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What is Wrong with Deductivism?
LILIAN BERMEJO-LUQUE
Department of Philosophy I
University of Granada
Edificio de Psicología, Campus de Cartuja. Granada 18001
Spain
lilian.bermejoluque@gmail.com
Abstract: In “Deductivism as an In-
terpretative Strategy: A Reply to
Groarke’s Defense of Reconstructive
Deductivism,” David Godden (2005)
distinguished two notions of deductiv-
ism. On the one hand, as an interpre-
tative thesis, deductivism is the view
that all-natural language argumenta-
tion must be interpreted as being de-
ductive. On the other hand, as an
evaluative thesis, deductivism is the
view that for a conclusion to follow, it
has to follow of necessity from the
premises—or, in other words, that
being a good inference implies being
deductive. The main goal of this pa-
per is to show that evaluative deduc-
tivism is wrong.
Résumé: Dans «Le déductivisme
comme stratégie interprétative: une
réponse à la défense de Groarke
contre le déductivisme reconstructif»,
David Godden (2005) a distingué
deux notions de déductivisme. D'une
part, en tant que thèse interprétative,
le déductivisme est l'idée que toute
argumentation en langage naturel doit
être interprétée comme étant déduc-
tive. À son tour, en tant que thèse
évaluative, le déductivisme est l'idée
que pour qu'une conclusion s’ensuive,
elle doit nécessairement découler des
prémisses - ou, en d'autres termes,
qu'être une bonne inférence implique
d'être déductive. L'objectif principal
de cet article est de montrer que le
déductivisme évaluatif est faux.
Keywords: evaluative deductivism, interpretative deductivism, linguistic nor-
mative model of argumentation (LNMA), inference vs. argument, types of in-
ferences, normativity of inference
1. Introduction
In “Deductivism as an Interpretative Strategy: A Reply to
Groarke’s Recent Defense of Reconstructive Deductivism,” David
Godden (2005) distinguished two notions of deductivism. On the
one hand, as an evaluative thesis, evaluative deductivism (D1) is
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the view that for a conclusion to follow, it has to follow of necessi-
ty from the premises—or, in other words, that being a good infer-
ence implies being deductive. On the other hand, as an interpreta-
tive thesis, interpretative deductivism (D2) is the view that all nat-
ural-language argumentation must be interpreted as being deduc-
tive. In that paper, Godden argued that evaluative deductivism is
wrong and that, for this reason, interpretative deductivism must be
grounded on something other than the claim that ‘q follows from
p’ means ‘q necessarily follows from p.’
Despite Godden’s remarkable observations in that paper, evalu-
ative deductivism has proven to be difficult to refute. The reason is
that its intuition on the meaning of ‘follows’ can always be saved
by means of a straightforward strategy for rendering deductive any
piece of argumentation—namely, to assume that it has an implicit
conditional premise with, as its antecedent, the conjunction of the
set of premises of the original argument and, as the consequent, its
conclusion (which, in turn, may be qualified as required with
modals such as presumably, likely, probably, etc.). Of course, such
a strategy blurs the distinction between monotonic and non-
monotonic inferences, and it is also available for Bayesian infer-
ences: all that is needed is the trivial conditional and the adequate
modal for the conclusion. Accordingly, for the deductivist, point-
ing to these types of inferences would not show that deductivism is
wrong.
The main goal of this paper is to show that evaluative deductiv-
ism is wrong. In order to do this, in sections 2 and 3, I build the
following modus tollens: as Godden has argued, “the correctness
of deductivism as an evaluative thesis can be invoked as a reason
for its acceptability as an interpretative strategy. Clearly, if [D1]
were true—that is, if the only acceptable standard of evidence was
that embodied in the rules of deduction—then [D2] would follow
as a consequence” (Godden, 2005, p. 170). Thus, by showing that
interpretative deductivism is implausible, I will show that evalua-
tive deductivism is wrong. My second goal is to explain why eval-
uative deductivism is wrong. Authors endorsing evaluative deduc-
tivism contend that the only possible standard of inference is to
require the conclusion not to be wrong if the premises are right. In
section 4, I show that the model of inference that I defend in this
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paper accommodates this standard in a certain way without imply-
ing that deductive inferences are the only inferences that can be
taken to be good. As I will point out, this alternative version of the
standard of inference springs from the very notion of inference:
what makes an inference good is constitutive of what an inference
is, not a matter of conforming to standards that, on some more
basic intuition, seem sound.
