In the book gamma of the metaphysics,
Aristotle advances what is perhaps one of the
few attempts to defend
the principle, and he called it the elenchus,
some kind of transcendental argument,
could you give us the gist of the argument?
Yeah, look, ok.
Again, this is not straight forward.
We’re talking about a passage from metaphysics gamma,
and it starts towards the end of the book three and it goes around the book four,
and what you find is a sustained argument – actually, a bunch of arguments –
for the law of noncontradiction.
A couple of things you might wanna know about this… First of all,
Aristotle does not take this to be a principle of logic.
Aristotle’s logic is found in the Analytics, not in the Metaphysics,
and the whole of metaphysics, Aristotle tells us, is about an analysis of being qua being,
so how do you interpret the principle of noncontradiction?
To Aristotle it’s a principle about reality, the nature of being,
it’s not anything to do with logic.
Now, this is not characteristically how contemporary logicians – or at least logicians since Leibniz –
have considered it, but it’s the way that Aristotle thinks.
His principle of metaphysics is not a principle of logic.
Ok. Second thing before we actually discuss the passages in question
is that Aristotle,
in book gamma of metaphysics
decides to enunciate and defend two principles of being qua being.
The first of these
is that no contradiction can be true, this is the principle of noncontradiction.
The second of these is the principle of the excluded middle, which says that
if you got a pair of contradictories, at least one of them must be true.
So, the principle of excluded middle says at least one, and the principle of noncontradiction says at most one.
So, this is what Aristotle does
in that text of metaphysics. Now,
people have focused less on this defense of the principle of excluded middle.
At least, it’s fair to say that even Aristotle thinks that noncontradiction is the more fundamental.
There’s another very strange passage in Aristotle,
in another text, De Interpretatione,
which is a rather notorious…
Its rather notorious chapter 9
is about contingencies about the future.
And, at least prima facie, what he seems to be saying in that
is that if you get a contingency about the future…
So, his example was there’d be a sea battle tomorrow.
Let’s just take… I don’t know, the number of deaths of coronavirus in New York will go up tomorrow.
We don’t know yet if it will or won’t,
this is a contingency about the future, and Aristotle seems to say that
these things might be neither true or false,
so you can have “it will go up” and “it won’t go up” and neither of those is now true, by tomorrow it will be,
but at the moment they’re not, so…
There’s a good reason to think that Aristotle thinks the principle of noncontradiction’s more
fundamental than the principle of excluded middle,
and history has tended to follow him in this.
As you mentioned in your introduction,
the people who have thought that noncontradiction might fail
are very, very few.
But the people who thought that excluded middle might fail is much, much bigger.
And, in particular, if you look at contemporary logicians, it’s a very, very standard move in many contexts.
So…
it looks like they kinda drew up principles,
but it hasn’t actually kind of worked out that way in history of philosophy,
and why that is is an interesting question, but maybe we should pursue that at another stage.
It’s true that the most important part
of that passage of metaphysics is where he defends the principle of noncontradiction,
and that’s what you were asking about. So, so, there’s been a rather long digression,
but I thought it would be easy to put this is context.
Ok, so…
In that passage, Aristotle enunciates the principle of noncontradiction.
And, you know,
let’s skip over all the narcissists and keep things very simple.
He enunciates the principle of noncontradiction and then he says “well, it’s so basic you can’t prove it”.
All argumentations stop somewhere and there’s nothing more fundamental than this.
And then he says something rather strange. He says “however, you can prove it by elenchus”.
And what that is, it’s a sort of technical term in logical Aristotle’s thought.
But Aristotle kind of explains it, he says that you can prove it provided
the person who will say something.
Ok. So, you can’t sort of establish it from anything more fundamental,
but, at least, if someone like me say “hey, some contradiction is true”, you can thrash my argument,
that’s the elenchus.
And thereafter, there is a long and tortured argument.
Let’s compact that in a minute.
It runs, you know,
maybe twelve pages of standard modern text,
and…
To put…
fairly neutrally, it’s tangled.
I mean, it’s
not clear exactly what the argument means, so it’s not clear that it works cause it’s not clear how it works.
But let’s compact that in a second. This is one… This is a major argument from the text.
After that, you get six or seven small arguments.
A lot of them of sort of one line, or one paragraph.
And somethings are notable about these arguments.
The first is that elenchus has completely disappeared.
So… What on earth Aristotle thinks he’s up to?
Because the elenchus only seems to be relevant in the first long argument.
The second point is that all the arguments after the one main argument are beside the point.
Because, if you read the text, Aristotle’s shift has shifted gear.
What he’s defending in these small arguments
is not the claim that no contradictions can be true, but the claim that not all contradictions can be true.
Ok. Let’s suppose that not all contradictions can be true.
That’s quite consistent with some contradictions being true.
And the law of noncontradiction says it’s not the case that some contradictions can be true, so,
Aristotle has kind of slid between some and all,
and that explanation in the text, why this is,
scholars speculated about this,
in fact, is even worse than that.
Because towards the end of this argument,
Aristotle slides from defending the thought that it can be the case that all contradictions are true.
To relieve him, we can claim no one can believe all contradictions are true…
Maybe there’s some, maybe there’s not. But, I mean, it’s…
That’s compatible, all contradictions being true, let alone some contradictions being true.
So…
the arguments are pretty clearly beside the point.
That leaves the one long argument, ok? Which we haven’t talked about yet.
So, I’ve been talking for a few minutes here…
when we look at the main argument
maybe you wanna jump in on this.
