Charles Peirce’s Limit Concept of

Truth

Catherine Legg
 Overview

1. TRUTH AS A PHILOSOPHICAL TOPIC

2. PEIRCE’S DEFINITION AND WHAT IT MEANS

Pragmatism

Fallibilism

‘The End of Inquiry’

3. OBJECTIONS AND RESPONSES
4. PEIRCE’S PRAGMATISM AS A PHILOSOPHY OF
ENGAGEMENT
 Truth as a philosophical topic

 I recently gave a talk on truth to a group of non-

philosophers.
 Playfully, I offered to tell them “everything you
ever wanted to know about truth but didn’t
have a philosopher to ask”, and asked them
what that would be.
 This led me to reflect on my own philosophical
practice, thinking and writing about truth.
 Interesting questions: What is a theory of truth
meant to do? What questions are we trying to
answer? What problems are we trying to solve?
And if we were to solve them, what would it look
like on the other side?
 Is the concept of a theory of truth even coherent?
 The search for a criterion of truth

 Criterion of truth: a desideratum that we could apply to our beliefs

and thereby determine whether those beliefs are true (or, failing that,
are more likely to be true).
 E.g. A belief is true if and only if it is...sufficiently well justified /
caused by the things that it is ‘about’ / self-evident / socially accepted
...
 What I see as one of the biggest lessons of pragmatism: Give up the
search for criteria of truth. It is a pipe-dream.
 But does that mean we should stop talking about truth altogether, as
philosophers?
 Some pragmatists have taught that, e.g. Rorty: “‘[I]t is true’ is not a
helpful explanation of why science works, or of why you should
share one of my beliefs” (1985, p.286)
 Peirce’s pragmatism, however, shows us another way.
Charles Sanders Peirce

 Sep. 10, 1839 – April 19, 1914

 American philosopher,
logician, mathematician,
chemist, cartographer,
psychologist…(and more)
 In 1934, the philosopher Paul
Weiss called Peirce: “the most
original and versatile of
American philosophers and
America's greatest logician”.
 Peirce placed logic within the
broader context of a theory of
signs, or semiotics.
 He founded pragmatism.
Peirce’s definition of truth and what it means

 Peirce famously defined truth as follows:

“The opinion which is fated to be ultimately agreed to by all who

investigate, is what we mean by the truth” (1878).

 In other words: Truth is what lies at the limit of inquiry.

 Note how this definition:
Peirce’s definition of truth and what it means

 Peirce famously defined truth as follows:

“The opinion which is fated to be ultimately agreed to by all who

investigate, is what we mean by the truth” (1878).

 In other words: Truth is what lies at the limit of inquiry.

 Note how this definition:
 links to a community – the community of inquiry
Peirce’s definition of truth and what it means

 Peirce famously defined truth as follows:

“The opinion which is fated to be ultimately agreed to by all who

investigate, is what we mean by the truth” (1878).

 In other words: Truth is what lies at the limit of inquiry.

 Note how this definition:
 links to a community – the community of inquiry
 links to a process – the process of inquiry
Peirce’s definition of truth and what it means

 Peirce famously defined truth as follows:

“The opinion which is fated to be ultimately agreed to by all who

investigate, is what we mean by the truth” (1878).

 In other words: Truth is what lies at the limit of inquiry.

 Note how this definition:
 links to a community – the community of inquiry
 links to a process – the process of inquiry

 links to the future

As Peirce reached the end of his life, he softened this idea of fatedness
from ‘will-be’ to ‘would-be’:
“If Truth consists in satisfaction, it cannot be any actual satisfaction,
but must be the satisfaction which would ultimately be found if the
inquiry were pushed to its ultimate and indefeasible issue” [1901]
 Truth and Peirce’s pragmatism

 The quote comes from Peirce’s paper “How to Make our Ideas Clear”
and it derives from his pragmatism.
 But it should not be thought that Peirce thought pragmatism offers a
theory of truth (and here he differs from James and Rorty)
 Peirce’s definition is not a theory of truth so much as a claim that this is
what we mean by the truth.
 The purpose of “How to Make Our Ideas Clear” is  as the name says!
 The tool Peirce offers us for this is the Pragmatic Maxim:
“Consider what effects, that might conceivably have practical
bearings, we conceive the object of our conception to have. Then, our
conception of these effects is the whole of our conception of the
object.”
 In other words: if you want to understand a concept, think of what it
would lead you to expect in a specific situation.
 Truth and Peirce’s Pragmatism