2. The relationship between evaluative deductivism and inter-
pretative deductivism
As Godden pointed out:
D: if it is true that for a conclusion to follow it has to follow of
necessity from the premises (evaluative deductivism), then
it is plausible to interpret natural language and argumenta-
tion as deductive (interpretative deductivism)
D is the way in which deductivism affects our theories of how to
interpret natural language argumentation and reasoning. For, in
principle, as Godden observes, if evaluative deductivism were
true, then we would have good reason to believe that individuals
aim at making deductions—for, otherwise, they would not aim at
arguing or reasoning well, which is implausible. Consequently, in
order to properly represent what people mean when they argue or
reason, we should render their inferences deductive, as far as pos-
sible.
Importantly, this is always possible. Certainly, people do not
always reason or argue in a way in which what they put forward as
their conclusion cannot be false if what they put forward as their
premises is true; but we can always assume that their argumenta-
tion is enthymematic and reconstruct what they say so as to render
their inferences deductive. This is then the way of understanding
interpretative deductivism: in it, ‘interpreting’ does not really
stand for ‘understanding’ but for ‘reconstructing.’
Because we can always reconstruct inferences as being deduc-
tive, evaluative deductivism turns out to be a requirement to re-
construct all natural language argumentation and reasoning as de-
ductive. This is why deductivists, such as Groarke, hold that the
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meaning of words like ‘therefore,’ ‘so,’ ‘hence,’ etc. announces
the speaker’s intention of making a deductively valid inference
(Groarke, 1992, p. 114). Consequently, mainstream deductivism
also endorses this conditional:
D’: if for a conclusion to follow it has to follow of necessity
from the premises (evaluative deductivism), then natural lan-
guage argumentation must be interpreted as being deductive
(interpretative deductivism)
Importantly, defending D and D’ on this ground requires acknowl-
edging that we build arguments as a means to represent natural
language argumentation and reasoning. That is, arguments would
be reconstructions from real things such as reasonings and pieces
of natural language argumentation as they occur in everyday life.
On the other hand, this line of defense of D and D’ would also im-
ply that being a deductive inference cannot be the same as being a
good inference. After all, that people intend to infer well—which
is the reason why, allegedly, we should interpret them as making
deductions—should not imply that they get to infer well, on pain
of making the task of appraising inferences pointless.
In a way, this was Copi’s view (1978: p. 32) when he pointed
out that deductiveness and validity are different notions. Yet, un-
less we are able to distinguish between the inferences that people
actually make—which according to the deductivist are supposed to
be deductive—and the arguments by means of which we represent
them—which may represent good or bad inferences—we could
not point to an instance of something that is both deductive and a
bad inference. This is so because any set of propositions that
stands for a deductive argument also stands for a valid argument.
For this reason, authors like Berg (1987), Vorobej (1992), and
Godden (2005) hold that whether an inference is deductive or not
is a matter of the arguer’s intentions. Specifically, an inference
would be deductive if its conclusion is meant to follow of necessi-
ty; and if it actually does follow of necessity, then the inference
will be not only deductive but also valid.
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Authors like Machina (1985) and Hitchcock (1980, 2017) disa-
gree with this intentionalist notion of deductiveness. For example,
Hitchcock says that:
(…) appeals to the intentions or claims or beliefs of reason-
ers and arguers are vacuous in many cases and are unneces-
sary for argument appraisal (…). As one can confirm for
oneself by immediate retrospection, reasoners who draw a
conclusion for themselves from information at their disposal
are typically unaware of whether they are drawing it conclu-
sively or non-conclusively. Reasoners just draw their con-
clusions, and it is only after that inferential act, if at all, that
they determine whether their conclusion follows conclusive-
ly or non-conclusively. As for arguers, they sometimes claim
a qualitative degree of support for their conclusion by quali-
fying it with terms like ‘must’ or ‘probably’ or ‘presumably’
or ‘may.’ But they do so in a minority of cases. (Hitchcock:
2017, p 252)
If we cannot discover an arguer's intentions in this respect, we
must construe the argument as ambiguous and test it against both
deductive and inductive (and conductive and…) standards. (Hitch-
cock, 2017, p. 5).
However, since interpretative deductivism urges us to take as
part of the inference any premise needed in order to make the cor-
responding argument deductive, following Hitchcock’s strategy on
such ground would require us to reconstruct any inference as a de-
ductively valid argument.
