining the nature of disagreement in metalinguistic negotiation3, she emphasizes that the essence of the discussion revolves around disputes over the validity of excluded middle. Despite the initial recognition that logicians may attribute different meanings to the contested word, the discussion does not end. Instead, it transitions to a higher level beyond the object language. At this level, logicians engage in arguments to establish the best meaning of the term, ultimately aiming to determine the right logic for the analysis of mathematics that aligns with their deductive goals:
We can see these two participants as arguing about the best way to approach analysis, in particular about what the term "theorem" ought to mean. In rejecting the claim that the fundamental theorem follows from the axioms of analysis, the intuitionistic analyst suggests that the classical analyst has the wrong axioms and logical rules in place [Kouri Kissel, 2019, p. 8].
3. Logic of metalinguistic negotiation
I must acknowledge that, unconsciously, I held the assumption that logical disagreements were synonymous with metalinguistic disagreements. Yet, upon delving into Kouri Kissel's article and examining her nuanced arguments, I am now convinced that this explanation lacks persuasiveness. In the subsequent section, I will scrutinize the shortcomings of this perspective and, concurrently, present my proposed solution to elucidate the nature of logical disagreements.
According to Kouri Kissel, in a dispute, the parties argue about the right meaning of a word in a metalinguistic negotiation. For instance, classical and intuitionistic logicians engage in a metalinguistic negotiation where they debate the meanings of terms like "or", "negation", or "theorem" to determine which logic better analyzes mathematics. In this context, if she employs the term "argumentation" in a logical sense, we must inquire about the logical rules guiding the parties' arguments. Are they following the rules of intuitionistic logic or classical logic?
According to inferential semantics for logical constants, a logical constant's meaning is established by the rules that govern it — introduction and elimination rules [Boghossian, 2003; Gentzen, 1934; Prawitz, 1977]. For example,
3It's noteworthy that Kouri Kissel herself acknowledges the complexity of determining the exact nature of disagreement in metalinguistic negotiation, and she defers the solution of this intricate problem for another time [Kouri Kissel, 2019, p. 11, footnote 14].
the divergence in the inference rules governing "negation" in the sequent calculus for classical and intuitionistic logic results in these logics allowing different meanings for this logical constant:
Classic
Intuitionistic
If classical and intuitionistic logicians are engaged in a metalinguistic negotiation about, for example, which meaning should be attributed to the term "or", they employ two distinct terms in their arguments. Consequently, resolving the dispute over the meaning of "or" in the very metalinguistic negotiation also necessitates a meta-metalinguistic negotiation. This is crucial to determine the best meaning for using that term in the metalinguistic negotiation. Clearly, to identify the optimal definition of "or" in a meta-metalinguistic negotiation, a meta-meta-metalinguistic negotiation is required as well. In other words, even if we consider most philosophical disputes to be a metalinguistic negotiation about which concepts should be used (as [Plunkett, 2015] does), the situation with logic and logical disputes differs.
During a metalinguistic negotiation in logical disputes, logicians use rules for their arguments that define the meaning of logical terms. Disagreements in the application of these rules lead to disagreements in the meanings of the terms. According to Kouri Kissel, engaging in a metalinguistic negotiation is necessary to transform the disagreement into a genuine one. In contrast, two metaphysicians, for instance, can use the same rules and meanings of logical terms in their disputes during a philosophical discussion about "time". However, when the subject of the dispute is the rules and terms themselves, how can they be compelled to apply the rules of inference or terms approved by the other one? Each logician certainly does not prefer any logic to his own and favors it over any other logic.
One might argue that, in an implicit convention, classical logic is assumed to be the logic of the metalanguage for all logics, used to express the semantics of their logical constants. Read challenges this traditional interpretation of metalinguistic logic, considering it fundamentally at odds with logical pluralism. The core concept of logical pluralism posits that all interpretations of "logical validity" are correct, and therefore, all judgments made by acceptable logics
regarding the validity of an argument are right. However, Read contends that allowing classical logic in the metalanguage of all logics implies that the only correct logic for the semantics of logics is classical. This, according to Read, contradicts the fundamental idea of logical pluralism:
If one allows object— and metalanguage to drift apart, then a split personality and logical pluralism are just around the corner. The right response is to insist on doing one's semantics in the logic in which one believes [Read, 2006, p. 17].
