Relativism, truth, and Protagoras
Timothy Chappell, University of Bath, August 3 2006
t.chappell@open.ac.uk
(For something like this argument see Chappell, “Reading the Peritrope”,
Phronesis 2006; also on my OU homepage
http://www.open.ac.uk/Arts/philos/chappell.htm.)
Today people often say things like “All perspectives are
equally valid”, or “This is my truth, tell me yours” (©
The Manic Street Preachers), or “This is true for me, and
that is true for you”.
They’ve been saying that sort of thing at least since
Plato’s time (425-345 BC).
Call such views examples of relativism about truth (here
just ‘relativism’ for short).
In the first half of this talk, I’m going to look at how
Plato, in his dialogue the Theaetetus (c.380 BC), argues
against relativism.
The exact shape of Plato’s argument is disputed. I’ll
criticise two interpretations. Then I’ll offer a third
interpretation (my own). This turns out, magically, to be
correct.
Half-time entertainment: an anti-relativist argument
that Plato never quite offers—but maybe should.
That will lead us, in the second half, to look at how we
today might argue against relativism.
The talk will go to extra time, where I’ll look at moral
relativism, and argue that the important non-realist view
expressivism is closer to moral relativism than
expressivists would like it to be.
1
First half: Plato’s argument against Protagoras’s
relativism
First, an outline of Protagoras’ position (Plato,
Theaetetus 152a2-10):
Socrates: Protagoras, or so I’ve heard, held
that man was the measure of all things: of
those that are, that they are; of those that are
not, that they are not…and isn’t this roughly
what he means: “Particular things are to me
just as they appear to me, and are to you just as
they appear to you”?
Theaetetus. Yes, that’s what he means.
2
First interpretation
Chappell CQ 1995)
(Bostock,
McDowell,
Protagoras’ relativistic thesis is that all beliefs are true.
In logicianese:
(R1) For any proposition p, if p is believed, then p is
true.
And Socrates’ objection to (R1) at Theaetetus 170-171 is
that some people don’t believe it (e.g. Socrates doesn’t):
some people believe that not all beliefs are true.
So we can argue against (R1) by showing that if it’s true,
then a contradiction is true:
a. (R1) For any proposition p, if p is believed, then p
is true. (Assumption for reductio)
b. Not-(R1) is believed. (Premiss)
c. So not-(R1) is true. (a, b)
d. But a contradicts c! Reductio.
The key move here is (b), which slots in Not-(R1) as a
value for p.
The argument applies (R1) to itself.
In Greek, this is called the peritropê (the turning-round
of the argument).
Protagoras could just deny (b), and tell Socrates that in
fact he does believe (R1); but that seems a bit highhanded and unconvincing.
3
Problem with the first interpretation:
The text of the Theaetetus makes it obvious how
Protagoras can reply.
He can say that Socrates doesn’t understand his
view properly.
Protagoras’ real view (he can say) is not that all
beliefs are true, but that all beliefs are true for
someone (= the believer). In logicianese:
(R2) For any proposition p and any believer x, if x
believes p, then p is true for x.
Now we can’t run an argument like (a-d) against
(R2). Try it and see:
e. (R2) For any proposition p and any believer
x, if x believes p, then p is true for x.
(Assumption for reductio)
f. Not-(R2) is believed.
g. So it’s true that, if x believes Not-(R2), then
Not-(R2) is true for x.
h. But g doesn’t contradict e! The reductio fails.
So, if we want Socrates’ argument against
Protagoras to work, maybe we should read
Protagoras differently?
4
Second Interpretation (Burnyeat, Denyer, Sedley)
Protagoras’ point is not (R1). (R2) is closer to the
truth, but still not the best expression of what
Protagoras is really getting at. For that, try (R3):
(R3) p is true iff there is someone to whom p
appears.
And Socrates’ objection is that there is no one to
whom (R3) appears.
So we get this argument against Protagoras:
i. (R3) p is true iff there is someone to whom p
appears. (Assumption for reductio)
j. But there is no one to whom (R3) appears.
(Premiss)
k. So (R3) is not true. (i, j)
l. But k contradicts i! Reductio.
The key move here is (j), which slots in (R3) as a
value for p. The argument is another peritropê.
5
Problem with the second interpretation
Why should we accept (j)? Doesn’t (R3) appear to
Protagoras (i.e. Protagoras believes (R3))? He
certainly says he does!
Of course we can reject his claim to believe (R3),
just as (as we saw) Protagoras can deny Socrates’
claim (b) in the first argument. But this is just a
dialectical stalemate.
6
Third interpretation (Chappell Phronesis 2006)
Protagoras is proposing two things: an account of
truth as truth-for, and an account of belief as truthfor.
That is, he’s claiming
(R4) p is true = p is true for someone, and x
believes p = p is true for x.
So whenever I say that something is true, I can
equally say that it’s true for someone (me).
And whenever I say that something is true for
someone (me, or you, or whoever), I can equally
say that it’s true.
And whenever we say that someone believes
something, we can equally say that that something
is true for him (and vice versa).
