Abstract
Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops.
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Notes
Quine himself on the following and much less quoted pages admits that one can, of course, consciously propose changing the subject and provide reasons for such a change. Yet I think it is fair to concur with him that most of the deviant logicians understand their proposals differently, as not changing the subject. Thus, if Quine’s thesis that change of logic amounts to a change of subject were right, they fall prey to a misconception and cause a misunderstanding in the debates.
The open-endedness of logical vocabulary, as well as of many other vocabularies of natural language, is more appropriately to be regarded as quite a fortunate property, as it allows our language to be flexible and adapt to the situations and challenges we actually face. But that would be a topic for a different debate.
In [20].
See pp. 78–79 in [1].
In fact, according to Brandom’s inferentialism, on the background of which he proposes also logical expressivism, the meaning of a given expression consists precisely in the inference rules it is submitted to. Although I myself agree with it, I will not dwell on defending this general inferentialist understanding of meaning here. It is enough for the present purposes to acknowledge that inference rules are an important part of the meaning of all expressions. This view, I believe, should be acceptable for most philosophers of language.
A non-controversial example is not easy to find here, yet perhaps we can say that in previous centuries, people used the word justice slightly differently than we do. Some behaviour which we consider as unjust was considered as just by our ancestors and vice versa. Maybe, they would even tend to define justice little bit differently then we would. Still, it is quite natural to say that we talk about the same thing, namely about justice and that the concept has somewhat developed. It would be much more stretched to claim that the concept has been replaced by a new one, at least if the differences are not all too great between our ancestors and us.
The dots on the side of the word signify, for Sellars, the role the given expression plays in the whole of the language, a role which is common, for example to English words and their adequate German translations. But this peculiar feature of Sellars’ notation and thought, however valuable in itself, does not have to be dwelled upon here.
Hardly ever does not mean never in general and maybe even in our particular case. The field of logical systems is so vast that virtually nothing can be claimed without exceptions or provisos. Polish logicians, inspired by ideas of Lukasiewicz, have developed the refutation systems, which are supposed to, contrary to the logical consequence relation according to the established orthodoxy, not bring us from true premisses to to true conclusions but rather from false or refuted premises to false or refuted conclusions. The basic ideas on which this approach is based were presented already in [16] and then rigorously developed in [23]. The history of these attempts is nicely summed up in [25] where the authors argue that refutation systems model the methods of falsification of a hypothesis in empirical science (see pp. 179–180). [4] offers a particularly straightforward example of such a refutation system, namely the anti-classical system in which a formula is consequence of a given set of premisses if and only if it is not a consequence in classical logic. Obviously, for a consistent set \(\Gamma \) we then have \(\Gamma \models \lnot \phi \) in the anti-classical system when we have \(\Gamma \models \phi \) in classical logic. This might be regarded as a counterexample to what I claim that hardly ever is the case. But besides the fact that hardly ever does not mean never, I can also defend my assertion by noting that although the logical symbols including negation can develop in multifarious and in general unpredictable manners, this does not mean that anything goes. Negation can have many flavours but it hardly makes sense to call the \(\lnot \) sign of the anti-classical system a negation. The authors of [4] (p. 6) themselves deny that it is a(seemingly paraconsistent) negation, claiming that the usage of the symbol \(\lnot \) merely reminds us of the origin of the new operator which is defined by means of the classical negation. I thank the anonymous referee for making me aware of the refutation systems.
See p. 76 of [2].
This article was supported by grant 17-15645S Logical models of reasoning and argumentation in natural language, led by Jaroslav Peregrin from Czech Academy of Sciences.
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This article was supported by Grant 17-15645S Logical models of reasoning and argumentation in natural language, led by Jaroslav Peregrin from Czech Academy of Sciences.
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Arazim, P. Beyond Logical Pluralism and Logical Monism. Log. Univers. 14, 151–174 (2020). https://doi.org/10.1007/s11787-020-00253-2
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DOI: https://doi.org/10.1007/s11787-020-00253-2