In the paper, Peirce lays out 3 grades of clarity of meaning:

1) [Naive usage] We can identify instances, without necessarily being
able to say how. (E.g. pornography, obscenity trial)
2) [Conceptual analysis] We can give a verbal definition, as found in
a dictionary. (This is where most philosophy stops)
3) [Pragmatic Maxim] We can derive future expectations from
hypotheses containing that concept. (This is how scientists think)
Thus if we consider the everyday concept ‘hard’, our three stages are:
1) “This table is hard”
2) “Hardness consists in the ability to resist pressure”
3) “If I rest my plate on this table, then it will not fall through”.

Peirce called stage 3 the “experimentalist’s theory of assertion”.

 Truth and Peirce’s Pragmatism

 But the Pragmatic Maxim is not just intended for everyday ‘practical’
concepts. Peirce’s great hope is that it will be used for clarifying
‘difficult’, abstract ideas of philosophy.
 One of the most contested and intractable philosophical concepts is of
course truth. Peirce’s definition is intended to raise this concept to the
third level of clarity. After all:
“The very first lesson that we have a right to demand that logic shall
teach us is, how to make our ideas clear; and a most important one
it is, depreciated only by minds who stand in need of it….
Here Peirce adds the following interesting observation:
It is most easily learned by those whose ideas are meagre and
restricted; and far happier they than such as wallow helplessly in a
rich mud of conceptions. [1878]
 Fallibilism

 Inquiry is a process. We never reach a point where we have the entire

truth and inquiry can cease.
 Given that we manage to negotiate the world without too many nasty
surprises, we can assume that many of our beliefs are true.
 However, we can never be sure which of our beliefs are the true ones.
This is Peirce’s commitment to fallibilism.
 This commitment to fallibilism is ‘operationalized’ in the way Peirce
defines the community of inquiry as containing infinitely many
inquirers and stretching across infinite time.
 This allows that no matter how wide a consensus exists on a given
belief, it is always possible that another inquirer will come along, at
a later time, and manage to overturn it.

“…out of a contrite fallibilism, combined with a high faith in the reality of

knowledge, and an intense desire to find things out, all my philosophy has
always seemed to me to grow” (1902).
 The Fixation of Belief

But what does the community of inquiry do? Don’t we need some
guidelines, so they don’t go off-base?
In a way, Peirce accepts this radical conclusion. Whatever the community
of inquiry does to begin with, they will get there in the end. However in a
paper entitled “The Fixation of Belief he does give some guidance.
 Belief as habit. Doubt as an unsettled state. (Distinction between ‘living’
and ‘paper’ doubt: turns on whether you really are unsettled.)
 what it takes to “fix belief”. Here we may identifies four fundamental
methods:
1) whatever you happen to believe now (The Method of Tenacity),
2) whatever an institution tells you to believe (The Method of Authority),
3) whatever seems most coherent and/or elegant (The A Priori Method).
4) seeks to conform beliefs to that which is independent of them, and has
as its key enabling hypothesis that, “there are real things, whose
characters are entirely independent of our opinions about them...and
any man, if he have sufficient experience and he reason enough about
 The End of Inquiry

 Peirce’s definition of truth is often summarised in the slogan:

Truth is the end of inquiry.
 This is correct but the phrase is crucially ambiguous.
 This is not ‘end’ in the sense of finish: some utopian future time where
all questions are settled.
 It is ‘end’ in the teleological sense of aim or goal.
 It is merely an idealised continuation of what scientific inquirers are
doing now, namely settling questions about which they genuinely
doubt.
 This answers the profound misunderstanding of Russell in his critique
of Peirce that because “the last man on earth”, “will presumably be
entirely occupied in keeping warm and getting nourishment, it is
doubtful whether his opinions will be any wiser than ours” (1939,
145)
 Objections: i) Incoherent

 Rorty: “there can be no such thing as an ‘ideal audience’ before

whom justification would be sufficient to ensure truth, any more
than there can be a largest integer” (1995, p.283).
 But we’ve seen the true meaning of ‘end of inquiry’ is not a perfect
epistemic resting place, so much as precisely the model which ensures
that inquiry might continue indefinitely.
 Also despite prima facie appearance to the naïve word-based
philosopher, thinking about infinity can be coherent and rigorous.

