Weinstein - 3 Naturalistic Accounts of the Epistemology of Argument


Three Naturalistic Accounts of the Epistemology of Argument   63 

Three Naturalistic Accounts of the 
Epistemology of Argument* 

Montclair State University MARK WEINSTEIN 

© Informal Logic Vol. 26, No. 1 (2006): pp. 63-89. 

Keywords: epistemology, argument, truth, inquiry, naturalistic epistemology, philosophy 
of science, metamathematics, logic,  physical science,  James Freeman, Robert Pinto 

 Abstract: Three contrasting approaches to 
the epistemology of argument are  
presented. Each one is naturalistic, drawing 
upon successful practices as the basis for 
epistemological virtue.  But each looks at 
very different sorts of practices and they 
differ greatly as to the manner with which 
relevant practices may be described. My 
own contribution relies on a 
metamathematical reconstruction of mature 
science, and as such, is a radical break with 
the usual  approaches within the theory of 
argument. 

Whatever the purpose of particular arguments and the contexts within which they 
occur, epistemic virtue is, arguably, one of the prerequisites for the goal being 
achieved. Whether the purpose is something akin to truth as in critical inquiry or, 
by contrast, the determination of a best compromise between competing positions, 
accurate information that reflects the determinants for the issues at contention is a 
requirement. And so the question, from whence the epistemic adequacy of 
arguments. In what follows I will look at three recent attempts to answer the 
question, they are all naturalist in the broad sense that they rely heavily on what is 
in order to ground what ought to be. But beyond that shared commitment they 
differ radically as to what epistemic virtue can be attributed and from whence this 
essential property is to be derived. 

The first of these, James Freeman in his recent book Acceptable Premises 
(2005) draws upon the core intuition of the common sense tradition in empiricism. 
This takes us quite a ways into the understanding of the epistemological virtue of 
many non-controversial arguments, and an indication of how controversy is to be 
analyzed and explored. But, as we shall see, such a stance gives little more than a 
beginning. For we will argue that epistemological virtue is better understood when 

Résumé: On décrit trois différentes 
approche sur l’épistémologie naturaliste 
des arguments. Chacune utilise les 
pratiques réussies, qui sont la base de la 
vertu épistémologique pour chaque 
approche. Mais chacune emploie des 
pratiques qui diffèrent largement dans leur 
façon de décrire les pratiques pertinentes. 
Ma propre contribution repose sur une 
reconstruction mathématique de la science 
mûre, et donc se dégage radicalement des 
approches typiques. 



64     Mark Weinstein 

the stakes are high. Commonsense justifications will lead to critical inquiry, where 
the relative merits of an epistemological stance is evaluated in the light of our 
doxastic needs. 

The second, Robert Pinto, in a recent compilation of essays (2001) and in an 
unpublished paper, “Reasons, Warrants and Premisses,” offers an account of 
epistemic virtue, which relies heavily on critical practices in context, that is relative 
to the variety of purposes for which reliable information is sought and the correlative 
epistemic demands put on the information, our ‘doxastic attitudes.’ This position, 
as Pinto readily acknowledges, tends toward relativism, which whether acceptable 
in practice, given our epistemic needs, is manifestly inadequate in theory, for as 
Harvey Siegel (1987) has forcefully argued, relativism is powerless in just the 
regard that epistemological virtue is demanded, that is a practice and its standards 
for argumentation must be grounded in a robust epistemology, that is one that 
serves to justify the practice. 

Third, my contribution will give a sense of how such a robust point view can 
be developed within a naturalist epistemology grounded in critical practice within 
disciplined inquiry, looking at the most successful critical practice of all, physical 
science. 

My choice focuses on what Sellars (1963) has called the ‘scientific image,’ 
that is the world as seen through scientific theories and their instruments, in contrast 
to the ‘manifest image,’ the world as available to ordinary understanding and 
perception, the obvious concern of both Freeman and Pinto. In both cases, the 
limits of their positions will point to the relevance of the scientific image. My 
contribution, a model of truth modeled on scientific inquiry shows the possibility 
of articulating a rigorous account of such illusive properties as increasing 
informational and explanatory adequacy, and depth and breadth of connectedness. 

Whatever the judgment as to the adequacy of the three approaches, each in its 
way shifts the theory of argument towards what I have called ‘applied epistemology,’ 
that is, looking to successful epistemic practices in order to identify the logic of 
their success (Weinstein, 1994). That is, as applied epistemologies they are rooted 
in successful practice. The issues that such a naturalist approach faces can be 
distinguished between, first, practical questions of which sorts of practice are 
most productive in terms of our epistemological ends in argumentation, and second, 
the theoretical question of which practice is most illuminative of epistemological 
principles. Once distinguished this squares nicely with root concerns in the theory 
of argument in so far as an essential role of argument is supporting judgments of 
epistemological relevance, that is applying conditions of adequacy to judgments in 
particular cases and, as essential, the development of some normative understanding 
of the principles as correctly used. The standards for argument need to reflect the 
epistemic goals, and arguments, particularly within the context of critical inquiry, 
are valuable in so far as they have epistemic warrant appropriate to the context in 
which they are offered. And as Pinto shows us, these are essentially tied to the 



Three Naturalistic Accounts of the Epistemology of Argument   65 

purposes for which the inquiry has been undertaken. But epistemic standards have 
to be grounded in something deeper than practice on pain of relativistic impotence 
(Siegel, 1987), and the practice of philosophy calls for very deep grounding indeed. 
That explains that foundational nature of my own contribution and my search for 
an approximation to traditional epistemic ideals by attempting to construct a model 
of truth. But if truth is to be relevant to argument and in particular to critical 
inquiry truth must be construed as an outcome of inquiry, rather than something 
external to it. This is obvious to Plato in the Meno, and it should be apparent to 
argumentation theorists as well. For unlike, for example, the study of arithmetic 
on the one hand and commonsensical problems in ordinary life on the other, truth 
in many substantive contexts is not available independent of inquiry. This should 
be apparent, for the utility of inquiry is that it permits the truth to emerge. 

1. Freeman: Commonsense Foundationalism 

James Freeman, in Acceptable Premises (2005), reflects what can easily be seen 
as the founding intuition of informal logic. That is, that a normative account of 
argument can be developed focusing on the realm in which the overwhelming 
majority of arguments occur; that is, in non-specialized contexts in ordinary life, 
and using no more technical apparatus than is readily available to an educated 
person. It is this core that supports its vaunted utility as the basis for critical 
thinking and other good things. 

Freeman draws heavily upon this tradition citing Thomas Reid more than any 
other single author. Like Pierce and Plantinga, Freeman sees the efficiency of 
epistemologically relevant mental functions as based on a naturalist account of 
their necessity for successful human functioning (planning, ordinary problem solving 
and the like). But genetic speculations aside, the essential nature of our faculties, 
reasoning, sense, memory and the like supports Freeman’s acceptance of what he 
calls ‘commonsense foundationalism,’ which he sees as furnishing the rejection of 
‘skepticism’ (Freeman, 2005, p. 367ff.). 

Freeman combines a logical concept ‘presumption,’ familiar in discussions of 
premise acceptability, with a concept he gets from Plantinga, ‘belief generating 
mechanisms.’ This gives him his analysis, stated boldly: a statement is acceptable 
as a premise iff there is a presumption in its favor. (p. 20). And it has presumption 
in its favor when it is the result of a suitable belief-generating mechanism, with 
appropriate hedges about challenges, malfunctions and utility (p. 42ff). “We shall 
be arguing that the principles of presumption connect beliefs with the sources that 
generate those beliefs. “‘Consider the source’ could be our motto for determining 
presumption” (p. 44). 

Belief-generating mechanisms are of a variety of sorts. These psycho/social 
constructs are presented in what might be seen as a philosophical anthropology, 
that is, a theory of persons seen in their most obvious light. Belief-generating 
mechanisms need to be adequate to the four-fold analysis of statements: analytic, 



66     Mark Weinstein 

descriptive, interpretative and evaluative (p. 97ff); and they need to engage with 
three sorts of beliefs: basic, inferred and received (p. 109). Descriptions, for 
example, rely on the belief-generating mechanisms of perception, which includes 
perception of qualities, natural and learned signs, introspection, and memory (p. 
124ff). Perceptions are of three sorts, physical, personal and institutional. 
Institutional perceptions are presented on the model of  “learned constitutive rules” 
(p. 136). This last is crucial for the modern condition: once mastered, systems of 
cognitive organization are manifested through mediated perception and enormously 
increase the range and relevance of sense perceptions, natural signs, and 
classifications. How far the notion of constitutive rule takes us into this broad and 
fascinating realm remains to be seen. 