7
(R4) yields a contradiction as follows:
m. (R4) p is true = p is true for someone, and x
believes p = p is true for x. (Assumption for
reductio)
n. Protagoras believes (R4). (Premiss)
o. Socrates does not believe (R4). (Premiss)
p. So (R4) is true for Protagoras. (m, n)
q. But (R4) is false for Socrates. (m, o)
r. So (R4) is true. (m, p)
s. And (R4) is false. (m, q)
t. But s contradicts r! Reductio.
This is a peritropê too: it feeds in Socrates’ and
Protagoras’ beliefs as instances of p, and Socrates
and Protagoras as instances of x.
8
Half-time entertainment: the anti-relativist
argument that Plato never (quite) presents
u. (R5) All truth is relative (to some believer or
some context of belief).
v. (R5), if true, is either a relative truth or a nonrelative truth.
w. If (R5) is a relative truth then the non-relative
truth “Not all truth is relative” is consistent with
(R5).
x. If (R5) is a non-relative truth then (R5) is a
counter-example to itself, and so false.
y. Either way, the opponent of relativism has
nothing to fear from (R5).
Another peritropê…look, in particular, at (v).
Does Plato run this argument against relativism
about truth?
I don’t think so.
He comes close to running it, especially according
to the First Interpretation.
Perhaps, on his own principles, he should run this
argument.
But he never quite does.
9
Second half: how we might argue against
relativism
First Argument
a. Relativism says that we should talk, not about
“truth”, but about “truth for people”. We
should say, for any proposition p that we agree
with, not “p is true”, but “p is true for me”.
b. But this loses the normativity of truth.
If I say “p is true”, I give you reason to believe p.
If I say “p is true for me”, you can just reply
“how interesting” or “so what?”.
“p is true for me” implies nothing about anyone’s
reasons to believe (not even mine).
So “true for someone” isn’t an adequate stand-in
for “true”.
So relativism about truth won’t do.
10
A worry about this argument
Does “p is true” give me reason to believe p? What
if p = “the 34562nd phone number in the current
edition of the Paris telephone directory is 76-3490”? Why should the truth of that proposition give
me any reason to believe it?
Possible answer
The truth of p at least gives me reason (a) not to
believe not-p, and (b) to believe p if I consider the
question whether p.
To put it another way: saying that
we have reason to believe what’s true
doesn’t have to mean saying that
we have reason to believe everything that’s true:
no more than
saying that we have reason to do what’s good
has to mean
saying that we have reason to do everything that’s
good.
So truth is still normative (just in a modester way
than we first proposed).
And truth-for still isn’t normative.
So the argument still works.
11
Second anti-relativist argument (or train of
thought)
What could “a relative truth” possibly be? Let’s
look at precise examples.
(RD) “Derek is to the left”
is a relative truth, indeed a doubly relative one.
But that doesn’t mean that (RD) is some sort of
sinister threat to non-relative1 truth!
It just means that (RD) is semantically incomplete.
“Non-relative”, not “absolute”, because it’s apt to sound like
some sort of spectacular achievement for truths to be absolute—
but it isn’t at all difficult for them to be non-relative. They are
non-relative when there is no non-trivial way of specifying some
believer or context of belief to which they are relative. I take it
most truths are like this most of the time. If that’s what absolute
truth is, then I guess I believe in absolute truth—but as before
would prefer to skip the boggle-inducing rhetoric of the word
“absolute”.
1
12
What semantic (in)completeness is
If I say
(BD) “Derek is taller”,
you’ll say “Taller than who?”; and I might reply
“Taller than Bashful”.
Likewise if I say
(RD) “Derek is to the left”,
that just prompts the questions (a) “To the left of
what?” and (slightly less obviously) (b) “From
what viewpoint?”
And we can answer these questions, e.g. by
(NRD) “Derek is to the left (a) of Grumpy (b) from
where Sneezy is”.
So when you fill out (RD), you get (NRD). But
(NRD) is a non-relative truth!
So semantic completion gives us a smooth and easy
road from (RD)’s sort of relative truth to (NRD)’s
sort of non-relative truth.
It shows how relative truth is a much more boring
phenomenon than the relativist hoped.
13
Objection from the relativist
‘You’re completely missing the point. I’m not
talking about the relativity of left or taller than. I’m
talking about the relativity of truth.
I am saying that “is true” is like “is taller
than”.
My point is that “is true” is semantically
incomplete as it stands.
You need to add a reference to who the truth is
true for.
“Is true” always needs to be spelt out as “is
true for [someone]”.
14
My reply to this objection
‘I see what you mean; but there’s a point that
you’re missing.
When we semantically completed (BD) “Derek
is taller” by turning it into “Derek is taller than
Bashful”, what we ended up with was a nonrelative truth.
And when we semantically completed the
relative truth (RD) by filling in who Derek was to
the left of, and from whose viewpoint, we got the
non-relative truth (NRD).
The point generalises: whenever you fill in
these semantic completions, you end up with a nonrelative truth.