For my part, I agree with Berg, Vorobej, and Godden that we
can only appraise an inference by considering what the subject
means by it. Particularly, we have to take into account the way in
which she means her conclusion to follow from her premises. For
example, imagine someone saying, “John’s car is in front of his
home; so, he’s at home,” It is only by ascribing a certain epistemic
force to their conclusion that we can say that their argumentation
is good or bad: if we take them to mean that necessarily John is at
home, we will say that their argumentation is bad; whereas if we
take them to mean that presumably John is at home, we will say
that their argumentation is good. At any rate, unless we attribute
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some intention in this respect to the speaker, we will not be in a
position to appraise their argumentation. Notice that, for the de-
ductivist, the latter would also be a deductive inference whose
conclusion is “presumably, John is at home,” which would follow
necessarily from the premise “John’s car is in front of his home”
and the implicit premise “if John’s car is in front of his home,
then, presumably, he is at home” (Groarke, 1992, p. 115).
Among others, Govier (1992) and Godden (2005) have argued
that we cannot add the conditional that makes explicit the inferen-
tial link between premises and conclusion as a premise because, as
Lewis Carroll (1895) would have shown, this conditional does not
play the same role as the other propositions of the inference. How-
ever, as Castañeda (1960) and Botting (2016) have observed, that
premises and associated conditionals play different roles does not
imply that we cannot reconstruct inferences as deductive argu-
ments. For, as pointed out, arguments are mere reconstructions of
the inferences that we make, and we build them in order to ap-
praise the semantic properties of these inferences; if the model ac-
tually helps to determine whether the inference is good or bad,
whether it does so by rendering the inference deductive is unim-
portant. Remarkably, if we think of interpretative deductivism as
the thesis that we can reconstruct inferences as deductive in order
to appraise them, then deductivism would be harmless. But, of
course, this is not what interpretative deductivists contend: their
claim is that we must reconstruct inferences as deductive in order
to accurately represent what people mean when they infer because,
in the deductivist’s view, ‘follows’ means ‘necessarily follows.’
Thus, my next step is to present a theory of inference that is able to
make sense of the two intuitions behind D and D’—namely, that
we build arguments to represent the inferences that we make in
arguing and reasoning, and that not all deductive inferences are
valid— and still also able to relieve us from the obligation to re-
construct natural language argumentation and reasoning as deduc-
tive in order to properly represent what individuals mean when
they aim at making good inferences.
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3. Reasoning, argumentation, inferences, and arguments. The
linguistic normative model of argumentation
Within the framework of formal logic, an argument is usually de-
fined as a set of propositions, one of which—the conclusion— fol-
lows from the others—the premises. But the problem with this def-
inition is: if the premises of an argument do not follow from the
conclusion, isn’t such a set of propositions just a set of proposi-
tions? As Fohr (1979, p. 5) observed, the common usage of the
term ‘argument’—and the very business of appraising argu-
ments—requires that there can be bad instances of it. This is why
he recommends that we refrain from thinking of arguments as
things that exist in vacuo, but instead think of them as being per-
son-related (Fohr, 1979, p. 5).
In Bermejo-Luque (2011), I proposed a linguistic normative
model of argumentation (LNMA) that captures Fohr’s intuition
that the best way of avoiding such problems is to adopt a pragmat-
ic linguistic perspective able to abandon Platonism altogether, that
is, the view that arguments as abstract entities exist so that people
just use them when they argue or reason. LNMA follows Bach and
Harnish’s (1979) speech-act schema (SAS) in order to characterize
argumentation as a second order speech-act complex, that is, as a
speech-act composed of a speech-act of adducing (the reason, R)
and a speech-act of concluding (the conclusion or target-claim, T).
Acts of adducing and acts of concluding are constatives, whether
directly or indirectly performed, literal or non-literal; but they are
second order because they can only be performed by means of first
order constative speech-acts. According to this model, a perfor-
mance of, for example, “I promise I’ll take care, don’t worry”—
which, in principle, involves just two first order speech-acts, that
is, a promise and a request—turns into a speech-act complex of
arguing because it turns these two first order speech-acts into the
constative speech-act of adducing that the arguer commits herself
to take care and the constative speech-act of concluding that the
addressee should not worry, respectively.
Two speech-acts become an act of adducing R and an act of
concluding T because of their relationship to an implicit inference-
claim whose propositional content is “if R, then T.” In a few
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words, it is by attributing to the speaker the implicit inference-
claim “if (it is true that) I commit myself to take care, then (it is
true that) you should not worry” that we interpret their utterances
of “I promise I’ll take care” and “Don’t worry” as a single speech-
act—namely, an act of arguing. Normally, the fact that the speaker
has used some epistemic modal (like “probably,” “necessarily,”
“presumably,” etc.) or an illative expression like “so,” “therefore,”
“since,” “consequently,” etc. is what authorizes us to interpret the
speaker’s performance as a speech-act of arguing. Very roughly,
the idea is that, illocutionarily, acts of arguing, so characterized,
count as attempts at showing a target-claim to be correct. To the
extent that they succeed in this—which means that the target-claim
has been correctly qualified by a certain epistemic modal (seman-
tic conditions) and that the act of arguing is a good means for
showing this (pragmatic conditions)— they will be deemed good
argumentation.
