Re: Question on Counterfactual Conditionals


"Herman Jurjus" <h.jurjus@xxxxxxxxx> wrote in message
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Dan Christensen wrote:
"Herman Jurjus" <h.jurjus@xxxxxxxxx> wrote in message
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Dan Christensen wrote:
"Herman Jurjus" <h.jurjus@xxxxxxxxx> wrote in message
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Dan Christensen wrote:

Just think of conditional sentences p > q with a hidden, silently
assumed extra condition: "if p 'and all other things remain the same',
then q".
Is this really necessary? I can easily prove, using my formalism, that,
no matter what lessons are taken, Bump & WeightOnDownhillSki => Fall.
For some purposes, that may be good enough. For others, it isn't.

Suppose you have sentences like:
"If it rains, i get wet"
(therefore) "if it rains, i use an umbrella"
(because) "if i use an umbrella, i don't get wet"

According to classical logic, these sentences together imply "if it
rains then i am the emperor of China".

Don't you mean "if I am the emperor of China" then "if it rains, i use an
umbrella?" [snip]

No, i don't mean that.

rain -> wet
rain -> umbrella -> not wet

You are setting up a self contradiction here. And of course, from a
falsehood, you can deduce anything.

Consider an alternate formulation:

rain -> [umbrella <-> not wet]

No contradiction here.


therefore
rain -> (wet and not-wet)
therefore
rain -> i am the emperor of China

Now one might say: Oh, but the sentences should really be:

"if it rains and i don't use an umbrella, then i get wet"
"if it rains and i use an umbrella, then i don't get wet"

That fits better with classical logic, that much is true.
But it still isn't good enough.
Because in reality, if it rains, and i don't use an umbrella, -and i
stay in the house-, then i -don't- get wet.

The point is that practical conditionals like these are never really
spot on. They may be translatable to classical logic, sort of, but the
translations are usually not 'stable', in the sense that the sentences
require re-translation when new conditionals are added, or when more
'aspects' or possible exceptional situations are taken into account.

[snip]

I don't see why such a re-translation would be problematic. Is it just a
matter of computing efficiency?

No, it's more.
The translation is not translating the -conditional-, it's translating the
theory as a whole. You could just as well first calculate all basic
formulas that are consequences, and 'translate' the theory as that set of
basic formulas.

Can you give a simple example in which use
of a counterfactual conditional is unavoidable?

Paradigm difference.
The point is not whether you can't translate a single theory, but that on
changing the theory, the re-translation shows that the previous
translation was not accurate at all.
Also: human reasoning easily combines the various translations, for
various levels of detail. Classical logic can't do that.


Again, can you give a simple example?


BTW, there's one more complication. After re-translating
rain -> wet
to
rain & -umbrella -> wet,
The re-translation does no longer allow you to draw the conclusion 'wet'
from 'rain' alone.

But you cannot conclude 'wet' from 'rain' alone. Sometimes, if 'rain,' you
are 'wet' and sometimes not 'wet' depending on whether you have an umbrella.
(See my formulation above.)


You must explicitly know 'not umbrella' first.

As it should be.


So in a way, the re-translation has removed conclusions that were
previously considered valid.


Not as I see it (above).

Regards,
Dan


.

Relevant Pages

  • Re: Question on Counterfactual Conditionals
    ... "If it rains, i get wet" ... They may be translatable to classical logic, sort of, but the translations are usually not 'stable', in the sense that the sentences require re-translation when new conditionals are added, or when more 'aspects' or possible exceptional situations are taken into account. ...
    (sci.logic)
  • Re: Question on Counterfactual Conditionals
    ... "If it rains, i get wet" ... The point is that practical conditionals like these are never really ... translations are usually not 'stable', in the sense that the sentences ...
    (sci.logic)
  • Re: Question on Counterfactual Conditionals
    ... "If it rains, i get wet" ... "if i use an umbrella, ... They may be translatable to classical logic, sort of, but the translations are usually not 'stable', in the sense that the sentences require re-translation when new conditionals are added, or when more 'aspects' or possible exceptional situations are taken into account. ...
    (sci.logic)
  • Re: Question on Counterfactual Conditionals
    ... "If it rains, i get wet" ... "if i use an umbrella, ... They may be translatable to classical logic, sort of, but the translations are usually not 'stable', in the sense that the sentences require re-translation when new conditionals are added, or when more 'aspects' or possible exceptional situations are taken into account. ...
    (sci.logic)
  • Re: Question on Counterfactual Conditionals
    ... You are setting up a self contradiction here. ... "if it rains and i don't use an umbrella, then i get wet" ...
    (sci.logic)