Chapter 3: Understanding the
Analytic Approach to Circularity and Begging the Question
Shepherd mentions arguing in a
circle and question begging in several places in her writings. First I shall
examine what we commonly mean by circularity.
There are many ways of trying to
clarify what circularity is. All descriptions try to elucidate the notion that
it is called circular because the structure of the thing in question, be it a
definition, term, concept or argument, goes around in a circle so that it ends
up coming full circle to where it began, just as one does when drawing a circle[i].
One way to simplistically demonstrate this symbolically is that a circular
argument takes the form of:
“P ⱡ P”[ii]
Circularity also tends to be
uninformative, for instance, it doesn’t further our knowledge or provide a
classification. In her second treatise, Shepherd seems to appeal to this when
she claims that the Idealist position is uninformative and possibly circular if
Idealism takes it to be axiomatic that knowledge only comes from perception[iii].
She points out that, conversely, if we didn’t perceive anything then we
wouldn’t know anything so it doesn’t develop the argument or help explain
abstract propositions[iv].
A description that I find
excellently captures the core of what constitutes circularity, is the “strong
condition” that it occurs when “there is a premise, either implicit or
explicit, that is logically equivalent to the conclusion. That is, the premise
and the conclusion must have the same truth conditions.”[v]
In Shepherd’s first treatise[vi],
she shows an awareness of this description of circularity:
“it is equally illogical, to
prove the conclusion by the premises, and the premises by the conclusion.”[vii]
Nevertheless, “There is no simple
argument form that all and only circular arguments have”[viii]
so they can be notoriously difficult to spot and prove with certainty. Even one
and the same argument can be circular or not depending on how one argues it.
For instance:
(1) “The
article on inference contains no split infinitives.
(2) The
other articles contain no split infinitives.
Therefore,
If we assent to (1) and (2) for
reasons, and perhaps evidence, that are autonomous from (3), then the argument
above is not circular[x].
However, if we were to begin by implicitly (or explicitly for that matter)
assuming and assenting to (3) and therefore argue for (1) and (2) to convince
people of (3) as a conclusion, then we would be arguing in a circle because we
would be both starting and ending with (3)[xi].
This is despite the fact that the premises (1) and (2) do not recycle the same
content as the conclusion (3)[xii].
A closely related problem to
circularity (although often used synonymously with circularity), but is actually
somewhat distinct from it, is begging the question. A way to check this
argument above to see if it begs the question is to ask oneself if not
assenting to the conclusion (3) would mean we would also be rejecting the
premises (1) and (2)[xiii].
Another consideration, just as with circularity, is whether we assent to (1)
and (2) autonomously of (3)[xiv].
I think, although question begging and circularity, are very related to each
other, they also benefit from being considered separately because a statement
can be one without being the other, or commit both or neither fallacy.
Shepherd’s preoccupation with
being precise and making clear distinctions is, I argue, part of what makes
Shepherd’s philosophy analytical. “A major technique of analytic philosophy is
to try to formulate precisely the meanings of terms”[xv].
This is especially because, “in doing analytic philosophy, we wish to be as
clear and precise as possible, we must find a way to eliminate the possibility
of confusion arising from this ambiguity”[xvi].
One way of doing this is to “distinguish A and B” to avoid circularity in our
definitions where A is the definiendum (that which is being defined) and B is
the definiens (that which gives the meaning for the term being defined,
preferably intuitively)[xvii].
The definiens helps to expose potential circularity because if the definiens is
left open to misunderstanding or too broad an interpretation then it introduces
vagueness which encourages a recycling of terms and concepts so potentially
leading to circularity[xviii].
In this way, analytic philosophy can move beyond the often inherently circular
nature of dictionary style definitions by specifying that when A means or is
defined as B we are trying to express an equality between the definiendum and
the definiens such that:
“A ꓿ df B”[xix]
Similarly, the “technique of explication”, like definitions, also
involves separating the explicandum (imprecise version of what we are trying to
explain)[xx]
from the explicatum (an alternative, more precise and clear version of the
explicandum, as advocated by the analytic philosopher, Carnap (1891-1970))[xxi].
Although giving definitions,
explanations and making use of the question and answer structure goes back
centuries before Shepherd and were made famous by Aristotle, I suggest that
Shepherd’s methodological approach is more in the style of contemporary
approaches to analytic philosophy, even though analytic philosophy is usually
seen as being founded by philosophers later on in the nineteenth century such
as Frege (1848-1925), who was born after Shepherd’s death. However, I think it
is plausible that Shepherd may have been the first philosopher (or at least one
of the first) to combine pure philosophy with a contemporary-style analytic
methodology. This is because this style already existed during Shepherd’s
lifetime, albeit expressed by someone who was not a pure philosopher but rather
saw himself as a theologian, logician, rhetorician, economist and social
reformer, Archbishop Richard Whately. So, although Shepherd was always
particularly interested by abstract thought and logic, was she somewhat
influenced by Whately (1787-1863)? I think she was, given that he was part of
her inner circle of friends[xxii]
and he published on subjects such as logic, circularity, miracles and argued
against Hume around the same time as Shepherd and seems to share a similar
approach to her so they may well have exchanged ideas, benefiting from each
other’s views and influence. Furthermore, it has been argued that Whately and
his book ‘Elements of Logic' (1826) is closer in style to those in the latter
part of the nineteenth century than those before his time[xxiii].