In order to determine whether a target-claim has been correctly
qualified, we have to build arguments. That is, in LNMA argu-
ments are mere representations of the particular inferences that
supervene on acts of arguing and on acts of reasoning (i.e., partic-
ular inferential processes that are the mental counterparts of acts of
arguing). In contrast with acts of arguing and acts of reasoning,
which are, so to speak, ‘objects’ of the world, arguments are con-
structions, not abstract eternal objects from a Platonic world. From
this perspective, we would not use arguments, but produce them in
order to represent the inferences that we make.
As such, arguments can be obtained by displaying a variety of
models, such as those of the different formal systems or informal
argumentative schemas. For its part, LNMA adopts Toulmin’s
model of argument (Toulmin, 1958), because its underlying con-
ception of material inference matches the analysis of argumenta-
tion that the SAS for the speech act of arguing provides (Bermejo-
Luque, 2011, chap. 3). Accordingly, LNMA follows Toulmin’s
intuition that modal qualifiers are key to the semantic appraisal of
argumentation. Yet, in contrast with Toulmin’s model, LNMA’s
model of argument incorporates two types of modals: ontological
and epistemic.
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In everyday discourse, we can make explicit the variety of ways
in which we can put forward a certain semantic content p in a first-
order constative speech-act by saying, for example “p is true,” “p
is (more or less) probable,” “p is (more or less) acceptable,” “p is
(more or less) verisimilar,” “p is plausible,” “p is necessary,” “p is
possible,” etc. By so doing, we make another type of second-order
speech-acts (Frápolli, 2012, p. 129). These ontological modals are
terms that make explicit the type and degree of the pragmatic force
of the constatives comprising an act of arguing. They are ontologi-
cal because they are meant to express the value of our propositions
as representations of the actual state of the world. When we put
forward a propositional content with the appropriate pragmatic
force given the actual state of the world, we make first-order con-
statives that are semantically correct—like the correct assertions
“(it is true that) snow is white,” “(it is necessary that) a bachelor is
an unmarried man,” “(it is plausible that) there is life on other
planets,” etc. Contrastingly, the modal that expresses the pragmat-
ic force with which we draw a conclusion is an epistemic modal.
This modal is meant to communicate what we take to be our cre-
dentials for concluding, that is, the type and degree of support that
our reasons are supposed to confer on our target-claims because of
our inference-claims. For example, in saying that a claim holds
truly, necessarily, possibly, plausibly, (more or less) probably, etc.
(i.e., in saying things such as “certainly p,” “necessarily p,” “it
might be the case that p,” “plausibly p,” “(more or less) probably
p,” etc.), we are expressing something about the status of this
claim as knowledge, about the confidence that we may place on it.
Thus, any second-order speech-act of concluding involves, either
explicitly or implicitly, not only the ontological modal of the first-
order constative that it is built on, but also the epistemic modal
that indicates the force with which this first-order claim is con-
cluded.
As representations of the inferences that supervene on acts of
arguing and acts of reasoning, arguments in LNMA consist of the
following elements: premises (corresponding either to the speech-
act of adducing a reason, R, or to the cognitive input in the act of
reasoning, CI), conclusion (corresponding either to the speech-act
of concluding a target-claim, C, or to the cognitive output in the
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act of reasoning, CO), warrant (corresponding either to the infer-
ence-claim in the act of arguing, IC, or to its counterpart in the act
of reasoning; i.e., the inference-motivation, IM) and the represen-
tations of the epistemic and ontological modals, em and om, of
each of the speech-acts making up the act of arguing (correspond-
ing to the type and degree of constative pragmatic force with
which the speaker, either implicitly or explicitly, puts forward the
propositional content of each constative) or of the judgments and
beliefs constituting the act of reasoning (corresponding to the type
and degree of assent to each propositional content constituting the
act of reasoning). Thus, an ascription of both epistemic and onto-
logical modals (ultimately, the ascription made by the arguer or
the reasoner, which, in case she does not make them explicit, is
something that we will have to infer from the context) is part of
the layout of arguments, and the semantic appraisal of an act of
arguing or reasoning results in the process of determining the right
ascription of modals to each represented claim or judgement/belief
(i.e., the process of ascertaining whether or not the ascription made
by the arguer or the reasoner is correct after all). This model of
argument can then be outlined as follows:
(omr/ci)Premise _________therefore___ (emx)(omc/co) Conclusion
|
since
(omic/im)Warrant: “if R/CI, then C/CO”
(The contents of the antecedent and the consequent of the war-
rant correspond to the whole first-order constatives R and C of the
act of arguing, i.e., to their propositional contents in conjunction
with their [implicit or explicit] ontological modals, or to the whole
cognitive input and output, CI and CO of the act of reasoning, i.e.,
to their propositional contents and their corresponding type and
degree of assent).
