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The Centrality and Diversity of the Invisible Constitution
153
not, would be a series of centrally important rules that the rule of recognition
must validate and yet that must remain unexpressed. The argument to this
conclusion depends upon certain ideas found in the philosophy of logic and
mathematics.
5.3.1. Hartian Positivism Compared to the
Conventionalist Account of Axiomatic Systems
Hart’s conception of a legal system yields a picture that evokes certain central
ideas of the analytic philosophy of the latter part of the nineteenth century
and the first half of the twentieth century. I want to explain how this is so,
in order to then derive consequences concerning the invisible elements of a
constitutional order.
A key concern in the analytic tradition just mentioned is understanding
the nature of axiomatic systems – that is, systems of propositions constructed
via logical or mathematical deduction from a set of axioms that are not them-
selves proved to be true. One core contention to emerge from this tradition
is the idea that what underpins an axiomatic system is convention. What is
meant by this is that the axioms of (say) a system of geometry or of arithmetic
should not be understood as expressing primitive truths that are known to intu-
ition but not capable of further analysis; rather, they should be understood as
establishing permissible ‘moves’ within the system, and as thereby implicitly
defining the terms that occur within them (e.g., if the axioms of a certain
system of geometry use terms such as point and line, then those axioms serve
to implicitly define the meaning of those terms, which meaning is fully given
by the ‘moves’ that may be made by way of deducing propositions in which
those terms occur).
21
From the inside, the axioms and the statements that are
deduced from them are necessarily true, in the sense that one cannot reject
them while nevertheless working with the system in question. But from the
outside, they are not necessary at all. Other axioms might be chosen, from
which different consequences would follow.
There is an obvious similarity here to Hart’s rule of recognition, which from
the external point of view is a mere empirical state of affairs,
22
but which is
necessarily ‘presupposed’
23
by statements that such-and-such a rule is a valid
law. Questions of validity arise within the system, and so treat the rule of rec-
ognition analogously to a (necessarily true) axiom; but when considered from
21
For an excellent discussion, see J. Alberto Coffa, The Semantic Tradition from Kant to Carnap:
To the Vienna Station (Cambridge: Cambridge University Press, 1991), 54–61, 128–40, 312–26.
22
See e.g., Hart, Supra note 9, 102–3, 107–8, 110–11.
23
For Hart’s use of this word, see e.g.,
ibid.
108–9.
154
Patrick Emerton
the outside, the rule of recognition is not necessary and clearly might have
been otherwise.
But how, exactly, does a conventional rule establish permissible ‘moves’? In
a system of mathematics or a system of law, these moves are governed by rules
of inference – but where do those rules come from, and how are they related
to the other elements of the system? The following two subsections take up
these questions.
5.3.2. The Necessarily Unwritten Character of Rules of Legal Inference
Lewis Carroll, in his essay ‘What the Tortoise said to Achilles’,
24
makes the
following point: while for every valid argument there is a corresponding con-
ditional statement that (a) takes the conjunction of the premises as its ante-
cedent and the conclusion of the argument as its consequence; (b) is logically
true; and (c) states the rule of inference that underpins the argument, we nev-
ertheless cannot require that this conditional statement itself be a premise in
the argument, on pain of incoherence. For instance, consider the argument:
(1) A;
(2) Either not-A or B;
Therefore:
(3) B.
This argument is valid. And there corresponds to it the following logically true
conditional, which takes the conjunction of (1) and (2) as its antecedent and
takes (3) as its consequent:
(4) If A and either not-A or B, then B.
The conditional (4) states the rule of inference that underpins the validity
of the argument from (1) and (2) to (3). However, it cannot be the case that
the validity of that argument depends upon affirming (4), as if it were a hither-
to-suppressed premise. If validity depended upon including the underpinning
rule of inference as a premise in the argument, then it would follow that the
new argument – from (1), (2) and (4) to (3) – could not be valid unless the rule
of inference that underpins it were also included as a premise, which would
then demand the inclusion of a further premise stating the rule of inference
underpinning this further argument, and so on in an infinite regress.
25
24
(1895) 4 Mind, 278.
25
For exposition and discussion of Carroll’s argument, see Coffa, Supra note 21, 161–2; Alan
Musgrave, ‘Wittgensteinian Instrumentalism’ (1980) 46 Theoria, 65, 88–9; Jan Willem Wie-
land, ‘What Carroll’s Tortoise Actually Proves’ (2013) 16 Ethical Theory and Moral Practice
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