Whatever concerns are to be raised, however, we have to grant Freeman’s 
main thesis. That is, we can account for many of our acceptable premises by 
virtue of their genesis. For if, as seems obvious upon reflection, we argue often 
and argue well on countless occasions, it should come as no surprise that the 
various mechanisms by which we come to our premises can be articulated in 
defensible ways. We should grant Freeman’s point immediately. There are mental 
(and social) structures of many sorts that are reliable as the basis for judgments 
ranging as Freeman sees, from the logical to the evaluative and including essentially, 
perceptual judgments and modest generalizations based on memory and other aspects 
of common sense. And of course, judgments that rely on the testimony or expertise 
of others. All of the kinds of belief generators have clear instances with presumptive 
status in contexts that permit easy resolution. As Freeman shows by examples, 
there are contexts for each one of them that yield acceptable premises. The key to 
the adequacy of belief generating mechanisms is that they are reliable. 

We can begin our discussion of Freeman by immediately conceding that if the 
target is radical skepticism, Freeman has won the day. We just accept as obvious 
that we argue from acceptable premises all of the time, because in whatever relevant 
sense of mechanism, there are things about us and about how we operate 
epistemically, that, for all practical and many theoretical purposes, work just fine 
in enumerable instances. 

The issue becomes interesting for me when there are questions to be asked. 
Although I will look at the three most basic belief generating mechanisms, a prior 
intuition, individual reports (based on sense perception) and memories, the challenges 
I will raise will be readily seen to apply even more severely to the more complex 
‘mechanisms’ including institutional intuitions and other intuitions that support 
causal and other general claims. 

Freeman asserts ‘some premises are straightforwardly acceptable as basic 
premises without argument…. However suppose one is faced with a ‘hard ‘case… 
Here the requirement is to justify the judgment that a particular premise is or is not 
acceptable as a basic premise…we call making such a determination an exercise in 
epistemic casuistry’ (p. 319). For a priori intuition, Freeman requires that it certify 



Three Naturalistic Accounts of the Epistemology of Argument   67 

a basic premise as both true and necessarily true (p. 323). The issue as Freeman 
sees it requires a challenge; that is, unless a challenger is aware of improper 
functioning, the presumption for the reliability of her faculty of a priori intuition 
remains as does the presumption for the statements for which it vouches (ibid.). 
The decision is made more complex because of the possibility of ‘pragmatic 
consideration’ that is ‘that cost of accepting the claim if mistaken is higher than 
the expected cost of gaining further evidence’ (ibid. and elsewhere). This caveat is 
included in all of the discussions of belief generating mechanisms, but will be 
sidestepped here. 

Freeman’s account of a priori intuition, like his other forms of belief generating 
mechanisms requires that it not be malfunctioning. With sensory intuition this is 
more readily fleshed out. A prior intuition is another thing entirely. When does an a 
priori intuition malfunction? Is this the same as logical error? But then identifying 
malfunctioning intuitions depends upon a prior commitment to logical adequacy. 
This is, of course, what we have available to us, we call it ‘logic.’ And although in 
dispute in areas, the basic outline is available in logical theory. But one does not 
comprehend logic theory by intuition alone. One must understand logic, that is, the 
correctness of the intuition is a function of the informed intuitions of logicians and 
others who study the field. This of course is a far cry from what various native 
abilities permit the job to get off the ground. And where is this basis? Students of 
logic who fail to get modus ponens may certainly be seen to have a failure of logical 
intuition, but what of students who are skeptical of the various complex logically 
true statements typified by tautologies such as ‘if A then, if B then A.’ The idea of 
a ‘malady’ of the a priori intuition presumably could be exemplified by a variety of 
examples, some rather simple and others quite deep. Simple cases include students 
who tend to confuse conditional with biconditionals, or better, someone who fails 
the Wason test, that is, not taking into account FT instances of conditionals when 
checking all cases. 

These are telling examples; many sorts of people fail at identifying the a priori 
status of such items on many sorts of occasions, including those trained in logic. 
It frequently has to be clearly explained for even people with experience in the 
field. So clearly, it is not the intuitive nature of the underlying logic that is at stake. 
Rather, and obviously, it is the underlying coherence of the theoretic understanding 
of logic that marks the error. The acceptability flows not from its genesis in a 
priori intuition but from its genesis (and constant reconstruction) in logical theory. 
And these are quite different things, for the status of the later is, as in all theory, 
provisional and open to the advance of inquiry, and so its birthright as an intuition 
is at best the beginning of the story. 

Although we may ultimately rely on something like a priori intuition, it is deployed 
in conjunction with an apparatus (the ‘institution’ of first order logic), which in 
this case is fairly clear, and which includes a meta-theory that permits of the 
deepest intuitions, both obvious and surprising to be expressed, discovered and 



68     Mark Weinstein 

abandoned. The problems of completeness of sub-theories of first order logic; the 
equivalence of alternative systems of proof, not to mention real problems for 
intuition such as Russell’s paradoxes, Lowenheim-Skolem and Gödel incompleteness 
all play havoc with our intuitions, and logic is richer for the havoc they play. For all 
of these test intuition by the complex constructions of logical inquiry, that even if 
ultimately ‘intuitive’ to those in the know, remain far from the attempts to grapple 
with logical inference that we find in students and in the everyday application for 
even propositional arguments. This is seen in a priori sciences other than logic as 
well. The notorious problem of the square root of 2, the well known story of 
Hobbes and his rejection of a counter-intuitive theorem in Geometry, Cantor’s 
problem and many others all point to the fundamental irrelevance of strong intuitions 
in the face of theoretic advance. That is not to deny that there are necessary a 
priori intuitions: failure to get modus ponens stops logic in its tracks. It is to say 
that which intuitions these are remains unknowable until the advance of inquiry, 
which, while using these very intuitions, sees them as defeasible as the inquiry 
progresses. This does not result in a challenge to the notion of a priori intuition, but 
rather makes any one of them suspect. Such fallibilism is generally healthy, but it 
precludes the sort of generative story that Freeman tells from being more than the 
beginning of the story. For me the story gets interesting when we start to talk 
about revision of our intuition. That is, when we engage with inference. Freeman 
draws the line in roughly the place I do and sees inference as another issue. But my 
point is that being acceptable as a premise ultimately relies on inference, although 
all inferences do start with some, putatively acceptable premises. And so for me 
the epistemological interest of presumption is not when it succeeds but when it 
fails. 

This can be seen easily in his next class of statements kinds, descriptions. 
Freeman construes these as sense perceptual but sees their scope to extend to the 
identification of summary and even non-projective generalizations (pp. 126-7 and 
pp. 345-6). Freeman offers a similar account here as well. He begins by asserting 
a presumption for first-person reports of perceptions unless the challenger is ‘aware 
of evidence that her perceptual mechanism is not functioning properly or that the 
environment in which this perception is occurring is anomalous’ (p.326). Again, if 
his point is there are perceptions that have presumption, he is correct. But how far 
does this point take us? Again, we look at the most basic case. Visual perception is 
both highly reliable and a mechanism in the clearest possible sense. The physiology 
of sight is well understood including the neurological basis in the brain. And so 
malfunction is easily diagnosed and accounted for in terms of the mechanism. 
That, of course, is not what Freeman has in mind. Rather it is the functioning of 
vision that is the ‘mechanism’ he is interested in. We know we are malfunctioning 
when we have issues, and when we have issues we go to the eye doctor. Short of 
very simple tests, response of the retina to light, eye charts and the like, the 
identification and remediation of a visual malfunction is a complex combination of 
phenomenology (what you say is taken seriously), long experience with coherent 



Three Naturalistic Accounts of the Epistemology of Argument   69 

symptoms, and focused and frequently efficient choices of test-sequences as when 
the Doctor changes lenses back and forth asking, ‘Which is clearer, this or this?’ 
But all of this, even the eye charts, rely not on the quality of the visual intuition of 
the patient, but on this intuition in combination with a long experience, codified in 
‘institutional’ (professional practice) the technology the supports the examination 
and underlying understanding of how deformities in the visual mechanism is to be 
compensated for by choice of lens shape. And so again, whatever the presumption, 
that for example, a first person report is correct, it is the interaction with a mode 
of inquiry that settles the case. Having seen well in the past is no argument against 
needing glasses, although it is a sufficiently reliable index of function that new 
patients frequently complain when confronted with the need to remediate. The 
same is clearly true for all sensory reports. We don’t have to have a history of 
auditory delusions for our reports to be delusional. The reports just have to be 
sincere and out of sync with the understanding of others. The distinction between 
perceptions and, for example, dreams is not vividness but continuity and coherence. 
Eyewitness testimony relies on corroboration not eye tests. 