Let represent the idiomatic function that, for each ontological
modal of a conditional, assigns the epistemic modal needed to
draw a conclusion having this conditional as its warrant; or, in
other words, the term that is used in a certain language for express-
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ing either the pragmatic force of any speech-act of concluding
having a conditional so qualified as its inference-claim, or the type
and degree of assent to the cognitive output having a conditional
so qualified as its inference-motivation.
(omi) = emi
In this account, an argument is valid (i.e., the inference is good,
whatever its type) iff emi = emx and omi is correct—that is, if it is
the ontological modal that actually corresponds to the inference-
claim as a constative or to the inference-motivation as a belief or
judgement, given the actual state of the world. In other words, an
argument is valid if and only if the epistemic modal that the
speaker (or reasoner) has used for concluding or coming to believe
the cognitive output is the epistemic modal that assigns to the
ontological modal of the speaker’s implicit inference-claim or in-
ference-motivation, and this ontological modal is appropriate for
this inference claim or inference motivation given the actual state
of the world.
In LNMA, deductive arguments are arguments representing
acts of arguing or acts of reasoning whose inference-
claims/inference-motivations are meant to be necessary truths (like
“if this is red, then it is coloured”). We know that an inference-
claim or inference-motivation is meant to be necessary because the
conclusion was drawn with such epistemic pragmatic force. In
case this conditional is a necessary truth indeed, the argument will
be valid, and the arguer will be entitled to epistemically qualify the
conclusion with a “necessarily.” For example, pieces of argumen-
tation such as “She is in the garden or in the living-room, and she
is not in the garden; so, necessarily she is in the living-room” or
“This may be red; so, necessarily, it may be coloured” are deduc-
tive and valid because their corresponding inference-claims are the
necessary truths “if (it is true that) she is in the garden or in the
living-room, and (it is true that) she is not in the garden, then (it is
true that) she is in the living-room” and “if (it is possible that) this
is red, then (it is possible that) it is coloured.” Likewise, valid
probabilistic arguments will be those representing acts of arguing,
or acts of reasoning, whose inference-claims/inference-
motivations are meant to be (more or less) probable so that they
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entitle us to epistemically qualify their conclusions with a “(more
or less) probably/likely.” For example, “Our currency is losing
value; so, very probably, the inflation rate will rise” has as its in-
ference-claim “if (it is true that) our currency is losing value, then
(it is true that) the inflation rate will rise,” which is very probable
indeed (and makes the argumentation inductively valid).
Because LNMA deals with inferences as kinds of doings, it al-
lows for an inference to be invalid and still be, for example, a de-
ductive inference. Specifically, in LNMA, validity is not the same
as deductiveness: “deductive,” “inductive,” “conductive,” “abduc-
tive,” “presumptive,” etc. are names for types of inferences (i.e.,
forms of inferring), and any of them may go wrong.
4. Evaluative deductivism
LNMA deals with arguments as reconstructions of the inferences
that we make in arguing and reasoning. On the other hand, it char-
acterizes deductiveness in terms of the way in which the speaker
or reasoner epistemically qualifies their conclusion, and it charac-
terizes validity as a matter of the correctness of the corresponding
inference-claim or inference-motivation. Thus, LNMA also pro-
vides an account of the distinction between deductiveness and va-
lidity. As a consequence, LNMA is able to make sense of the two
intuitions underlying conditionals D and D’, as pointed out in sec-
tion 2. In turn, by means of LNMA’s particular account of deduc-
tiveness and the theory of interpretation and reconstruction that
this model involves, we can have a fair representation of what in-
dividuals mean when they reason or argue without rendering de-
ductive all of their inferences. Consequently, by modus tollens, I
have indirectly shown that evaluative deductivism is wrong.
Unfortunately, I think this is the most we can do as regards
showing that evaluative deductivism is wrong, because, as pointed
out in section 1, this thesis is but a basic intuition on what ‘fol-
lows’ means. In the remaining sections of this paper, I would like
to explain, in turn, what is wrong with evaluative deductivism so
understood.