As you like
Now that you mentioned
the view that every proposition is true, the trivialism,
We might
we might move on to some logical aspects of contradictions
and perhaps go back to the elenchus after we said that,
in a classical…
Up to you, how do you want to run things?
Well,
let’s continue for a bit talking about the elenchus, and see where we get.
Ok.
Alright, so let’s talk a bit about the one long main argument.
And it really is long, and it’s tortured,
and scholars don’t agree on how to interpret it.
I might say that what I’m saying about this passage in the metaphysics
is not simply my view.
I mean, you mentioned Łukasiewicz, the polish logician
who wrote a famous book in polish in 1910
where he examines meticulously the arguments and comes to conclusion they are pretty worthless.
And one commentator that’s most in favor to subscribe to the principle of noncontradiction
also think that the passage is highly problematic, unclear, beside the point.
So, the contemporary scholarly evaluation of this argument is that it’s not very good.
Quite persuasive argument.
Anyway, so let’s return to…
this long passage.
It starts with the elenchus
and Aristotle says
“ok, you know, I can’t prove the principle of noncontradiction to you,
but if you say anything I’ll just trash your argument”,
all sure that you have refuted yourself, or something like that.
And it turns out you actually have to say that anything, because,
as it becomes clear in the text, all I could’ve said is something meaningful, like man.
Ok. So…
Aristotle says “ok, ok Priest, say something”. I say “man”,
he says “yeah, well, alright, of course that’s ambiguous. You know, man is ambiguous.
It might mean a human being and it might mean someone of the male gender.
And of course someone can be a man and not a man if you play with de ambiguity."
Angela Merkel is a man and not a man because she’s a female but a human being.
Ok, that’s not interesting. I mean,
it’s an interesting fact that we choose to use the man ambiguity that way,
I mean, there are many interesting questions there,
but that’s not relevant at the moment,
What’s relevant is that, of course, if the meaning of the word man slides around, then
of course, you can have P and not P – something and its negation – in different senses of the word.
Ok, that’s boring. So,
Aristotle says “ok, well, let’s fix on one definite meaning”.
And he says, let’s see, “two-footed animal”.
That’s kind of puzzling in itself, cause the Aristotelian definition of man is a rational animal.
Why he fixes on two-footed animal God only knows, but he does, but anyway, that’s not really relevant either.
We can choose the meaning that we want
Yeah, fix on the meaning, let’s just fix it.
And then there’s a swift argument with a bit of modern logic on it,
and it goes something like this:
if man is a two-footed animal,
then it can’t be the case that something is a man and not a two-footed animal,
so it can’t be the case that something is a man and not a man, cause man just means two-footed animal.
So, what it seems to be established is that it's not possible something to be a man and not a man, and
it would seem that
Aristotle thinks this is kind of an example of noncontradiction while involving man,
but it seems clear that Aristotle thinks you could do the same with any word you started with.
But even that is contentious because some
commentators
have
argued that Aristotle intends
the word you choose to be a substance word, an essence word.
So, we needn’t go into the details too much,
but Aristotle thinks some words refer to a substance, where some
refer to what medieval called an accident, or property.
So, if I say, if asked you what you are and I say “you’re a man, a person”, right?
That gives your essence. If I say “what are you, you’re a Brazilian”,
that’s an accident, right?
And some scholars have suggested that Aristotle’s argument works only,
or even that Aristotle intended it to work only
for these sort of substance terms, like man.
Which is not what Aristotle specific says. It has to do but,
I mean, as I said, this is a very tortured passage, and scholars disagree about how to
understand it.
Ok, but set that complexity aside again,
assuming that everything is right, so far, what
Aristotle established is that it's not possible for something to be a man and not a man.
and maybe that generalizes to all words.
And you might think “hey, well, you know,
that establishes the principle of noncontradiction”,
but this brings us back to this rather trickiest issue that we started by talking about,
about what you mean by principle of noncontradiction.
Let’s agree that that’s established,
that it’s not possible for something to be a man and not a man.
It’s yet quite opened to a dialetheist
to hold that it can yet be the case the something is a man and not a man
and, therefore, that is possible.
So,
the fact that you’ve established that it’s not possible for something to be a man and not a man
is compatible for a dialetheist to the thought that it’s also possible that something is a man and not a man.
So, this is where it’s tricky. Obviously that…
that’s not what Aristotle wants… that’s not a move Aristotle wants you to be able to make.
But it’s hard to see how it can rule it out without begging the question.
So…
That argument, if indeed its his main argument, looks to be question-begging.
This is a phenomenon we see quite a lot over the recent years,
I mean… people have now started to get other arguments for the principle of noncontradiction,
but they tend to beg the question.
So…
That argument doesn’t seem to be so good.
And it might sound cheating to say
“oh, it’s not possible because it could be possible”,
not necessarily, because
of something we’ll presumably talk about in more detail later,
it’s how this relates to developments in modern logic.
So… I mean there’s a kind of logic
of which, as you know, Brazil has played in almost all of… in developing this paraconsistent logic.
And if you look at various paraconsistent logics,
which contain modal operators – that’s words like “must” and “may” and “can” – so,
in many of these, that’s the exactly a contradiction of the…
The contradiction that it can be the case and it can’t be the case
is exactly a contradiction of the kind you find in these logics.
So,
in that context,
this isn’t just a subtle point of begging the question, it’s a serious issue.
Because
this… The question being begged as to what kind of logic you can subscribe to here.
And if you rule out the kind of logic that dialetheism is probably going to endorse,
then, of course, that just begs the question.
So…
ok, that’s… That’s kinda complicated,
but I’ll try to keep it as simple as I can.
That's perfect.