Another major source of beliefs is memory and of course Freeman is correct 
to write that we remember all sorts of things and rely upon them extensively: 
‘Memory, as long as what is remembered is distinct and not vague, again is a 
presumptively reliable belief-generating mechanism’ (p. 329). But when we look at 
memory we notice first that much of it is dispositional in the sense of knowing 
how, and so the issue of functioning is clearly tied to performance rather then 
some internal vividness or other phenomenological marker (p. 141). For propositional 
memory it would be, perhaps, rude to question someone’s vivid memory of events 
etc. except when they prove incoherent with another narrative. But politeness 
aside and looking at the phenomena in general, we now know that whether or not 
accompanied by phenomenological states that support conviction, even within the 
agent, memories are tied to coherent networks of other memories, peculiarly 
connected, with all sorts of other affective and classificatory bundles in the 
mechanism that supports them, the knowing brain. This is manifest in behavior in 
well-known ways and accounts for memory bias of all sorts. (Brainard and Reyna, 
2005) Memories that enter into public narrative are even more fraught with difficulty 
as all sorts of biasing choices of centrality and focus distorts memories in ways 
that are well known within cognitive psychology. This alters the perspective on 
what makes memory reliable. To ask if someone remembers (except in the context 
of first-person interviews that do no more than report opinions) is to engage with 
an inquiry into the memories’ surround. Whether internally in terms of introspective 
narratives or more importantly externally in reports of first-person experiences for 
the purpose of offering useful information, our acceptable memories are those that 
can serve as premises because of their coherence with other things we remember, 
which in turn are judged by their coherence and so on. 

I won’t go through Freeman’s other belief mechanisms for I believe my point 
to be made. The remaining belief generating mechanism all having to do with 



70     Mark Weinstein 

generalities including ‘subjunctives’ that support counterfactuals whether empirical 
or ‘institutional,’ that is, codified by experts in light of the best evidence and 
firmest opinions (p. 171ff. and p. 347ff.). I leave it to the reader to provide examples 
of similar complaints to those just raised, which I believe to be all too available in 
the history of science and in common affairs. Generalities of whatever sort rely on 
their persistence as inquiry advances, the founding intuition rarely even affords a 
clue as to their reliability. Even so truncated a discussion gives us a clue as to 
another way of looking at things, moving from the genesis of a belief, to how it 
fares when scrutinized in light of various doxastic ends. 

2. Pinto: Critical Contextualist 

Robert Pinto in a recent compilation of his efforts presents an interesting contrast 
with Freeman’s view. As we shall see Pinto’s work engages with the crucial notion 
of ‘critical practice,’ thereby placing the source of epistemic virtue outside of 
psychological belief generators and into the sociological. But this is no mere shift 
of foundation, it carries consequences for the problems that Freeman’s view bring 
to fore, and deeply challenges the root notion that it is intuition that is the source of 
our beliefs. 

The concern with critical practice grows out of Pinto’s logical concerns, the 
relation of argument to persuasion (Pinto, 2001, chapters 1 through 3) and most 
essentially, the relation of inference to argument (op. cit., chapter 4 and elsewhere). 
As he puts it ‘arguments are invitations to inference’ (idem, p. 36ff.). The move 
has many virtues. Pinto contrasts his view with the more standard view seeing 
argument as a relationship between premise and conclusion. His recommendation 
has immediate fruitful consequences. As is well known, the standard view of 
inference makes looking at the truth of premise secondary to the ascertaining of 
the relationship of support from among the premises. And the adequacy of argument 
is seen on some analogue to validity. Although informal logicians express similar 
concerns offering variations on the truth of premises— acceptability and the like, 
Pinto’s move towards inference consolidates such concerns by seeing premises in 
light of the inference to be drawn. This shifts the discussion to an interesting 
complex of issues and outcomes. 

The focus on inference enables him to make significant contributions to the 
notion of argument appraisal. Argument seen as ‘an invitation to inference’ calls 
for assessment in terms of the reasonableness of the premises and the inference 
seen in respect of a range of doxastic attitudes, construed to be broader than belief 
(idem, chapters 2 and 3). Unwilling to commit to the task of a general theory, Pinto 
sees himself as offering reminders in the sense of Wittgenstein rather than an 
alternative theory (idem., p. 129) Pinto is concerned with how particular arguments 
function. Such a naturalistic approach leads to general issue of non-deductive 
inference in a very broad sense and yields insight in relation to problems of relativism. 
Pinto opts for what he calls ‘sophisticated epistemic relativism’ which he expresses 



Three Naturalistic Accounts of the Epistemology of Argument   71 

as: ‘There is no set of epistemic standards or criteria of which it can be said that it 
is uniquely correct or correct sans phrase’ (idem., p. 54). He distinguishes inferences 
from the their argumentational outcomes, e.g. persuasion in the standard view. He 
had already argued (chapter 2) that a range of doxastic attitudes, indicating six 
levels of conviction including such modifications as ‘being inclined to believe and 
suspecting’ are all possible outcomes of argument (idem., p. 12). He expands the 
conception from differing levels of conviction to qualitatively distinct outcomes 
such as desiring, hoping, and intending, fearing etc. Arguments that support such 
a range of doxastic and non-doxastic outcomes are judged in light of particular 
outcomes as indicated by the relevant attitude. This is an important move for it 
moves the issue to the substance of the propositional (or even a non-propositional, 
p. 17ff.) attitude rather than to a ubiquitous notion of belief, to which other doxastic 
attitudes tend to be reduced. He summarizes this provocative line of thought as the 
very general claim that ‘argumentation is the attempt to modify conscious attitudes 
through rational means’ (idem., p. 19, italics in the original). Pinto’s intuition is 
that it is the attitude that is the argumentational goal that determines the criteria by 
which supporting inferences should be evaluated. 

The import of this move to a qualified and contextualized image of inference 
will be at the center of his reformulated theory in ‘Reasons, Warrants and Premises,’ 
offering both the direction that the study of inference should move, and a crucial 
test for such a point of view.  Pinto’s arguments and my own predilections prompt 
me to move in similar directions. But that does not alter the key question for 
argument evaluation: whether to accept the invitation to inference in support of the 
outcome, whatever its doxastic nature.  Pinto sets his position in relation to the 
positions he rejects. The strategy here, and in later essays, is to argue that the 
range of inferences that need to be evaluated can not be characterized in the terms 
of formal logic or the alternatives that informal logic provides. 

Not surprisingly he rejects the idea that the inferences need be as strong as 
entailment in the classical sense (op. cit., p. 38) and sees his earlier concerns with 
the range of doxastic and non-doxastic attitudes in terms of Peirce’s notions of 
habits of mind and guiding principles (idem., p. 40). This raises a version of what 
will be an essential critical question. Can habits of mind and guiding principles be 
articulated in a fashion sufficient for the normative constraints needed if an invitation 
to inference is be accepted on, roughly, epistemological grounds—that is, because 
it moves the cognitive purposes of argument forward? 

Early on, Pinto indicates an underlying normative substructure—and this will 
become a major theme in his reformulation of his point of view—‘a practice of 
criticism’ (idem., pp. 43-4). As we shall see, Pinto will eventually see the appeal to 
critical practice to be as a good as we can get, something short of a full theory of 
inference, but yet strong enough to ground our normative endeavors. Looked at 
generally, Pinto’s strategy is to broaden the purview from the logical to the contextual. 
So, in the discussion of coherence as a basis for belief (idem., chapters 7 and 8) he 



72     Mark Weinstein 

begins with a narrow logical view of coherence and quickly shows it to be inadequate 
(p. 64ff.). The discussion, driven by a range of examples and with reference to 
relevant philosophical positions, moves the discussion of coherence to the context. 
Viewed psychologically, in terms of coherence as a hallmark of the validity of 
inferencing, Pinto looks to an overview that will offer a sense of the subjects 
‘understanding’ that could furnish a psychological surrogate for the reasoning 
process, something akin to a narrative whole, but which, unfortunately, does not 
seem to be available (idem., p. 71, see also chapter 12). Coherence is viewed as 
the ‘objective correlate’ of such nuanced understanding and requires that a critical 
overview of the domain to be available to understanding (idem., pp.70-1). Reasoning 
‘takes place on the basis of understanding that involves an overview of the domain 
we are reasoning about’ (idem., p.67). He offers a number of constraints, including: 

(a) to make intelligent nondeductive inferences from any body of data we 
need a grasp of what the plausible alternative are to the hypothesis we are 
adopting and we cannot have that without some general understanding of 
the ideas we are reasoning about 

(b) to make intelligent deductive inferences from any set of assumptions or 
premises, it is not enough to assure ourselves that our conclusions follow 
from the premises we have strong reasons to accept; we also need assurance 
that our conclusion doesn’t run counter to propositions that are more 
entrenched than the premises from which our inferences begin; and to have 
such assurance we need a general understanding of the field we are reasoning 
about. (Idem., p. 67.) 