Evaluative deductivists endorse the intuition that for an infer-
ence to be good, its conclusion cannot be false if the conjunction
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of its premises is true. But how do we establish what the actual set
of premises of an inference is if, as we have seen, interpretative
deductivism requires that we add whatever premises are needed in
order to precisely warrant this? No doubt, rendering inferences
deductive by including the associated conditional as a premise
may be a functional strategy for evaluation: by doing so, we can
“discover” where the eventual failure of the argument lies. As we
have seen, there is no problem in reconstructing inferences as de-
ductive in order to appraise them. The worst thing we can say
about this kind of weak interpretative deductivism is that, because
it turns any inference into a good one—for example, an instance of
modus ponens—it does not seem a good strategy to determine
whether or not a certain inference is good after all. Actually, the
deductivist strategy only works for assessing inferences as a
whole; according to this strategy, bad inferences are bad because,
despite being deductive, they include one or more unacceptable or
false premises.
For its part, LNMA also deals with the evaluation of inferences
in terms of the evaluation of the claims that inferences consist of.
In LNMA, we reconstruct inferences by means of a theory of in-
terpretation that does not require us to put in the speaker’s mouth
anything else but the first order constatives that they made in their
act of arguing, including the implicit inference-claim. An obvious
advantage of this method is to avoid the dilemma of being either
too strict or too charitable in our reconstructions. All that we need
to represent an inference is being able to understand it as involving
the propositional content that has been adduced (i.e., the reason or
set of premises) and the propositional content that has been drawn
from it (i.e., the conclusion). Once we have these constatives, we
also have the implicit inference-claim, and all we have to do is to
check whether or not all of them have been correctly qualified, just
as interpretative deductivism maintains. Yet, because LNMA dis-
tinguishes between premises and inference-claims, it is also able to
distinguish between overall inference goodness and validity.
Alternatively, we can understand evaluative deductivism as the
view that for an inference to be good, the conclusion has to follow
of necessity from the premises. As we have seen, in LNMA this
amounts to requiring the conclusion to be advanced with a "neces-
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sarily" and the corresponding inference-claim or inference-
motivation to be a necessary truth. Yet why should we require the
conclusion to be advanced with a "necessarily" and not with any
other epistemic modal? As we have seen, LNMA allows us to ep-
istemically qualify our conclusions in a variety of ways, which
correspond to a variety of types of inferences different from de-
duction, and it explains what it means to say that such inferences
are good. From this point of view, deductivism would simply look
extravagant.
However, evaluative deductivism has, no doubt, a significant
appeal. As Johnson put it,
According to some, the strongest argument for deductivism is its
solid theoretical development. (…) the desirability of having an
objective evaluation of argument is, historically, one of the con-
siderations that has led theorists to opt for it. It is not just that
there is the possibility of objective evaluation but as well the be-
lief that arguments can settle (philosophical and other) issues once
and for all …conclusively” (Johnson, 2011, p. 23).
As Johnson observes, theories of inductive strength do not get the
consensus that theories of deductive support get. This is why, de-
ductivists such as Musgrave contended that “the only valid argu-
ments are deductively valid arguments, and that deductive logic is
the only logic that we have or need. The deductivist ploy regarding
so-called non-deductive or inductive or ampliative arguments is to
recast them as deductive enthymemes with unstated or missing
premises of one kind or another” (Musgrave, 2012, p. 125). So,
what is so good about modus ponens and other schemas of deduc-
tively valid arguments? The obvious answer is that they settle the
highest epistemic standard for inference. After all, the requisite
that the conclusion cannot be false if the conjunction of the prem-
ises is true makes inferring an utterly safe tool for getting new be-
liefs.
However, such requirement invites us to think what “cannot”
actually means here. Consider this example of an alleged deduc-
tively valid argument by Shecaira:
During an election year, you cannot trust a politician who provides an
optimistic prediction about a social problem that his party vowed to
solve.
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Jones, a member of the labor party running for re-election this
year, says that unemployment rates will go down.
You cannot trust Jones on this (2018, p. 477).
Shecaira defends what he calls a methodological deductivism and
offers this kind of example in order to explain the benefits of sup-
plying as many premises as needed for producing deductive argu-
mentation whenever it is possible. He claims that by doing so,
speakers make their argumentation more easily scrutable, which I
think is true. However, it is far from easy to render deductive a
piece of argumentation by adding more information. Going back
to Shecaira’s own example: is it really impossible that the premis-
es of this argument are true and yet the conclusion is false? What
about if Jones is under oath or is a close friend of the addressee,
for example? Most of the times, non-monotonicity can only be re-
deemed by adding as a premise the associated conditional.