Consider the integral calculus. This shows it is

not logically inconsistent to posit an infinite
process of adding infinitesimally small
quantities  which nevertheless yields a finite,
determinate answer.
 Objections: i) Incoherent

 Quine: the idea of approximation to a limit “depends on that of

‘nearer than’, which is defined for numbers and not for theories”
(1960, p. 23).
 It’s true that we can’t compare our current best theory and ‘things-in-
themselves’. We cannot experience things-in-themselves directly: thus
the idea is useless metaphysics (comes out as meaningless under the
pragmatic maxim)
 However, the notion of a theory being nearer to the truth than
one’s present theory is something scientific inquirers work with on
a regular basis.
 What does it mean that a theory is nearer to the truth than one’s
present theory? Just that it solves some problem that the other
theory doesn’t.
 Because that is how scientific inquiry moves forward – not by
contemplating reality, or counting leaves on a tree (which is also a fact),
but by solving problems.
 Objections: ii) Definition ‘too realist’

 We have seen that Peirce’s account of truth assumes that if inquiry

proceeds long enough our belief will settle on a single answer to any
given question. This is the idea of Convergence. Many have
wondered: what reason do we have to believe this?
 Russell asked: Is this an empirical generalization from the history
of research? Or is it an optimistic belief in the perfectibility of man?
Does it contain any element of prophecy, or is it a merely
hypothetical statement of what would happen if men of science
grew continually cleverer? (1939, 146).

Even if inquiry produces convergence in belief,

why should it be to one, single end-state? Can’t
we have Pluralistic Convergence?
 Objections: ii) Definition ‘too realist’

 Here Peirce falls back on the focus that his pragmatism puts on
meaning.

“The opinion which is fated to be ultimately agreed to by all who

investigate, is what we mean by the truth” (1878).

 As noted, this is not a theory of truth. It is not stating that convergence

on a single opinion is what will happen. But it is stating that this is
what we mean by the truth.
 Popular today to say: You believe P and that is true for you. I believe
not-P and that is true for me. This is often justified as ‘respecting each
others’ beliefs’.
 But think about what it means, pragmatically, if we say this to one
another.
 We might have respect. But we lose the opportunity to learn from each
other, and both take our views further. In this way, convergence is a
regulative hope.
Objections:iii) Definition ‘not realist enough’

 Shouldn’t truth be kept free of ‘epistemic’ notions such as belief, and

agreement within the community of inquiry? (Horwich: “Truth has a
certain purity”)
 Can’t we at least imagine that the community of inquiry might all fail to
agree on something true, forever?
 Lost facts: This worry is often pressed by imagining certain truths
which it seems it would be clearly impossible to discover:
 Smart: “[t]hat Winston Churchill sneezed twice more on a certain
date in 1941 than did Franklin Roosevelt”
 Johnston: “the number of cakes on a particular tray at a specific time
during a party held years ago”
 Field: the number of dinosaurs that ever existed
Objections:iii) Definition ‘not realist enough’

 Here Peirce says – Not so fast! How do we know we will never find out
these things? Our fallibilism applies here too:

“...it is unphilosophical to suppose that, with regard to any given question

(which has any clear meaning), investigation would not bring forth a
solution of it, if it were carried far enough...Who can be sure of what we
shall not know in a few hundred years? (1878).

 The history of science is littered with embarrassing claims that a certain

thing can never be found out.
 E.g. Comte, who when asked for a clear example of something
scientifically undiscoverable cited the chemical composition of
stars. But, ‘…the ink was scarcely dry upon the printed page before
the spectroscope was discovered and that which he had deemed
absolutely unknowable was well on the way of getting ascertained’
Objections:iii) Definition ‘not realist enough’

 To state categorically that certain facts cannot ever be discovered is

much worse, Peirce urges, than cherishing a foolish hope that any given
fact can be:

…there is no positive sin against logic in trying any theory which may come
into our heads, so long as it is adopted in such a sense as to permit the
investigation to go on unimpeded and undiscouraged. On the other hand,
to set up a philosophy which barricades the road of further advance
toward the truth is the one unpardonable offence in reasoning....(1898).