He continues: 
When we learn to engage in argumentation, and when we learn to make all 
but the most rudimentary inferences, we are initiated into an intersubjective 
practice of criticism that enables us to appraise inferences on the basis of 
certain broadly or commonly recognized features and/or standards… that 
this practice of criticism in its developed form cannot be reduced to that 
application of any simple or straightforward sets of rules… 20th century 
epistemology—and in particular, 20th century philosophy of science—has 
made us aware that the goodness of our most fateful and highly prized 
inferences does not yield to any simple analysis in terms of patterns or 
guiding principles. And yet the value of those inferences, is not something 
that is arbitrarily accepted; rather it is something that is open to discussion 
and rational evaluation. (Op.cit., p. 81.) 

But this, of course, creates an enormous problem for Pinto, for once the complexity 
is known, a theory of inference looks further away rather than closer. This may 
not daunt Pinto who eschews contributing a theory of inference, but it should 
concern us. For if inference in the complex sense of critical practice and with all 
of the modifications across the range of appropriate doxastic attitudes is to lead to 
an account of epistemic virtue, something much worse than relativism raises its 
head, that is vacuity or anarchy. If we are to have a normative theory of argumentative 
virtue we need a theory of how arguments are made good. But Pinto’s relativism 



Three Naturalistic Accounts of the Epistemology of Argument   73 

has an enormous yield. It focuses us on differences and should make us agnostic 
about the possibility of getting a general theory, all at once. The downfall of the 
theory of argument may very well be the drive to come up with a unified account 
too soon. But whether unified or not, some general account is required if we are to 
have a theory of virtue in argument at all. 

But where to begin? In “Reasons, Warrants and Premisses”, Pinto sees a deep 
general structure supporting the myriad of argumentation contexts that his work’s 
insight forces us to accommodate. Although he works from ordinary examples, 
choosing apples is the most detailed, the generality he provides can be easily extended 
to all sorts of arguments. What Pinto sees in the work of David Hitchcock is a 
refocusing of the problem of warrant through the notion of enthymeme and an 
elegant solution to the problem of from whence premises that are required if an 
argument is to be warranted. Epistemology moves forward from premise 
acceptability to the acceptability of those crucial premises that serve as warrants 
for inferences. 

Hitchcock’s solution is deceptively simple (Hitchcock, 1998). A missing premise 
that can serve as a warrant can be generated from the other premises and the 
conclusion by generalizing across content expressions. If done with appropriate 
care, the generalization indicates a substantial connection between the other premises 
and the conclusion, and so the solution does not suffer from the triviality of seemingly 
similar suggestions such as the construction of the minimal conditional, ‘if premises 
then conclusion’ added to the premise set. Generalizing on non-logical variables is 
of course an ancient insight. Pinto sees Hitchcock needing to admit generalizations 
with scope less than the standard requirement, universality across a class. 
Generalizing need not be universally quantifying, but only requires sufficient 
generality to get the job done. This rather obvious move has profound consequences 
for logic, for if the quality of generalization is a property of the generalized predicates 
rather than of the quantifiers and connectives we can’t possibly have a formal 
logic, for formal logic is just an account of the architecture we have moved beyond. 
Naturally there will be a formal logic associated with such inferences, some version 
of non-monotonic logic no doubt. And thanks to an essential contribution of Arnold 
Koslow (2000) we do not have to deal with traditional logicians task of defining 
connectives and the like. Koslow shows that any logic can be described just in 
terms of its inference structure. That puts the focus just where it is required, for 
Hitchcock and Pinto tell us what an inference structure adequate to substantive 
argument needs to look like. An inference structure has to be sensitive to the 
substantive relations between extra-logical terms and to the restrictions on power 
in the entailment relationships (the strength of the ‘inference ticket’ or alternatively 
that depth of commitment to the warrant). That is, entailments range from very 
weak to almost as strong as you can get. Pinto’s rule for choosing apples relies on 
an inference that is super-weak, you are always ready to except exceptions both in 
terms of outcomes and in terms of circumstances, yet it happily satisfies his 



74     Mark Weinstein 

wife’s demands. On the other end of the spectrum chemical formulas support 
inferences of the most robust sort, although the history of science warns us to 
always be ready to accept modifications in light of deep theoretical restructuring 
of their surround. 

But although such a logic cannot possibly be formal, its very complexity points 
to the need for it to be mathematical. The use of mathematics (in logic, 
metamathematics) to describe complex symptoms is hoary with age and unparalleled 
in practical application. Logicians should not confuse formal and mathematical 
logic, although historically such confusion is understandable. A metamathematical 
account need be no more than a mathematical description of any logical system 
and does not prejudice the substantive properties of the system. To confuse the 
two is to open up the doors to logical chaos, paradox and even worse, bad analogies, 
for the properties of mathematical description are not the same as the properties of 
the object described and vice versa. Metamathematics as a descriptive language 
has enormous power, for the understanding of the tools of metamathematics is 
among the most rigorous in the intellectual repertoire, while it permits of the 
consolidation of vast domains through concise abstract formulations. So it is to 
metamathematics that I will turn but only after some rather extensive preliminaries. 

3. Weinstein: Truth through Inquiry 

The complexity inherent in Pinto’s account, both by virtue of the ranges of doxastic 
attitudes and the enormous complexity that the notion of generalizing on substantive 
predicates with all of the rich variety of the underling strength of generalizations 
across concept types, might make us despair of ever getting a handle on how 
arguments work, except in some crude outline of heuristics or perhaps by 
relinquishing normative epistemology and focusing on broad general principles of 
the sort that pragma-dialecticians propose. That is, rules governing dialogue 
indifferent to the internal complexity of the subject matter being discussed and 
focusing on the dialogic interactions instead. This has proved very helpful in 
understanding the over-all architecture of argument. But as long as the argument 
stage is left unresolved, and there is no reason to share in the optimist view, 
sometimes present in pragma-dialectics, that logic can take care of itself, there is 
little insight to be got from pragma-dialectics into the deep epistemologies that 
support the role of acceptable because true(ish) premises in furnishing warranted 
conclusions. 

Freeman at the end of his book sees the possibility of an alternative account, 
that he equates with the metaphor of a network drawn from Quine (pp. 374-5). He 
rightly laments that this is no more than a metaphor. One way of looking at my 
work in critical thinking and applied epistemology is as an attempt to make sense 
of this metaphor. Previously, I focused on what I saw were the crucial aspects of 
disciplined discourse as a prototype of adequate argument. I too was very general, 
identifying the language of the disciplinary frame with special concepts, substantive 



Three Naturalistic Accounts of the Epistemology of Argument   75 

rules of inference and paradigmatic practices (Weinstein 1990). Although I think 
all of that is correct and perhaps useful it doesn’t touch on the logical issues. It 
wasn’t until I began to reconsider my work begun some time ago on the notion of 
reduction in science that I realized that I had the beginning of a solution. In my 
earlier discussions of applied epistemology (Weinstein, 1994) as well as my 
‘ecological approach’ to critical thinking I relied heavily on the availability of 
powerful modes of inquiry that were no less likely candidates for an epistemological 
foundation than common sense, in that they represented enormous amounts of 
warranted and useful knowledge. It seemed to me that epistemologically, in the 
scientific era, the special disciplines were more appropriate as a paradigm than 
common sense. Which, although rooted in our success in knowing many ordinary 
things, was riddled with error. And moreover, that the logical lessons available 
from the exploration of such a range of successful inquiry would be more valuable 
than those learned from the success of individuals arguing about ordinary affairs. 
The reason was that my candidate for the most successful inquiry I knew, physical 
chemistry, could be seen to have the sort of structure that mirrors some of the 
deep intuitions of philosophers as to the unity of the known. I saw the 
epistemological effectiveness of physical chemistry to be drawn from three obvious 
and powerful desiderata for any inquiry clearly exemplified by the history of the 
discipline. That is, that over time, physical chemistry showed, on average, an 
increase in the breadth of its application to a range of cases, increasing depth in the 
levels of explanatory frameworks that accounted for the increase in range because 
of the great increase in explanatory yield when a heretofore unrelated explanatory 
frame (set of laws) enables whole hosts of phenomena to be given chemical or 
physical models, that is, explained by the same or analogous principles, themselves 
connected by increasingly deep chains of explanation: the grand reductions, organic 
chemistry and material science (metallurgy, crystallography, etc.) and all of this 
with increasing refinement both in the ability to measure and compute. 