Consider also this example by Musgrave:
[If a and b share property P, and a also has property Q, then it is reason-
able to conjecture that b also has property Q.]
a and b share property P.
a also has property Q.
Therefore, it is reasonable to conjecture that b also has property Q (2009, p.
224).
Again, what about if b also has property R, which is incompatible
with Q? My point with these examples is to show that unless we
render inferences formally valid, it is difficult to render them de-
ductively valid.
1
This is why deductivism is typically associated
with a defense of formal deductive logic (Johnson, 2000, chapter
3); playing by the rules of formal deductive logic seems to warrant
that if our premises are true, our conclusion cannot be false.
However, formal-logical deductivism needs to prescribe rules
of inference that cannot be justified in turn. They are supposed to
be self-evident; yet, as Vann McGee (1985) pointed out, even mo-
dus ponens has counterexamples. Contrastingly, in LNMA, infer-
ential normativity is a matter of the constitutive conditions of the
1
LNMA explains this fact by pointing out that what makes an inference deduc-
tively valid is that its inference-claim or inference-motivation is a necessary
truth. Only conceptual, mathematical, and formal truths seem the kind of truths
that can be necessary.
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very practice of inferring. That the normativity of inferring is con-
stitutive of the practice of arguing explains why people are usually
good at inferring and at distinguishing between good and bad in-
ferences even if they know nothing or very little about formal log-
ic. Learning to infer amounts to mastering the use of epistemic
modals, and much in the same way in which learning to make as-
sertions involves learning what counts as making a good assertion,
learning to infer is eo ipso learning what counts as inferring well.
Certainly, the idea that if things are as I say or believe, then my
conclusion also has to be as I say or believe is a high epistemic
standard for a conclusion. This standard enables us to determine
inference wrongness independently of any other consideration or
rule of inference that might be in need of justification itself. If the
premises are true and the conclusion is false, there is something
necessarily wrong with our inference.
In its own way, LNMA is also able to incorporate this standard.
Assessing an inference according to LNMA is a matter of deter-
mining whether or not the ontological modal that the speaker at-
tributes to the inference-claim is the one that it actually deserves.
Accordingly, in LNMA, being good argumentation implies that if
things are as the speaker adduces, the conclusion has to be as the
speaker claims; and this standard holds not only for deductive in-
ferences but also for any type of inference.
There is still one last move for the deductivist to make: to give
up defending interpretative deductivism and contend that it is only
good natural language argumentation that we have to interpret as
being deductive. That would amount to refusing D and D’ alto-
gether. However, this is a difficult move for them to make. For, in
principle, the procedure to render deductive a piece of argumenta-
tion is the same whether the argumentation or reasoning is good or
bad. So, in order to contend that it is only good natural language
argumentation and reasoning that must be reconstructed as being
deductive, the deductivist must offer a reason (basically, a theory
of interpretation) able to outlaw this procedure in the case of bad
argumentation. Without this theory of interpretation, the prohibi-
tion to reconstruct bad argumentation as deductive can only be
obeyed if we can intuitively recognize argumentation goodness
without first recognizing deductiveness. Yet this view would go
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against the main intuition behind evaluative deductivism, which is
that the essence of inference goodness is deductiveness.
The absence of a theory of interpretation also poses a problem
for the use of formal logic as a tool to determine inference good-
ness. This is so because the use of formal logic requires the for-
malization of natural language argumentation and reasoning in ac-
cordance with the definition of well- formed formulae of the for-
mal system to be used. That means that the selection of a particular
formal system to appraise argumentation affects our verdict about
its value: choosing two different formal systems may end up with
contradictory verdicts. This is not a problem when systems are
compatible with each other, like classical propositional logic and
classical predicate logic; in those cases, the right verdict is the one
that renders the inference valid—even though, as Gerald Massey
(1975) observed, if no system renders the inference valid, we will
not be allowed to say that it is invalid. But, what about if we
choose systems that involve different notions of validity, as classi-
cal, intuitionistic, or paraconsistent logical systems do? As I ar-
gued in Bermejo-Luque (2009), in light of this quandary, we
should rather say that formal logic does not serve to determine in-
ference validity, but only to show that a given inference is/is not
good according to one system or another. Contrastingly, an addi-
tional advantage of LNMA is that it does not rely on brute intui-
tions to reconstruct and assess argumentation and reasoning, but
on an independent theory of meaning such as the Speech Act
Schema for the act of arguing. By interpreting, in the sense of “un-
derstanding,” what the subject said or thought, we obtain an argu-
ment that allows us to determine the goodness of her inference
without the need to edit her words or thoughts.
