Abstract
Logics—that is to say logical systems—are generally conceived of as describing the logical forms of arguments as well as endorsing certain principles or rules of inference specified in terms of these forms. From this perspective, a correct logic is a system which captures only (and perhaps all of) the correct principles, and good—that is, logical—reasoning is reasoning which at the level of logical form conforms to the principles of a correct logic. In contrast, as logical particularists we reject the idea that logical validity is a property of logical forms or schema, and instead take validity to be a property of particular inferences. In this chapter, we describe and defend this radically different approach to validity and explore the particularist understanding of the relationship between logical systems and logical reasoning.
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Notes
- 1.
Although we have argued elsewhere that giving the same rules to connectives does not mean that the connectives have the same meaning qua natural language connectives (Wyatt and Payette 2018), we do not doubt the mathematical significance of the construction and the purely mathematical conception of proof-theoretic meaning used in the construction. It is the mathematical significance of the constructions that interests Franks, if we have understood him correctly. We are not at odds on this point.
- 2.
- 3.
As will become clear from the subsequent discussion, we do reject the view on which formal logic sheds light on the validity of arguments by directly representing the semantics of natural language sentences. See Stokhof (2007) for a discussion of the relationship between formal languages and natural language semantics that is somewhat parallel to the view of the relationship between formal logics and natural language argument advocated here.
- 4.
Cook’s account of how logics model validity is very similar to that of Shapiro (2014): the primary difference is that Shapiro takes logics to be only in the business of modelling mathematical argument, while for Cook mathematical argument is a special case of a more general goal.
- 5.
Cook refers to models as ‘mock-ups’ (Cook 2002).
- 6.
Notice that this picture is absolutely neutral on the nature of the relationship between the phonological realization or the syntax of natural language sentences and their logical forms .
- 7.
See Payette and Wyatt (2018) for more discussion of this point.
- 8.
Abstraction here covers both idealization and fictionalization in science, where fictional models are those in which no amount of de-idealization—that is, no amount of adding in details left out or correcting false assumptions—would recover a correct description of the actual world (Bokulich 2011).
- 9.
Hindriks (2008) also argues that models in the economics context can be better when containing a larger number of unrealistic assumptions.
- 10.
The periodic table does not, contra the usual historical story, indicate directly the presence of missing elements, nor does it generate any predictions of specific quantitative properties. See Woody (2014) for further discussion.
- 11.
Giere proposes that the representative features of models fall under the general schema: S uses X to represent W for purposes P. Some of this purpose relativity is already present in Cook’s view since which components are representors and which are artifacts may depend on the goal of the model. That goal is, presumably, imposed on the model. It is possible that Cook would be in closer agreement than we have suggested here, but note that critics, for example, Smith (2011), describe Cook’s view as one where representation is a relation between (parts of) models and reality, rather than the 4-ary relation above. We won’t enter any further into debates about how to interpret Cook here since our goal is to advance our own view.
- 12.
This is not a descriptive claim; that is, we are not claiming that this is how logicians understand what they are doing, whether collectively or individually. Rather this is a claim about how we should understand logical practice. In line with our anti-exceptionalism, we are approaching the epistemological and metaphysical questions in logic in the same way in which the philosopher of biology approaches those questions in biology. In both cases one must attend to the messy business of how science actually gets done. For further discussion of our methodology, see Payette and Wyatt (2018).
- 13.
For example, □p ⊃ p is true at every world in every model on a Kripke frame (W, R) iff ∀w, wRw.
- 14.
- 15.
See van Benthem (1997) for an overview.
- 16.
Here we are using ‘completeness’ in the (common) sense which includes both completeness and soundness theorems.
- 17.
See Franks (2010) for more on interpretations of completeness.
- 18.
You cannot add a formula that isn’t a theorem to CPL as a new theorem without being able to then prove everything.
- 19.
All of the admissible rules are derivable rules. For more on that distinction, see Iemhoff and Metcalfe (2009).
- 20.
See Wyatt and Payette (2018).
- 21.
See, for example, the discussions in McKeever and Ridge (2005), Cullity and Holton (2002) for moral particularisms, and Lakatos (1976) and Larvor (2001, 2008) for particularism in mathematics. John Norton’s material theory of induction is, we think, a particularist approach to inductive argument (2003, 2010).
- 22.
- 23.
- 24.
We argue in Wyatt and Payette (2018) that attributions of logical form are only possible from within a logic.
- 25.
Logical particularism can be seen as a form of instrumentalism, but not at the level of theory justification. That is, we don’t take it that a ‘correct’ logic is the most useful one. Rather we take it that the practices and methods of formal logic are instrumentally justified because of their effectiveness in explanation.
- 26.
Of course one could give other interpretations of the connection modeled by classical logic, and some people disagree with the classical interpretation of truth preservation, see, for example, Read (1994).
- 27.
The examples above are not very interesting sets. Each has only its partition into unit sets, and so something follows when it follows classically from at least one of the formulas.
- 28.
This is at least true for certain parts of the models in Castañeda (1981).
- 29.
This is done in Searle and Vanderveken (1985).
- 30.
a.k.a. mathematically defined logical connectives.
- 31.
Note that we did not say that ⊢ explicates the arguments from L′. We agree with Woody, if we have interpreted her correctly, that what is often called ‘explication’ is simply a stage in explanation. Models, particularly mathematical ones, become part of the understanding of phenomena.
- 32.
This is similar, we think, to the project in Field (2015) where commitments to relationships between degrees of belief are translated into logical rules. Particularism assumes that logical connections can be about things other than degrees of belief.
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Payette, G., Wyatt, N. (2018). Logical Particularism. In: Wyatt, J., Pedersen, N., Kellen, N. (eds) Pluralisms in Truth and Logic. Palgrave Innovations in Philosophy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-98346-2_12
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