This was a difficult story to tell but yet seemed readily amenable to mathematical 
expression because all of the criteria are scalar, at least roughly, that is depth, 
breadth and articulatability all permitted of rough linear order. The rational 
reconstruction that results has metamathematical interest and permits of elaboration 
in a way that may very well support its application in artificial intelligence and the 
creation of expert systems since it, in principle, enables weights to be assigned and 
calculated for the warrant of items and thus their power in sustaining inferences. 
But more important it seems to me to furnish a structure in terms of which interesting 
logical concepts can be saliently explicated, including the three that I see as central 
to logical theory, truth, entailment and relevance. This moves me away from the 
weak entailments of ordinary inference to the strong entailments of mature scientific 
theories. For informal logicians, however, an immediate question arises: why mimic 
the mathematical by looking for strong substantive entailment measures? I am 
interested in very strong entailment relations because I am interested in truth. I 
won’t argue for that interest, rather rely on the work of Harvey Siegel (1987) to 



76     Mark Weinstein 

support the untenability of the alternatives. So the problem for me is how to define 
a notion of truth adequate to inferences in the complex sense of Pinto and Hitchcock, 
that approaches the power of the traditional model of inference. 

Freeman tells us is that we have many unexceptional beliefs generated by a 
variety of mechanisms and reflecting a broad range of abilities, both individual and 
corporate. Pinto adds that these beliefs, or in his happy phrase ‘entitlements,’ 
include a broad range of creedal kinds, what he calls ‘doxastic attitudes’ nicely 
suited to the enormous variety of interests and concerns that require reasonable 
argument. Pinto’s examples of micro arguments that exemplify the range of purposes 
and epistemic contexts set a standard for adequacy of any account. An account of 
the epistemology of argument must speak to the range of epistemic entitlements 
across the range of context and of epistemic need. Warrants, as inference tickets 
require only as most robustness as the epistemic demands put on conclusion requires 
and have only as much logical power as the quality of the background knowledge 
affords. This is an embarrassment of riches. Such a welter of small things offers 
a dizzying variety of kinds and concerns. So we take a page from Plato’s Republic; 
not daring to address the small in its particularity, we look to the large and seek 
some structural principles. Rather than look at the dizzying variety of epistemic 
tasks for which argument is required, let us look at the largest and most imposing 
of the knowledge structures available in the last century, that is physical chemistry. 
And in doing so, instead of working from weak ordinary entailments we start at 
the other end with the strongest substantive relationships among terms. This leaves 
open the possibility of weakening the model to make it applicable to less 
epistemologically demanding concerns. Taking our clue from the history of logic 
we construct an ideal model and put off worrying about approximations that capture 
more ordinary cases. 

As indicated, the choice of chemistry has long standing in my work, where, 
for a period of time my main focus in thinking about informal logic and 
argumentation was the role of disciplined knowledge, what I called ‘applied 
epistemology’ (Weinstein, 1994). More recently I have moved from such pragmatic 
interests to the logical foundations of such a view, both to afford a secure foundation 
for the theory of argument and for its promise as an aid to constructing knowledge 
structures with the study of artificial intelligence. The first of these pursuits may 
give informal logicians pause, for informal logicians, until recently, have rarely 
engaged with foundational concerns, taking a more Wittgensteinian approach that 
looks to successful practice rather than deep foundations. Informal logic may not 
need a foundation, but a wrong foundation is a positive evil leading to deep errors, 
and Tarski’s foundation is just the wrong one. For a theory that supports the 
equivalence ‘‘snow is white’ iff snow is white’ presupposes model relations in 
which mappings are clear and defined in terms of stable model structures. That is 
clearly the case in arithmetic, but there is much too argue about that cannot be 
captured in arithmetic constructions. That of course is not to deny the importance 
of arithmetic or the pragmatic importance of the theoretic fact that once we have 



Three Naturalistic Accounts of the Epistemology of Argument   77 

a model it will have a model in arithmetic. And if my view is consistent there is an 
arithmetic model of changing inquiry as well. That is trivial, since it follows from 
the first if we have a model of such change. What is decidedly not trivial is whether 
we have a model of change (Weinstein, 2006). 

Hitchcock’s work has immediate yield for it shows us how to do away with 
extensional interpretations by dealing with content expressions in a direct way. But 
of course that leaves open the aspect of generalization that the extensional model 
provided. That is to say an account of what generalization (logically) comes to and 
an indication of the strength with which the generalizations hold. The traditional 
account (all, some, none) was fine as far as it went and formal logic had much to 
say about it, but unfortunately it told us very little about how generalizations function 
in an enormous range of essential cases where they are neither extensional (universal) 
nor statistical. Extensionality gives us a clear view of entailment, here seeing 
probabilistic entailment as a species of the genus. But our reasoning with warrants 
goes far beyond this. Hitchcock gives us the clue to continue, but it is Pinto who 
begins to see what the stakes are. For generalizations play many roles and fit many 
purposes, and the extensional model with its standard theory of truth tells us very 
little about much of what we want to do. Pinto’s general use of entitlement points 
us in the right direction. The many things we require demand correlative degrees 
of robustness. His example of a rule of thumb for buying sweet apples indicates 
the sorts of arguments both he and Freeman explore, that is ordinary arguments at 
relatively low stakes for which ordinary information and common sense are adequate. 
But, as indicated, we have bigger fish to fry. 

There are two philosophical intuitions that support the choice of physical 
chemistry as the paradigm for epistemology. The first is as old as Plato’s love 
affair with geometry. We can get no better than our best available knowledge 
structures if we want a model from which epistemologists might draw their 
understanding. Like Kant and Newtonian physics, the philosopher will do well to 
heed the call of the most effective practice, lessons are to be learned from the 
most successful human engagement with coming to know. The second is that 
physical chemistry forms a coherent structure that sufficient logical complexity to 
offer exemplifications of how our ideas hang together. 

Like all human knowledge, including the logical, physical chemistry begins in 
intuition. Two of Freeman’s belief generating mechanisms are at the beginning of 
the process. Sense perceptions (including such relatively recondite sense percepts 
as taste: acids were initially defined in terms of their feel on the tongue) are essential 
as well as the ability to identify natural kinds. Of course, contrary to Freeman and 
his reading of Peirce, the identification of natural kinds in Chemistry was fraught 
with error and was subjected to extensive revision as the field progressed. As 
essential were the early discoveries of deep principles, such as the conservation of 
mass as determinative of the key procedure of weighing carefully, and of course, 
various primitive ideas about atomic theory. These higher-order intuitions, as applied 
to the weighing and sorting of physical objects offered the beginning of an 



78     Mark Weinstein 

interesting layer of chemical models. Ranging from the crude models of Dalton to 
the sophisticated models in organic chemistry. Some of these are found fairly early 
as the result of the application of new concepts, procedures and technology, and 
the result, over a century, intervening layers of practical applications understood 
both in terms of their experimental outcomes and their success, forming a roughly 
stable body of generalizations that permitted analogical application to similar cases 
as chemistry advanced. Thus, not only are there levels of description, but accepted 
descriptions at a particular level reach out to neighboring phenomenon on the same 
level creating nests of similar chemical knowledge, for example the differentiation 
of acids and bases, the distinction of metals, the analysis of the family of substances 
formed by carbon rings, the structure of crystals and the like. Major theoretic 
advance, however, occurs when these nests of analogous chemical generalizations 
are subsumed under higher levels of laws and models as began with the development 
of physical chemistry. This started moving rapidly in the nineteenth century with 
enormous advances in chemical knowledge, but the power of unification is best 
seen with the Periodic Table of Elements at the core. It offers powerful substantive 
model that is the engine that has driven chemistry from its creation until now, for 
it opens the door to the deeper connection between chemistry and the maturing 
physics of the molecule, that atom and ultimately theories of elementary particles 
(Langford and Beebe, 1969). The yield, modern physical science with all of its 
riches. 

The image should be clear. A knowledge structure, its end points in experience 
(or other sorts of intuitions as in mathematics) increases in depth as higher order 
explanations capture (generally, only in part) aspects of the lower order 
generalizations as explananda. It expands laterally in breadth both through analogy 
as similar discoveries form nests of similar classifications and through common 
causal and other functional connections. This breadth is substantive (that is, more 
than additive) when a nest of similar generalities are subsumed under a higher 
order explanatory theory and these create the major advance in both theory and 
practice. These are the grand unifications, as classes of similar and even apparently 
dissimilar phenomena are seen to be the result of the same underlying forces and 
geometry. In addition to all of these, across the range of different components of 
the structure, understanding, frequently manifested in measurements, are expected 
to increase in precision. Chemical understanding requires the relationship be better 
borne out in the details of the process, driven by deep principles such as the 
conservation laws that set ideal values to which experiments are to increasingly 
approximate. Chemistry as a knowledge structure can be seen to yield three essential 
criteria of epistemic adequacy: breadth of applicability (at all theoretic levels); 
depth of theoretic understanding; and progressive improvements of measurement 
and other relevant describabilia as understanding improves. 