Furthermore, in this book, Whately briefly describes what begging the question
and a circular argument is:
“The remaining kind, “petitio
principii,” (begging the question,) takes place when a Premiss, whether true or
false, is either plainly equivalent to the Conclusion, or depends on it for its
own reception. It is to be observed, however, that in all correct Reasoning the
Premises must, virtually, imply the conclusion; so that it is not possible to
mark precisely the distinction between the Fallacy in question and fair
argument; since that may be correct and fair Reasoning to one person, which
would be, to another, begging the question, since to one the Conclusion might be more evident than the Premiss, and to the other, the reverse. The most
plausible form of this Fallacy is arguing in a circle; and the greater the
circle, the harder to detect.” [xxiv]
So both Shepherd and Whately are
discussing circularity and good logical, analytic argument forms around the
same time as each other. However, unlike Whately, Shepherd only applies her
logical, analytic approach to pure philosophy so, I suggest, she should be
considered the first analytical philosopher. Whately is rather her academic
peer who is revolutionising his disciplines in a similar, parallel way to the
way she is revolutionising her discipline of philosophy: Whately influenced
logic at Oxford[xxv]
just as Shepherd influenced the Edinburgh School[xxvi]. Both also knew the Mills very well.
Thus, I pose the question that,
if Whately can be considered to have a latter nineteenth century style
of logic and still, all this time later, be a canonical thinker to study on
topics such as analysis and logical fallacies[xxvii],
then why not see Shepherd in a similar light? I suggest that Shepherd could be
seen as having a later nineteenth century style of analytic philosophy (and
thereby possessing this style of philosophy earlier than the commonly
considered father of analytic philosophy, Frege) just as Whately can be seen as
possessing a style of logic that was ahead of his time.
[i] D. H. Sanford, ‘Circular Reasoning’, ed.
R. Audi, The Cambridge Dictionary of Philosophy (USA: Cambridge
University Press, 1999), p144.
[ii] E. J. Lemmon, Beginning Logic, 2nd
edition (London, United Kingdom: Chapman & Hall, 1994), p34.
[iii] Shepherd, Essays on the Perception of
an External Universe and Other Subjects Connected with the Doctrine of
Causation, 82.
[iv] Shepherd, 82–83.
[v] Michael O’Rourke, ‘Handout: Circularity
and Begging the Question’, educational, University of Idaho, USA: M. O’Rourke’s
profile, summer 1999, http://www.webpages.uidaho.edu/~morourke/404-phil/Summer-99/Handouts/Philosophical/Circularity-and-Begging-the-Question.htm.
[vi] Mary Shepherd, An Essay upon the
Relation of Cause and Effect : Controverting the Doctrine of Mr. Hume,
Concerning the Nature of That Relation, with Observations upon the Opinions of
Dr. Brown and Mr. Lawrence Connected with the Same Subject (London, United
Kingdom: Printed for T. Hookham, 1824), https://archive.org/stream/essayuponrelatio00shepiala#page/n7/mode/2up.
[vii] Shepherd, 90.
[viii]
Sanford, ‘Circular Reasoning’, p144.
[ix] Sanford, p144.
[x] Sanford, p144.
[xi] Sanford, 144.
[xii] Sanford, p144.
[xiii]
O’Rourke, ‘Handout: Circularity and
Begging the Question’.
[xiv] O’Rourke.
[xv] S. Gorovitz and R. G. Williams, Philosophical
Analysis: An Introduction to Its Language & Techniques, 2nd edition
(New York, USA: Random House, 1969), 101.
[xvi] Gorovitz and Williams, 103–4.
[xvii]
Gorovitz and Williams, 104.
[xviii]
Gorovitz and Williams, 105.
[xix] Gorovitz and Williams, 104.
[xx] Gorovitz and Williams, 105.
[xxi] Patrick Maher, ‘Lecture 2 The Methodology
of Explication’, educational, Patrick Maher, Spring 2007, http://patrick.maher1.net/517/lectures/lecture2.pdf.
[xxii]
Jennifer McRobert, ‘Mary Shepherd and the
Causal Relation’ February 2002, p48, p52, https://philpapers.org/archive/MCRMSA.pdf.
[xxiii]
J. Van Evra, ‘Richard Whately and the
Rise of Modern Logic’, History and Philosophy of Logic 5, no. 1 (1984):
1–18, https://doi.org/https://doi.org/10.1080/01445348408837059.
[xxiv]
Richard Whately, Logic (Elements of
Logic) (London, UK: J. J. Griffin & Co., 1849), p61,
https://archive.org/stream/logic00whatgoog#page/n3/mode/2up.
[xxv] O. L. Pence, ‘The Concept and Function of
Logical Proof in the Rhetorical System of Richard Whately’, Speech
Monographs (National Communication Association,Taylor and Francis Group)
20, no. 1 (1953): 23–28,
https://doi.org/https://doi.org/10.1080/03637755309375076.
[xxvi]
McRobert, ‘Mary Shepherd and the Causal
Relation’, p5.
[xxvii]
Pence, ‘The Concept and Function of Logical
Proof in the Rhetorical System of Richard Whately’.
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