Furthermore, Read asserts that if a proponent of relevant or intuitionistic logic considers a classical inference, such as EFQ or Double Negation, to be invalid, they should not permit classical logic even in the semantic framework of their own logic:
...if one believes that, e.g., double negation elimination, or EFQ are invalid (as constructivist and relevantist do, respectively), then one should reject the canons of classical logic even, or especially, when applied to the semantic study of one's chosen account of validity [Ibid., p. 17].
Read raises the question: "if we take classical logic as the only way of meta-theoretical semantic interpretation, then how can we understand the main speech of non-classical logic?" To address the concerns of non-classical logics, such as relevant and intuitionistic logics, it becomes imperative to relinquish the combination of non-classical theory with classical meta-theory. Instead, one must embrace alternative forms of non-classical semantic theories to comprehend the core essence of these logics [Ibid., p. 13].
In summary, Read contends that the reduction of logical disputes to mere verbal disagreements stems from the inclusion of the semantics of a specific logic (namely, classical logic) in the metalanguage of non-classical logic. As an illustration, he references Routley's semantics for negation:
Either this has nothing to do with semantics, but enables one to manipulate the uninterpreted symbol "in pure semantics for relevance logic; or it does explain the meaning of "in which case, classical and relevance logic are discussing different connectives. If (T*) gives the meaning of " then its meaning is different from the negation in classical logic and, as Prior put it, classical and relevance logicians are "simply talking past one another" [Ibid., p. 14].
Hence, if the selection of a single logic for the metalanguage of all logical systems goes against the essence of logical pluralism, and every logician is permitted to adopt a logic in the metalanguage, how can a metalinguistic negotiation be effectively resolved? Kouri Kissel establishes a criterion to distinguish between
a purely verbal dispute and a metalinguistic negotiation. In a purely verbal dispute, the contention ends once the parties recognize that they ascribe different meanings to the same term. This is because such a dispute does not involve a genuine disagreement over the desired term's meaning. On the other hand, in a metalinguistic negotiation, even after acknowledging their disparate meanings of a word, the discussion persists until a consensus is reached regarding its correct use or meaning. However, what if they persist in arguing for their accepted meaning against each other, employing different meanings of the word in their dispute? Would this not also qualify as a purely verbal argument? Their ongoing disagreement over the word's meaning, rather than merely mentioning it, suggests that, based on Kouri Kissel's criteria, they do not bring the dispute to a close.
4. What is the purpose of logical disagreements?
In reviewing the example presented by Kouri Kissel, where two individuals in a room held different meanings of "coldness", it initially seemed that their dispute over room temperature was merely verbal. However, Kouri Kissel argued that they were engaged in a metalinguistic negotiation, disputing the right meaning of "coldness" to determine the appropriate action: whether to maintain or change the room temperature. In this context, the dispute appears to be ultimately about determining the right course of action.
According to Kouri Kissel's perspective on metalinguistic negotiation, the dispute wouldn't be considered verbal because it doesn't end without any resolution after revealing their disagreement over the meaning of "coldness". Instead, the discussion culminates in a decision — whether to maintain or change the temperature. Focusing on the ultimate purpose of the dispute provides an explanation that extends beyond mere verbal disagreement. Despite attributing different meanings to "coldness", the discussion results in a tangible outcome, demonstrating that the dispute is a genuine disagreement over the concept of "coldness" rather than a purely verbal dispute.
In essence, by examining the ultimate reaction and the resolution of the dispute, we can discern the actual nature of the disagreement. This suggests that, far from being merely verbal, there was a substantive and real dispute over the meaning of "coldness".