This can be seen in the physical sciences construed as the roughly unified 
structure with the Periodic Table of Elements at the core and the array of supporting 
and supported knowledge structures understandable in its terms. Uses of physical 



Three Naturalistic Accounts of the Epistemology of Argument   79 

knowledge whether in explanations, or practical application draw upon data (actually 
models of data) that are reconstructed through theoretic vocabularies according to 
appropriate inference procedures (subsumption under laws; performance of 
acceptable transformation as in balancing chemical equations and the like). But 
most important, the physical sciences are constructed around core theories and 
procedures, even given the discontinuities (Cartwright, 1983). The discontinuities, 
once the concern of radical philosophers of science (notoriously, Feyerabend, 
1975) are clearly only problematic if our ideal is the sort of model relations drawn 
from the mathematical paradigm, that is to say, explanation and reduction as requiring 
deduction in the standard sense. A more adequate account of scientific truth shows 
how discontinuities are well managed and how progress towards greater coherence 
is assessed. Setting too high a standard for coherence robs us of the epistemic 
richness of the dynamics of knowledge production and assessment. A standard as 
high as deductive certainty freezes the dynamics into the useless statics of all or 
nothing confirmation, a situation rarely if ever encountered outside of the contrived 
worlds of textbook examples and philosophers’ discussions. 

In the appendix below I include a meta-mathematical model of emerging truth 
that attempts to capture these intuitions. As in many non-standard analyses of 
truth, the model offered here is sensitive to the preponderance of evidence and 
changes in the evidence. In contrast to the standard mathematical construal of 
truth, truth based on the paradigm of mature physical science requires ambiguity 
in evolving model relations. Truth, in the final analysis, is identified with the 
progressive appearance of a model that deserves to be chosen (so both the intuitions 
of correspondence and coherence are saved) but the model, not unlike in Peirce, 
evolves as inquiry persists. It is the substance of how judgments of epistemic 
adequacy are made antecedent to the truth predicate being defined that is the main 
contribution of the construction below. In place of strict implication contrasted 
with induction in its various senses, the construction permits of degrees of necessity 
reflective of the extent of model relations, that is, it permits inferences within 
models (that are relatively strict) to be reassessed in terms of the depth and breadth 
of the field of reducing theories from which models are obtained. That is to say the 
theory of truth yields a theory of entailment that permits of degree (Weinstein, 
2006). It affords a systematic way to organize, articulate and evaluate changes in 
the field of theories in terms of which the evidence is interpreted and explained. 
This is accomplished by the identification of two different sorts of functions. 
First, fairly standard functions that map from a theory (construed as a coherent 
and explanatory set of sentences) onto models, that is, interpretations of theories 
in a domain (Appendix, 3-3.3) and a second, much more powerful set of functions, 
that map from other theories onto the theory, thereby enormously enriching the 
evidentiary base and furnishing a reinterpretation now construed in relation to a 
broader domain (Appendix 4-4.3).  This is the insight that reflects the choice of 
physical science as the governing paradigm. Mature physical science is characterized 
by deeply theoretical reconstruals of experimental evidence, laws and theories in 



80     Mark Weinstein 

light of higher order theories as they are seen to unify here-to-fore independent 
domains of physical inquiry. These unifications, or ‘reductions’ offer a massive 
reevaluation of evidentiary strength and theoretic likelihood. It is the weight of 
such reconstruals in identifying the ontology that grounds the truth predicate that 
the construction attempts to capture. And in so far as the formalism captures what 
is salient in physical theory it affords a vision of emerging truth that may have 
significant implications for the computation of epistemic adequacy in systems that 
include a rich and theoretically structured data-base as in medical diagnostic systems. 

Mature physical science is also characterized by the open textures of its models 
and the approximations within which surrogates for deductions occurs (in the 
standard account idealizations and other simplifications).  The construction here 
attempts to make sense of the need for approximations and other divergences 
among models at different levels of analysis and articulation by offering intuitive 
criteria for assessing the epistemic function of the approximation in light of emerging 
data and the theoretic surround (Appendix, 1-2). The yield is a notion of truth as a 
function of the history of theoretic adequacy (Appendix, 5-6.33). 

The construction enables us to distinguish particular models and their history 
across the field, giving us criteria for preference among them. It is this ex post 
facto selection from among the intended models in light of their history that affords 
ontological commitment and the related notions of reference and truth. The main 
contribution of the formal model is how it elucidates the criteria for model choice 
in terms of the history of a scientific theory embedded within a  complex scientific 
structure of evidence and related theories. We define plausible desiderata, not only 
upon the theory and its consequences, but also in terms of the history of related 
theories that donate models to the theory under appropriately selected reduction 
relations. Reductive inferences are theoretic connectors that donate sets of models 
down a chain (Appendix, 4-4.4) and in doing so subsume inferences within another 
conceptual framework. Epistemically, they transform the understanding of the 
micro inference in terms of broader and more pervasive vocabularies and inferential 
procedures drawn from here-to-fore unrelated domains of understanding. 
Computationally they add whatever weight the reducing theory has to the reduced. 
And to the extent that the reducing theory has power of its own, increases the 
epistemic adequacy of the reduced theory in a manner that ‘swamps the posteriors’. 
That is we don’t have to wait for instance confirmation over time to readjust our 
priors. Our priors are always being readjusted as a function of the effectiveness of 
our theories across the board. And we search for our posteriors accordingly. 

Reductions offer the large unifications that support reconstruals of empirical 
understanding. Such ‘seeings as’ are rife in modern physical science and constitute 
the major advances in the domain. They include, but are not limited to seeing 
minerals as crystals, seeing chemical substances as molecules, seeing biological 
functions as organic chemical interactions, seeing mental events as neuro- 
physiological etc.  It is the structure of the field under these reduction relations, 



Three Naturalistic Accounts of the Epistemology of Argument   81 

and in particular the breadth and depth of the model chains donated by interlocking 
reducing theories that determine the epistemic force and ultimately the ontology of 
the theory. 

The intuitive appeal of the construction is first, based on accepting the brute 
fact that mature physical science is the most effective epistemic enterprise available, 
and thus a likely paradigm for a theory of truth; second, on the construction 
having captured what is essential in mature physical science, in this case the 
elaboration of how a theory takes weight from the epistemic surround, rather than 
merely in light of confirming evidence; and third, in terms of the novelty and 
richness of the formal construction. Its prima facie novelty is readily seen when 
contrasted with truth drawn from standard account. Rather than seeing truth as 
true in a model that is available independent of the truth seeking process, truth is an 
emergent property that becomes clearer as our truth gathering practices converge 
on a model. 

The construction here attempts to give mathematical substance to views that 
see epistemic adequacy tied to a web of theories as in Quine, and see truth as 
inherently tied to inquiry, as in Peirce, in a manner that both calls for and hopefully 
supports computation. 

4. Consequences for Epistemology 

The intuition my view reflects may be stated boldly: true theories ramify. A theory, 
whatever its initial intended models, takes its ontological commitment in light of 
how the theory fares in relationship to other theories whose models it incorporates 
under reduction. That is, we fix reference in light of the facts of the matter, the 
relevant facts being how the theory is redefined in the light of its place in inquiry as 
inquiry progresses. The awareness by inquirers of the history of success of scientific 
structures enables them to set standards for model choice rationally, in terms of 
plausible criteria based on successful practice. The formal model enables us to 
look at the history of approximations to the original interpretations of the theory 
(intended models) in terms of their goodness-of-fit, and most crucially the relations 
between ontologically relevant models donated from above (from reducing theories) 
reinterpreting or even replacing intended models. That is, it enables us to look at 
how intended models fare under the impress of higher-order reducing theories. 
Finally, it permits a natural definition of truth internal to the scientific structure 
(Weinstein, 2002). Truth is defined as an ideal outcome as in Peirce but with 
mathematical content as in Tarski. Truthlikeness becomes a quantifiable metric as 
the theories in the structure move towards truth. That is, as the intended models of 
reducing theories substitute for intended models of reduced theories, increasing 
the confirmatory basis and the depth of explanatory adequacy. The confirmatory 
basis is increased since under reductions, confirming evidence of theories connected 
via reduction indirectly confirms the reduced theory as well. If my intuitions could 
be modeled with actual assignments of physical properties and relations, the model 



82     Mark Weinstein 

chains and their relations could be displayed, weighted and evaluated. Designing 
such an array would require a period of testing and adjustment, possibly through 
computer simulations of fragments of physical theory. The yield would be a rational 
reconstruction of argumentation in a substantive field of inquiry.  And it offers an 
available formal metaphor for increasing truthlikeness as the outcome of inquiry of 
the sort found in physical chemistry, our presumptive candidate for a naturalist 
ontology, that is realist within a theoretic framework, which as Putnam has shown 
us is the most we can hope for (Putnam, 1983). 

The deep epistemic intuition should be clear. A theory, whatever its intended 
interpretation, makes its ultimate commitments in light of how the theory fairs in 
relationship to other theories whose models it incorporates under reduction. That 
is, we fix reference and therefore truth in light of the facts of the matter, the 
relevant facts being how the theory is redefined in light of its place in inquiry as 
inquiry progresses. 