Upon this first, and in one sense this sole, rule of reason, that in order to
learn you must desire to learn and in so desiring not be satisfied with what
you already incline to think, there follows one corollary which itself
deserves to be inscribed upon every wall of the city of philosophy, Do not
block the way of inquiry! (1898).
 Philosophy of Engagement

 We have seen Peirce’s fallibilism teaches that there is no criterion of

truth.
 This means that the solution for poor opinions is not attempting to
dictate methods that must be followed to avoid error.
 One might dub this: Epistemic Managerialism (a concern in an age of
“Knowledge Capitalism” (Peters and Besley, 2006))
 The solution for poor opinions is more opinions. Apply more
perspectives to the problem and trust the process of inquiry.
 This is how Peirce’s understanding of truth is a philosophy of
engagement.
 As pragmatists we trust that as we are all located in the one world, and
interacting with it, false beliefs will be found to have uncomfortable
consequences, which will motivate us to correct them.
 If a belief is never found to have uncomfortable consequences by any
person across all time, what does it mean to say that the belief is false?
 Implications for Education

 Our great task as teachers is not to endow students with the truth
 Our task is not even to endow students with a failsafe algorithm for
finding the truth. (Gil Burgh: The “banking model of education”)
 Much mainstream epistemology with its talk of finding prior
justifications and warrants for our beliefs is enormously misleading on
this point (e.g. Audi, Greco, Sosa, Plantinga). (Tracy Bowell:
modernist epistemology demands indefeasible reason for belief)
 The truth (or otherwise) of our beliefs does not lie in their immediate
past, but in their future, which no-one can predict.
 Our task is to invite students into the community of inquiry
to stand, and inquire, alongside us.
 To the degree that we are able to do this, the end result will surprise
and excite all of us.
 These are the most exciting classes. Transformative, in fact.
 The University

 Peirce’s fallibilism led him to have some thoughts about the University:

The first thing that the Will to Learn supposes is a dissatisfaction with one's
present state of opinion. There lies the secret of why it is that our American
universities are so miserably insignificant…The English universities, rotting
with sloth as they always have, have nevertheless in the past given birth to
Locke and to Newton…The German universities have been the light of the
whole world. The medieval University of Bologna gave Europe its system of
law…
The reason was that they were institutions of learning while ours are
institutions for teaching. In order that a man's whole heart may be in
teaching he must be thoroughly imbued with the vital importance and
absolute truth of what he has to teach; while in order that he may have
any…success in learning he must be penetrated with a sense of the
unsatisfactoriness of his present condition of knowledge. The two attitudes
are almost irreconcilable. [1898]
 Inquiry Grows

 So it seems that Peirce wanted to encourage more genuine inquiry to

take place in Universities.
 However it’s important to note that, once again, Epistemic
Managerialism, a.k.a. ‘planning how to inquire’ is not the answer.
When the conditions are right, inquiry will grow:

[I]nquiry of every type, fully carried out, has the vital power of self-
correction and of growth. This is a property so deeply saturating its
inmost nature that it may truly be said that there is but one thing
needful for learning the truth, and that is a hearty and active desire to
learn what is true. If you really want to learn the truth, you will, by
however devious a path, be surely led into the way of truth, at last.
No matter how erroneous your ideas of the method may be at first,
you will be forced at length to correct them so long as your activity is
moved by that sincere desire. [Even] if you only half desire it, at first,
that desire would at length conquer all others, could experience
continue long enough. [1898]
The End of Inquiry
 REFERENCES
THIS TALK WAS ADAPTED FROM:
 Legg, C. “Charles Peirce’s Limit Concept of Truth”, Philosophy Compass 9(3),
2014, pp. 204-213.
OTHER REFERENCES:
 Peirce, C. “How to Make our Ideas Clear”, 1878.
http://www.peirce.org/writings/p119.html
 Peirce, C. Collected Papers vol. 1–6 C. Hartshorne and P. Weiss, A. Burks. vol
7–8 C. Hartshorne, P. Weiss, A. Burks. (eds.). Cambridge, Mass: Harvard
University Press (1931–1958).
 Peters, M. and Besley, T. Building Knowledge Cultures: Education and
Development in the Age of Knowledge Capitalism. Rowman and Littlefield,
2006
 Quine, W.V.O. Word and Object. New York: MIT Press, 1960.
 Rorty, R. “Is Truth A Goal of Enquiry?” The Philosophical Quarterly 45(180),
1995, pp. 281–300.
 Russell, B. “Dewey’s New Logic”, in Schilpp, ed., The Philosophy of John
Dewey. Evanston IL: Northwestern University Press, 1939, pp. 135–156.
 Thank you!
clegg@waikato.ac.nz