So when you fill out the relative truth
(T1) “p is true”
as, say,
(T2) “p is true for Protagoras”,
(T2) will be a non-relative truth.
But relativism about truth is the claim that all truths
are relative!
So (T2) is a counter-example to relativism about
truth.’
15
What the relativist might reply to this reply
‘No, (T2) isn’t a counter-example. (T2) is
semantically incomplete too. It needs to be filled
out as (T3) “It’s true for someone else that it’s true
for Protagoras that p”. And (T3) too will be
semantically incomplete…’
My reply to this reply to my reply
‘It’s just plain barmy to say that every time we
have a truth we have an infinite regress of extra
relativisations that we need to add to that truth to
make it semantically complete.’
The relativist’s next move
‘Why is it barmy? You non-relativists like to say
that, for any true p, you can assert that it’s true that
it’s true that p, and it’s true that it’s true that it’s
true that p, and so on ad infinitum. Why is my
regress any more vicious than yours?’
My next (and winning?) move
‘There’s no parallel. I say that, for any true p, you
can assert that it’s true that p, etc. You say that, for
any true p, you must go on adding the
relativisations, or you won’t have a semantically
complete statement. That means you never have a
semantically complete statement of sub-infinite
length! And that’s a disastrous consequence,
because
semantic
incompleteness
means
meaninglessness.’
16
Extra time: is expressivism a moral relativism?
Our argument about relativism can be modified a
little to deal with the case of moral relativism.
We can say: the moral relativist thinks that moral
utterances are semantically incomplete: e.g.
“Stealing is bad”,
to be semantically complete, needs to be spelled
out as
“Stealing is bad from my perspective”,
or something like that.
But this analysis faces the objection about
normativity that I offered to relativism about truth:
“Stealing is bad” gives people reasons in a way that
“Stealing is bad from my perspective” just doesn’t.
17
What if we try and reinstate the normativity by
saying this?
It’s good for people to say things like “Stealing is
bad from my perspective”.
The problem is obvious: moral relativism says that
we have to treat this too as semantically
incomplete, and turn it into
It’s good from my perspective for people to say
things like “Stealing is bad from my perspective”.
In short, the moral relativist will have to choose
between finite semantic completeness and
normativity. (Cp. the relativist about truth, who
could only get semantically complete assertions by
making them of infinite length.)
And this looks like a hopeless position.
So moral relativism is bunk.
18
Now most modern non-realists in ethics are not
moral relativists of the kind discussed here.
Many of them (e.g. Simon Blackburn, Allan
Gibbard, Mark Timmons, Jimmy Lenman, Mike
Ridge, and (so he tells me) Derek Matravers) are
expressivists.
Expressivism: moral utterances aren’t (really)
assertions: they’re expressions of our attitudes.
(E.g. “Stealing is bad” is (really) more like “Boo
for stealing!” than it is like “Derek is short”.)
Question: Is expressivism really a form of moral
relativism?
Official answer: Of course not. Moral relativism
says that moral utterances are not truths2, but
truths-for-someone.
But expressivism says that moral utterances aren’t
truths at all: they’re expressions of attitudes.
A fortiori, then, expressivism doesn’t say that
moral utterances are truths-for-someone.
Or falsehoods, of course—but for simplicity I concentrate on
“correct” moral utterances.
2
19
However…
If the realist tells you that moral utterances are
truths, then you won’t want to ask “Whose truths?”
unless you’re attracted to relativism. (And you
shouldn’t be: as above, relativism is bunk.)
But if the expressivist tells you that moral
utterances are expressions of attitudes, then you
surely will want to ask: “Whose attitudes?”
When we answer this question, we start relativising
attitudes to their holders.
So then we have to rewrite
“Stealing is bad”,
not simply as
“Boo for stealing!”,
But as
“‘Boo for stealing!’ according to Derek.”
20
And now expressivism is in deep doo-doo.
For if we’re expressivists, all we can do to restore
reason-giving force to “‘Boo for stealing!’
according to Derek” is to say that we approve of
Derek’s attitude.
This is meant (on the official expressivist line) to
come out as
Hurrah for (Boo for Stealing!)!
But once we ask the question “Whose attitudes?”,
we see that actually it comes out as
(X) Hurrah according to us for (‘Boo for
stealing!’ according to Derek)!
And (X) is no more genuinely reason-giving than
the relativist’s
It’s good from my perspective for people to
say things like “Stealing is bad from my
perspective”.
For (X) to become reason-giving, we’d have to
stick another “Hurrah!” on the front of it.
But then the same question about whose attitude
this is would arise... and so on indefinitely.
21
Hence expressivism collapses into something very
like moral relativism:
For expressivism faces just the same problem as
moral relativism about keeping hold of both finite
semantic completeness and normativity.
Therefore, and finally, a quick argument in modus
ponens:
1. If moral relativism is bunk then expressivism
is bunk.
2. Moral relativism is bunk.
3. [Exercise to do in your own time: fill in the
conclusion.]
22