It is the awareness on the part of inquirers of the history of success of scientific 
structures that enables participants in the inquiry to rationally set standards for 
model choice in terms of plausible criteria, based on successful practice. Crucially, 
the formal model enables us to look at the history of approximations, and most 
essentially, goodness-of-fit relations between models donated from above, from 
reducing theories, and the original interpretations of the theory. Truthlikeness 
becomes a quantifiable metric as the theories in the structure move towards truth, 
that is, as the intended model of strong reducing theories substitute as intended 
models for reduced theories. Finally, it permits of a natural definition of truth 
internal to the scientific structure. Truth is defined in an ideal outcome.  (Appendix, 
6-6.33; Weinstein 2002 offers an elaborated discussion). 

Even given all of these virtues, why should argumentation theorists and informal 
logic tolerate such an idiosyncratic extension of their methods, especially with its 
resonance with just those methods against which informal logicians inveighed so 
heavily? Its value is first to show that it can be done. That is, complex knowledge 
structures can be described mathematically in a manner that supports weighting 
and connectivity, both obvious criteria in natural argument. Second, like Tarski, it 
gives an abstract metaphor that then supports the elaboration of particular less 
global and even non-mathematical intuitions. It is a truism of ordinary argument 
that interlocutors come to argumentation with belief stores. It is a travesty to think 
argumentation can disregard levels of commitment in the name of simple tests like 
consistency. We give up items in our belief stores with more or less difficulty and 
good arguers strike at available targets. This requires the structure of commitments 
to be, at least in principle, theoretized if we are to have a theory of argument at all. 
Consulting an oracle is evidence of despair both in logic as in life. A test of the 
structure is to take a range of examples we seem to understand and see to what 
extent the criteria of breadth, depth and articulatability can confirm and give 
substance to our intuitions. But that is to call for a research agenda. All a paper of 
this sort can hope to do is to intrigue future participants in the agenda. 



Three Naturalistic Accounts of the Epistemology of Argument   83 

Appendix 

Scientific Structures: A Model of Emerging Truth 

I have attempted to make the formalism more available by forgoing the usual 
array of Greek letters, italics and the like. Lower case letters name individual 
functions, models or sentences; upper case letters are (ordered) sets of such 
items; double upper case letters are (ordered) sets of such (ordered) sets. Ordered 
sets are indicated by angle brackets. All indices, asterisks etc. are written on the 
line. An item is often used as its name; use/mention should always be clear in 
context. I use ‘|-’ to mark implication; ‘||-’ for semantic entailment; ‘|-e’ is our 
defined restriction on implication appropriate to explanations in mature physical 
science. I use ‘U’ for set theoretic union. A ‘field’ is a structured set of sets, with 
various elements ordered in a variety of ways. Ordered sets enable us to keep 
track of items and discuss relations among them. 

1.  A scientific theory, T, is a set of sentences, {t
1
,...,tm}. The explanandum, s, 

is a sentence. The explanans, Tc is the longest sequence, tc
1
,...,tc

n
, of truth 

functional components of T and |- (Tc iff T). We say that T explains s, in symbols, 
T|-e s, just when: 

a) Tc  implies s, 
b) Tc does not imply not-s, 
c) for some tc

i
 in Tc, tc

i 
 is a nomic generalization, 

d) for any tc
i
 in Tc, neither tc

i
 implies s, nor s implies tc

i
, and 

e) there is no sequence of sentences r
1
,...,r

k
, available within the set of 

     sentences accepted by the discourse community that accepts T, such 
    that, for some sequence of tc

1
,..., tcj in Tc 

i) tc
1
,...,tc

j
 implies r

1
&,...,&r

k
, 

ii) r
1
,...,r

k
 does not imply tc

1
&,...,&tc

j
, 

iii) upon replacing tc
1
,...,tc

j
 in Tc by r

1
,...,r

k
, in symbols Tc

r
, Tc

r
 implies 

    s. 
Since our concern is with physical science there is an obvious constraint that a 
substantial number of the tc

i
’s will describe experimental or other empirical 

phenomena. As required by condition (c), some of these are nomic generalizations. 
Condition (d) prohibits explanatory ‘bushes’ (circularity). Condition (e) is the ground 
for relevance. 

2. The basis for the construction is a scientific structure defined as an ordered 
triple, TT = <T, FF, RR>, where: 

a) T is a theory closed under an appropriate consequence relation, Con, 
    where Con(T) = {s: T|-e s}. 
b) FF is a field of sets, F, such that for all F in FF, and f in F, f(T’) = m 
    for some model, m, where either: 



84     Mark Weinstein 

i)  m ||-T, or 
ii)  m is a near isomorph of some model, n, and n||-T. 
iii)  FF is closed under set theoretic union: for sets X and Y, if X and 
     Y are in FF, so is X U Y. 

c) RR is a field of sets of functions, R, such that for all R in RR and 
   every r in R, there is some theory T* and r represents T in T*, in 
   respect of some subset of T, k(T). We close RR under set-theoretic 
   union as well. 

FF includes primary evidence based on what T predicts or explains. RR includes 
secondary evidence based on the ‘reduction’ of T to another theory T*. The 
notion of reduction relies on the availability of  ‘effective representing functions,’ 
a purely syntactic operator that maps formulas and variables of some theory, one 
to one, onto formulas and variables of another theory, and, in addition, preserves 
identity. An effective representing function, r, represents T in T* in respect of a 
non-empty subset k(T), of expressions of T, such that for every expression e of 
k(T), if e is in k(T) then r(e) is an expression e* in (T*). An important property of 
such representing function is: r reduces T to T* is equivalent to, for every model m 
of T there exists a model m* of T* such that, for every sentence s of k(T), s is 
true in m if and only if r(s) is true in m* (Eberle, 1971). 

This enables us to define key notions, articulating the history of T under the 
functions in F and R of FF and RR respectively. An example of the sorts of 
construction is the basic notion of model chain. The intuition of a model chain 
permits us to formalize the intuition that a progressive theory expands its domain 
of application by furnishing theoretic interpretations to an increasingly wide range 
of phenomena. The basic interpretation is the intended model. Thus, theories have 
epistemic virtue when all models are substantially interpretable in terms of the 
intended model, or are getting closer to the intended model over time. 

3. We define a model chain, C, for theory, T, as an ordered n-tuple  <m1,…,mn>, 
such that for each mi in the chain, m

i
 = <d

i
, f

i
,> for domain d

i
, and function f

i
, d

i
 

= d
j
, and where for each i

 
and j, i< j< n, m

j
 is a realization of T later in time than mi. 

A realization can be thought of as an experimental array or other set of data 
acceptable in the light of the standards in the field of inquiry that T sits.  We say 
‘realization’ because the various mi’s may not be models of T, rather, near enough 
approximations. This is a consequence of the pragmatic turn that pervades the 
construction. 

3.1. Let m* be an intended model of T, making sure that f(T) = m for some f 
in F, and that m||-T. We then say that C is a progressive model chain if: 

a) for every m
i
 in C, m

i
 is isomorphic to m*, or 

b) for most pairs m
i
, m

j
 in C, i,j, i<j<n, m

j
 is a nearer isomorph to m* than m

i
. 



Three Naturalistic Accounts of the Epistemology of Argument   85 

The notion of a progressive model chain permits us to formalize the intuition 
that a progressive theory furnishes closer theoretic interpretations to the range of 
phenomena within its domain of application. The basic interpretation is the intended 
model. Thus, theories have epistemic virtue when all models are substantially 
interpretable in terms of the intended model, or are getting closer to the intended 
model over time. We say ‘most’ since we cannot assume that theoretic advances 
are uniformly progressive. Frequently, theories move backwards without being, 
thereby, rejected. We are looking for a preponderance of evidence or perhaps, 
where possible, a statistic. We do not define this a priori. What counts as an 
acceptable rate of advance is a judgment in respect of a particular enterprise over 
time. This is another instance of the pragmatic turn. 

A related, but distinguishable notion, a theory being model progressive, begins 
with the intuition that theories transcend their initial domain of applications as they 
move from limited conjectures to effective explanatory theories. This notion defines 
a sequence of models that capture increasingly many aspects of the theory. 

3.2. Let T´ be a subtheory of T in the sense that T´ is the restriction of the 
relational symbols of T to some sub-set of these. Let f´ be subset of some f in F, 
in some realization of TT. Let <T´

1
,...,T´

n
> be an ordered n-tuple such that for 

each i,j, i<j<n, T´j reflects a subset of T modeled under f´ at some time later than 
T´

i
. We say the T is model progressive under f´ if: 

a) T´k is identical to T for all indices k, or 
b) the ordered n-tuple  <T´

1
,...,T’

n
>  is well ordered in time by the 

    subset relation. 
3.3. Let  <C

1
,...,C

n
> be a well ordering of the progressive model chains of TT, 

such that for all i,j, i<j<n, C
j
 is a later model chain than C

i
. TT is model chain 

progressive if the n-tuple <C
1
,...,C

n
> is well ordered in time by the subset relation. 