5. Conclusion
The above considerations might give rise to the following ques-
tions. I hope I have provided the following responses:
1) Is LNMA’s account of inference normativity different from
or equivalent to that of deductivism? In LNMA, an inference is
valid if its inference-claim or inference-motivation is correctly
qualified (ontological modal qualifier), and it is a good inference if
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the conclusion is also correctly qualified (epistemic qualifier),
which requires that the reason is correctly qualified too. In LNMA,
validity is a matter of the correctness of a conditional regarding the
actual world, not a matter of conforming to standards of inference.
No doubt, deductivism has resources to turn any valid inference
into a deductively valid argument. But most of the time it does so
at the expense of dealing with inferential normativity as a matter
of formal rules or axioms. Contrastingly, LNMA deals with infer-
ential normativity as constitutive of the practice of inferring. As
pointed out, the main advantage of a constitutive account of infer-
ential normativity is that we do not need to appeal to the alleged
self-evidence of formal rules or justify the obligation to follow
them when inferring. In LNMA, counting as inferring—either in
reasoning or arguing—amounts to counting as following the
pragmatic constitutive rules of inferring, which involve endorsing
a conditional in a certain way. In turn, assessing our success in so
doing—that is, assessing our inferences—involves assessing this
conditional and the rest of the propositions that we endorse by in-
ferring and checking whether or not we are right in endorsing them
with the pragmatic force with which we do so.
On the other hand, in LNMA ‘follows from’ allows for differ-
ent standards. In fact, an additional advantage of LNMA is that it
provides a general framework to characterize what all these stand-
ards have in common, which is the correctness of the correspond-
ing conditionals. Thus, in Bermejo-Luque (2012, 2014), I have
dealt with analogical reasoning as reasoning in which the condi-
tional is supposed to be justified by means of an analogy (like in
“A is F; therefore B is F”). In turn, in Bermejo-Luque (2016,
2019a), I argued that “presumably, p” is different from “p, I pre-
sume,” and I gave a linguistic-pragmatic account of both in order
to provide the correctness conditions for presumptive inferences.
Finally, in (2019b) I explained that LNMA provides a general
framework for plausible inferences and allows for the possibility
of dealing with other types of inferences that are not normally tak-
en into account (for example, those that regulate the use of ‘truly’
and ‘possibly’).
2) Is a speech-act account (or LNMA’s account in particular)
really necessary to deal with the notion of validity? No doubt, ar-
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guments as products consist of propositions. However, my conten-
tion is that we have arguments as products because we have infer-
ences (i.e., reasonings and speech-acts of arguing where proposi-
tions are put forward with a certain pragmatic force, which is what
makes them correct or incorrect, given the actual state of the
world). We have an argument when someone puts forward a prop-
osition as a reason for another claim, it is not that we know that
someone is arguing or reasoning because she “used” an argument.
Otherwise, we would never have a reason to say that someone is
arguing badly instead of not arguing at all, because bad arguments
are just sets of propositions, and “using a set of propositions” is
something that we also do, for example, when we describe a land-
scape or tell a story.
3) Is LNMA really a tool to determine validity and argumenta-
tion goodness? What is the use of defining ? As pointed out be-
fore, the main feature of LNMA is to deal with the normativity of
inferring as resulting from the very practice of inferring. In partic-
ular, the idea is that competence in the use of epistemic modals
involves ability to distinguish between good and bad inferences.
But, at this point, the worry might be that LNMA succeeds at the
expense of failing to be informative, because in order to use this
model we must already have function . Contrastingly, my claim
is that mastering the use of epistemic modals is mastering the dis-
tinction between good and bad inferences—or, in other words, that
we already have the connection between epistemic and ontological
modals, because this is no more than the meaning of the corre-
sponding epistemic modals. This means that LNMA does not pre-
tend to regulate the use of these modals but to provide their se-
mantics as expressions of the pragmatic force that reasons confer
on conclusions. It is because we know their meaning that we know
whether a specific use of an epistemic qualifier is right or wrong
and, therefore, whether an inference is good or bad. In this ac-
count, what we do when we assess an inference is to check wheth-
er the use of an epistemic modal is appropriate, which depends on
the meaning of the epistemic modal in question and on our own
view of how the world actually is.
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Acknowledgements
My deepest gratitude to David Godden for reading a first version
of this manuscript and making the key questions to improve it.
Thanks also to the two anonymous reviewers from Informal Logic
for their helpful comments and suggestions.
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