Now let us consider a dispute between two logicians: two logicians disagree about the validity of an argument; Despite taking different meanings of "validity", both of them argue in favor of the judgment of his logic about the validity (or invalidity) of the argument. This dispute seems verbal because they have different meanings of "validity" (or terms like "or" or "negation", etc.). However, compared to the last example, if we ask what is the purpose of the
dispute and what is the appropriate reaction after resolving the dispute for the logicians, there will be no need to resort to metalinguistic negotiation to explain the disagreement. Why do logicians oppose rival theories of "validity" or its instances (or both) and present a new theory to solve potential problems? Isn't the essence of that dispute what appropriate reaction they should take to the conclusion if they believe the argument premises? In fact, the best explanation for the fact that the dispute is not merely verbal is the changes in the belief system of those two logicians, which creates the validity of that argument; compare it with the example where the dispute was whether to maintain or change the room temperature. Thus, it seems that, regarding the ultimate reaction, the best explanation for logical disagreement is applying normative restrictions to the premises and the conclusion of the argument.
The idea that the logical validity of an argument implies that we cannot (or should not, or there is no reason to) believe its premises without believing its conclusion, and how our belief system is structured based on logical rules, has been introduced in philosophical literature as the normativity of logic. [MacFarlane, 2004] explored 36 different forms of normativity in logic (if it is normative), analyzing their strengths and weaknesses. Field expanded on this exploration, recognizing the challenges linked to a traditional definition of validity as necessarily truth-preserving. He suggests that applying normative restrictions on beliefs in premises and conclusions is a crucial condition for logical validity:
If an argument is valid, then we shouldn't fully believe the premises
without fully believing the conclusion [Field, 2015, p. 43].
Field, while not explicitly considering the normativity of logic as a sufficient condition for logical validity, [MacFarlane, 2017] argues, essentially acknowledged it as such, leading to a normative analysis of validity. However, taking a definitive stance on this matter is not necessary to articulate my perspective. Regardless of whether validity is defined as necessarily truth preservation or construed through normative constraints on belief in premises and conclusion, what is crucial for my argument is that the best explanation for elucidating the logical disagreement between two logicians lies in their ultimate response to resolve their dispute. This response entails a requirement for the acceptance of the conclusion, assuming belief in the premises of an argument.
The Inference to the Best Explanation methodology can elucidate how normative constraints on premises and conclusion can be a better explanation for genuine disagreements between logical theories. This methodology does not prioritize the manner in which an explanation is deemed the best. There is no imperative to scrutinize the specific events leading to the determination
that a theory qualifies as the best explanation. It disregards how the dispute between logicians unfolds and the specific logical rules or logical terms they employ for their argumentative disputes or whether their arguments are conducted on a metalinguistic level. The assessment of a theory as the best explanation involves external factors such as adequacy to the data, simplicity, consistency, explanatory power, and so on [Priest, 2016, p. 32].
Crucially, this approach provides a straightforward resolution to the challenging issue of meaning variance of logical constants. Despite the apparent incommensurability arising from the meaning variance of logical terms, logicians often assert that their logical systems disagree with others and engage in arguments to support their respective systems. The normative constraints approach, by transcending the specific meaning of particular system for logical terms, provides a straightforward explanation for these logical differences. The focus shifts from what logicians mean by logical terms to whether they should accept the conclusion after accepting the premises. Consequently, the normative constraint on the premises and the conclusion serves as a simple and effective explanation for the intricate problem of the meaning variance of logical constants. Furthermore, even when considering logical disagreements as disputes about logical terms, as Kouri Kissel suggests, the metalinguistic negotiations about these terms are deferred to a higher level, which remains indefinitely open-ended and lacks a clear resolution. This advantage brings more simplicity and explanatory power to this approach than Kouri Kissel' view at the same time.
To assess the superior data adequacy of the normative constraints approach, let us scrutinize an argument governed by different logics. Kouri Kissel aligns herself with a version of domain-dependent pluralism, contending that the appropriate logic or connectives depend on the domain or context of use. Consider the mixed argument from [Tappolet, 1997, p. 209]:
a) Wet cats are funny.
b) This cat is wet.
c) This cat is funny.
Sentences (a) and (c) pertain to the aesthetic domain, while (b) belongs to the empirical domain. Setting aside concerns about soundness, an inquiry into its validity arises. If logic is indeed domain-dependent, the predicament surfaces: which logic should be employed to assess the validity of an argument with premises and a conclusion from different domains? As argued by [Stei, 2023, p. 107], "the governing logic is that of the argument's weakest member.
