Thought ISSN 2161-2234
Intertranslatability, Theoretical Equivalence,
University of Leeds
I investigate syntactic notions of theoretical equivalence between logical theories and a recent
objection thereto. I show that this recent criticism of syntactic accounts, as extensionally inade-
quate, is unwarranted by developingan account which is plausibly extensionally adequate and more
philosophically motivated. is is important for recent anti-exceptionalist treatments of logic since
syntactic accounts require less theoretical baggage than semantic accounts.
Keywords philosophy of logic; theoretical equivalence; anti-exceptionalism; revising logic;
intuitionistic logic; non-classical logic
It’s increasingly common to claim that logic isn’t special, that a logical theory is just a
theory like any other (Hjortland 2017; Priest 2014; Russell 2014; Williamson 2017) ese
anti-exceptionalist views use theoretical virtues of alternative logics—simplicity, strength,
etc.—in order to evaluate them analogously to how we evaluate scientic theories.
doing so, it’s helpful to know when two seemingly distinct theories are really dierently
words, it’s helpful to have an account of theoretical equivalence between logics.
For example, axiomatic and natural deduction presentations of classical propositional
logic initially look quite dierent even though they’re intuitively theoretically equivalent.
Now, natural deduction is less metatheoretically tractable while axiomatic accounts
do worse at revealing obvious entailments. Neither disadvantage is problematic once
we’re justied in treating them as theoretically equivalent; perceived disadvantages
of a logical theory that are merely presentational can be ignored in calculating its
We have options when developing a notion of theoretical equivalence. One standard
way uses semantic properties, like having the same set of models, to account for when two
logical theories are equivalent. However, as the required model theory can only be devel-
oped by appealing to signicant logical resources, many of which are in contention when
choosing between logics, it’s natural for anti-exceptionalists to prefer less theoretically
taxing syntactic accounts of theoretical equivalence. Syntactic accounts require lighter
metatheoretic resources (roughly a basic theory of syntax) which can oen be developed
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58 Thought 7 (2018) 58–68 © 2018 The Thought Trust and Wiley Periodicals, Inc.