The intuition should be clear. A theory’s models in the sense of the sets of 
phenomena to which it is applied must confront the logical expectations the theory 
provides. That is to say, as the range of application of a theory moves forward in 
time and across a range of phenomena, the fit between the actual models and the 
ideal theoretic model defined by the intended model is getting better or is as good 
as it can get in terms of its articulation. The model history of a theory T, enable us 
to evaluate the theory as it stands. By examining T under RR we add the dimension 
of theoretic reduction. The key intuition here is that, under RR, models are donated 
from higher-order theories. Theories under RR form a strict partial order (transitive, 
irreflexive and asymmetric) but with constraints on transitivity since we are dealing 
with approximations. The models (or near models) of T donated under functions 
in R are differentiated from models of T under functions in F by their derivational 
history and by the particulars of the members of RR. Similar constructions offer a 
precise sense of progressiveness under RR. This will enable us to offer essential 
definitions resulting in a principled ontological commitment in terms of the history 
of the theory and its relations to other essential theories with which it comports. 



86     Mark Weinstein 

We can distinguish particular models and their history across the field, giving us 
criteria for preference among them. The ex post facto selection of an ontologically 
significant model from among the intended models in light of their history will be 
seen to ultimately yield a truth predicate in a Tarskian sense. More importantly, it 
yields an image of how judgments of epistemic adequacy are made before such a 
truth predicate is defined. It elucidates the criteria for model choice in terms of the 
history of the scientific structure, TT, within which a theory sits. That is, plausible 
desiderata are defined, not only upon the theory and its consequences (its models 
under functions in F), but also in terms of the history of related theories that 
donate models to the theory under appropriately selected reduction relations (sets 
of functions in R). It is the structure of the field under these reduction relations, 
and in particular the breadth and depth of the model chains donated by interlocking 
reducing theories, that determines the epistemic power of the theory. 

4. We now turn our attention to the members of RR. Recall that the members 
of R represent T in T* in respect of some non-empty subset of T, k(T). Let 
<k

1
(T),...,k

n
(T)> be an n-tuple of representations of T over time, that is, for i < j, 

k
j
(T) is a representation of T in T* at a time later that k

i
(T). We say that TT is 

reduction progressive if, 
a) k(T) is identical to Con(T) for all indices, or 
b) the n-tuple is well-ordered by the subset relation. 
4.1. We call an n-tuple of theories,  RC = <T

1
,...,T

n
> a reduction chain, if for 

all i,j there is a r
i
 in R

i
 such that r

i
 represents T

i
 in T

j
 in respect of k(T)for all i<j< 

n. RC = <T
1
,...,T

n
>  a deeper  reduction chain than  RC´ = <T´

1
,...,T´

j
>, if T

i
 is 

identical to T´
j
 for all i< j and j< n. 

4.2. We call a theory reduction chain progressive if T is a member of a series of 
reduction chains,  <RC

1
,…,RC

n
> and for each RC

i+1
, RC

i+1
 is a deeper reduction 

chain than T
1
. 

This leads to an even more profound extension under RR. 
4.3. T# is a branching reducer if there is a pair (at least) T´ and T* such that 

there is some r´ and r* in R´ and R*, respectively, such that r´ represents T´ in T# 
and r* represents T* in T# and neither T´ is represented in T* nor conversely. 

4.31. B = <TT
1
,TT

2
,...,TT

n
> = < <T

1
, F

1
, R

1
>, <T

2
, F

2
, R

2
>,..., <T

n
, F

n
,R

n
>> 

              is a reduction branch of TTn if Tn is a branching reducer in respect of T
i
 

            and T
j
, i, j > 2; j < n 

4.4. We say that a branching reducer, T is a progressively branching reducer if 
the  n-tuple of reduction branches  <B

1
,...,B

n
> is well ordered in time by the subset 

relation. 
5. Let  TT# = <TT

1
,...,TT

n
> be an ordering of scientific structures seriously 

proposed at a time. Let  <<T
1
,F

1
,R

1
>,...,<T

n
,F

n
,R

n
>>  be their respective realizations 

at a time. We say that a set of models M, M = <m
1
, m

2
,...,m

n
> is a  persistent model 

set if for domains, d, 



Three Naturalistic Accounts of the Epistemology of Argument   87 

a) M = <<m
1
=<d

1
,f

1
>, m

2
= <d

2
,f

2
>,..., m

n
 = <d

n
,f

n
>>  and for all i, j  d

i
 = d

j
,  or 

b) M is a persistent model set in a set of ordered subsets of TT#, such that the 
         sequence is well ordered in time by the subset relation. 

Intuitively, M contains the ordered models that define what the theory can be 
seen to really be about. At each level in the ordering a model of what the theory is 
about has shown itself to be adequate over time and available for reinterpretation 
and integration with other adequate models. Physical chemistry tells the tale. We 
live in a world of substances, which are indicative of chemical processes, which 
are indicative of molecular structure, which are indicative of atomic structure, 
which is what chemistry may be seen to be about in reality. If particle physic ever 
gets truly sorted out, there will be another layer. I stop with the Periodic Table of 
Elements as the most coherent and pragmatically effective picture of the 
‘architecture of matter’ that we have. That is, I take the Periodic Table of Elements 
to be true, in the sense elaborated below (6-6.33) even though changing and evolving. 

5. Let  TT# = <TT
1
,...,TT

n
> be an ordering of scientific structures seriously 

proposed at a time. Let  <<T
1
,F

1
,R

1
>,...,<T

n
,F

n
,R

n
>>  be their respective realizations 

at a time. We say that a set of models M, M = <m
1
, m

2
,…,m

n
> is a persistent model 

set if for domains, d, if, 
a) M = <<m

1
=<d

1
,f

1
>, m

2
= <d

2
,f

2
>,..., m

n
 = <d

n
,f

n
>>  and for all i, j 

    d
i
  = d

j
,  or 

b) M is a persistent model set in a set of ordered subsets of TT#, 
    such that the sequence is well ordered in time by the subset relation. 

5.1. M is an ontic set for TT#. 
5.2. We say that a ontic set, O, is a favored ontic set if: 

a) O is the set of intended models of a theory, T, standing at the head of 
     a progressive reduction chain. (Notice, O is thus the ontic set of all 
`    of the theories in the chain.) 
b) the members of the reduction chain are themselves reduction 

progressive. 
c) T is a progressively branching reducer. 

Notice that the set consisting of an ontic set and the sets that it generates (the 
set of sets under the reduction relation) form a persistent model set. An interesting 
yield of the notion of persistent model set is that it explains instrumentalism in 
theoretically primitive or dubious contexts. Without a theory that donates models 
the most persistent models are models of the data, whence instrumentalism or 
other brands of positivism. Of course, working with mature physical science our 
concern is with theoretic coherence. Which, although requiring that functions 
map onto models of data or other empirical models, takes its ontology from the 
deeper theoretic commitments as a function of reduction. For the scientifically 
informed the world is really made up of atoms and molecules, even though exactly 
what atoms and molecules will come to be seen as waits on the progress of 
science. 



88     Mark Weinstein 

We now define the ideal of truth emergent. 
6. TT is progressive if: 

a) TT is model progressive (3.2). 
b) TT is model chain progressive (3.3). 
c) TT is reduction progressive. (4). 

6.1. We call T a progressive reducer if: 
a) T is reduction chain progressive (4.2). 
b) T is a progressively branching reducer (4.4). 

6.2. We say T is a favored reducer, if: 
a) TT is progressive (6). 
b) T is a progressive reducer (6.1). 

6.3. T is a most favored reducer if T is a maximally progressive reducer, that is, 
T is the nth member of a reduction chain such that for all Ti, <Ti…,Tn> i<n, T is 
a favored reducer. (Notice, Tn is not reduction progressive, since it stands at the 
head of the longest reduction chain.) 

6.31. The set, O, of ontic models of Tn, is thus, a favored ontic set in respect 
of every Ti in the reduction chain. 

6.32. If Tn is a most favored reducer, and O is its favored ontic set than O is 
the ontology of scientific structure TT. 

6.33. An ideal truth predicate for TT can then be constructed in fairly standard 
Tarskian as ‘s is true’ for s in Tn in TT, iff O||-s where O is the ontology of TT and 
Tn is the most basic theory of all. 

Notes 

* Acknowledgement is owed to Christoph Lumer for his thoughtful criticism. 

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Mark Weinstein 
Educational Foundations 

Montclair State University 
Upper Montclair, NJ 07043 

weinsteinm@mail.montclair.edu