Alternatively, in case the logics in question cannot be ordered according to their strength, the argument will be governed by the intersection of the logics in question". Regardless of the choice, the outcome is consistent: "The result is that, in broadening the frame of reference in terms of the domains involved in an argument, the domain-pluralist's assessment of validity-in-D approaches the monist's conception of validity" [Stei, 2023, p. 108].
However, a critical concern arises: How can a pluralist, especially one subscribing to domain-dependence, maintain her pluralistic approach when assessing the validity of arguments involving different domains governed by distinct logics? The initial concern in this article was to explain logical disagreements while preserving a pluralistic approach. Yet, the question of the logical validity of mixed arguments and the ensuing disagreement seems to erase pluralism. Can the metalinguistic negotiation approach to logical disagreement resolve the tension between logical pluralism and the assessment of validity for these arguments? It appears that logical pluralism has already dissipated, leaving no room for metalinguistic negotiation to choose the best logic for assessing the validity of the arguments.
Contrastingly, the normative constraints approach to logical disagreements adeptly elucidates the assessment of argument validity governed by different logics while unwaveringly upholding the tenets of logical pluralism. The domain-dependent pluralist was compelled to choose the weakest logic or intersection between the involved domains to evaluate the validity of mixed arguments, and this reduced pluralism to monism. However, in the normative constraints approach, there is no prerequisite to initially agree on a logic to resolve the dispute over the validity of that argument. It suffices to examine whether, by accepting the premises of that argument, we can (or should or there is a reason to) believe the conclusion as well. In this case, the disagreement between two logicians regarding arguments containing sentences from different domains, can be resolved without abandoning the logics that govern those domains and without necessitating a consensus on a singular logic. Therefore, the normative constraints approach can explain cases of logical disagreements that the metalinguistic negotiations view cannot resolve, establishing its superiority in terms of data adequacy.
5. Conclusion
Logical systems, being theories of logical consequence relations, can disagree on the nature or instances of this relation, or both. However, the semantic variety of logical constants and the presence of logical pluralism pose significant obstacles, rendering logical systems incommensurable and their alleged disagreements seemingly meaningless. Kouri Kissel attempts to elucidate this
disagreement through metalinguistic negotiation, wherein parties engage in argumentation to convince each other about the optimal meaning of the disputed terms.
However, a critical question arises: which logic should they employ in their arguments during the metalinguistic negotiation? If the subject of the dispute is not logic itself, the metalinguistic negotiation might not end as a purely verbal dispute, and the parties may reach an agreement on the meaning to be adopted. Conversely, if the disputed subject is logic, the metalinguistic negotiation necessitates a meta-metalinguistic negotiation to establish the meaning of the disputed terms in the metalinguistic negotiation. This recursive pattern continues with each level requiring an additional metalinguistic negotiation, creating an infinite regress.
Therefore, while adopting Kouri Kissel's framework of ultimate reaction to explain metalinguistic negotiation, I posit normative restrictions on the premises and conclusion of an argument as the superior explanation for logical disagreement. Utilizing the inference to the best explanation, I argue that the normative constraints approach effectively addresses logical disagreements while circumventing the challenges posed by the semantic variance of logical constants and logical pluralism.
Acknowledgements. 1) This article is based upon funded by Iran National Science Foundation (INSF) and University of Isfahan under project No. 4004481. 2) I am grateful to Graham Priest for reading the draft of this paper and for his valuable feedback.
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М. Альвлнд
Переосмысление логических разногласий:
критика вербализма и подход, основанный на нормативных ограничениях
Масуд Альванд
Исфаханский Университет, Иран. E-mail: [email protected]
Аннотация: Логический плюрализм утверждает, что различные концепции логики могут сосуществовать, предполагая, что все приемлемые суждения о достоверности аргумента действительны без соперничества. Эта точка зрения подразумевает, что разногласия между логическими теориями носят чисто словесный характер. Вопреки предложению Коури Киссела о метаязыковых переговорах в качестве объяснения логических разногласий, эта статья ставит под сомнение представление о том, что такие споры носят чисто вербальный характер. Используя вывод наилучшего объяснения, автор приводит доводы в пользу нормативных ограничений на веру в посылки и выводы как более убедительного объяснения логических разногласий.
Ключевые слова: логический плюрализм, металингвистические переговоры, логические разногласия, нормативность логики, вывод наилучшего объяснения
