[Bups-dis] Question on the Conditionals
Tim Short
t.short at ucl.ac.uk
Sun Aug 3 10:48:30 PDT 2008
OK.
The only time we falsify the sentence (if p then q) is if the antecedent
is true and the consequent is false (consistent with what you say
below). As you also say, the sentence (if p then q) is always true if p
is false i.e. the sentence is true whether or not q is true or false.
In your case 1.), the sentence is true because you did not go to the
shops and you did not have an ice cream (both p and q are false but in
fact we don't care whether q is true or not). In your case 2.), the
sentence is true because again p is false but you have inverted the
definition of q such that if it was previously false it is now true and
vice versa. (This is fine I think; I am not pointing it out because I
think it is a problem.)
So the counterintuitive element is that case 1.) "if I went to the shops
then I would have had an ice-cream" is true because you did not go to
the shops. Likewise, "if I went to the shops then it is not the case
that I would have had an ice-cream" is also true as a sentence because
you did not go to the shops.
I guess what is happening is that we simply do not tie down q in the
situation where p is false...
Note further that the following sentence is also true if p is false:
(if p then (q and not q))
- for any definition of q!
It might be the case that the quasi-mathematical world of logic does not
always map cleanly on to our perceptions of how the world seems to
work...in particular I seem to recall that there is some hand-waving
around the truth table selection for (if) related to 'we already used
that for something else so this one has to be (if)'...there are only so
many combinations of T and F in two dimensions.
josh seigal wrote:
> hmm. I guess I'm saying the following. Suppose p = I went to the shops
> and q = I would have had an ice-cream. If (if p then q) is a
> counterfactual conditional, then we assume the falsity of p (ie, we
> assume that p is 'contrary to fact'). Now, given the truth-conditions
> of (if p then q), if p is false then (if p then q) is true, so it is
> true that if i went to the shops, I would have had an ice-cream.
> However, for the same reason, it is also true that (if p then not-q);
> it is true that if I went to the shops then it is not the case that I
> would have had an ice-cream. So, we have a situation where the
> following two sentences are both true:
>
> 1.) if I went to the shops then I would have had an ice-cream
> 2.) if I went to the shops then it is not the case that I would have
> had an ice-cream.
>
> This seems to me to be something of a contradiction. However, as I've
> said, I'm probably making some kind of extremely basic error
> somewhere. Probably in my interpretation of the truth-conditions for
> counterfactual conditionals as opposed to material conditionals.
>
> And, yes, there was a formating error...
>
> cheers,
> Josh
>
>
>
> > Date: Sat, 2 Aug 2008 16:00:24 +0100
> > From: t.short at ucl.ac.uk
> > To: bups-dis at bups.org
> > Subject: Re: [Bups-dis] Question on the Conditionals
> >
> > To reply to this message or start a new topic please email:
> BUPS-DIS at bups.org
> > -
> >
> >
> > Josh -
> >
> > I can't quite see your notation because of a formatting or font
> problem,
> > but it looks like you are saying the following. Apologies if I have
> > misrepresented you.
> >
> > You say that the sentence (IF P THEN Q) is true if P is false because
> > that is how the truth table for the sentence works. That's fine. Then
> > you point out that (IF P THEN NOT Q) is also true for the same
> reason if
> > P is false. That's also fine.
> >
> > Then you say that you have a contradiction and this is where I think
> the
> > problem is. I guess the issue is that if both of these sentences are
> > true and P is false, then Q must be true and so must NOT Q. That isn't
> > the case though because (IF P THEN Q) is still true as a sentence
> when Q
> > is false.
> >
> > Is this what you were getting at...?
> >
> > josh seigal wrote:
> > > To reply to this message or start a new topic please email:
> BUPS-DIS at bups.org
> > > -
> > >
> > >
> > > I've noticed a not completely unrelated problem for the analysis
> of counterfactual conditionals (a problem for which, I am sure, there
> is a very easy solution).
> > >
> > > The (putative) problem is this: a counterfactual is a subjunctive
> conditional where the falsity of the antecedent is assumed. However,
> it seems to me that, if this is the case, contradictions can easily be
> generated.
> > >
> > > For example, take the counterfactual conditional (p É q). Using
> the above definition of counterfactuals, and the standard
> truth-conditions for conditionals, this comes out as true, since it
> antecedent, being counterfactual (ie contrary to fact) is false.
> However, this generates a problem when we notice that the
> counterfactual conditional (p É Øq), for the same reasons, also comes
> out true, hence yielding a contradiction.
> > >
> > > As I’ve said, I’m sure there is a very easy way around this, and
> I’m sure it is no more than a superficial difficulty. It is just
> something I noticed when studying first-year logic and it is something
> that I haven’t got round to investigating further.> From:
> andrew.bacon at philosophy.ox.ac.uk> Date: Fri, 1 Aug 2008 17:18:38
> +0100> To: rezakhs at yahoo.com> CC: bups-dis at bups.org> Subject: Re:
> [Bups-dis] Question on the Conditionals> > To reply to this message or
> start a new topic please email: BUPS-DIS at bups.org> -> > Hi Reza,> > >
> (if (P AND Q), then R), logically entails ( (if P, then R) OR (if Q,
> then R))> > One thing to note is that it's not clear that this *is* a
> logical entailment. We> should not confuse the above, which seems to
> be schematic for an inference form> couched in English, with the
> following, which is a logical entailment:> > > ((P & Q) -> R),
> logically entails ( (P -> R) \/ (Q -> R))> > One reason that first
> inference might fail is that if the English conditional> goes by a
> Stalnaker semantics, then it is not valid. What is possibly more>
> striking is that, if we go by a possible world semantics for
> conditionals, it is> no longer clear that "if ..., then ..." is a
> logical constant! It will depend on> the criteria of logicality for
> modal connectives.> > Also worth noting that the Stalnaker semantics
> appears to get the right verdict> for both your examples. We might
> just take this as a point for Stalnaker over> the material conditional
> analysis.> > Andrew> > > > > > > But there are dozens of examples
> which make trouble for this inference. E.g.:> > > > P: Diego is Jim's
> father> > Q: Mary is Jim's mother> > R: Diego and Mary are Jim's
> parents> > > > or may be a better one:> > > > P: I call her by her
> first name> > Q: I call her by her last name> > R: She loves it!> > >
> > The translation of the sentence at the left side does not match with
> the> equivalent sentence at the right side:> > > > For the first
> example, one might say it's a possible world conditional. (well> then
> try it with P: Plato is a fool. Q: Quine is a fool. R: Russell is a>
> fool.... still I think what is meant in the left side is different
> from what is> meant in the right side). But let's see the second
> example which works better:> > > > At the left side, the sentence
> tries to say that "she loves it if I call her> by her full name",
> while the second side says "she loves it either I call her by> her
> first name or her last name". > > > > This seems to be a famous
> problem. I saw the problem just recently; but there> was nothing on
> the solutions. Many of similar examples seemed to me to be> indicative
> conditionals and yet they got this translational problem. Any idea on>
> what should I look in? :-)> > > > Best,> > Reza> > > > > >
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