[lit-ideas] Re: Negativity Can Pull You Through (was: Re: The Educational Value of Slips of the Whatever

From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
To: lit-ideas@xxxxxxxxxxxxx
Date: Wed, 7 Oct 2009 08:28:54 +0000 (GMT)
--- On Wed, 30/9/09, Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx> wrote:

> Add-on: consider "All swans are white" and three boxes -
> the first contains 'A black swan', the second 'A white
> swan', a third is 'Empty'. Instinct or intuition might
> suggest the empty box is irrelevant as a test of the rule
> whereas the other two are relevant. On P's logic only the
> first box is logically relevant as it falsifies the rule.
> The other two are equally irrelevant - the only sense in
> which they are logically relevant is that they are both
> cases of the absence of a counter-example, and in this sense
> both boxes are examples of points in space-time where the
> rule passes an observational test since no counter-example
> is observed. But the second box no more confirms the rule
> than the third.
> 
> While logical, this is not intuitive to many people I would
> guess.

Amplifying this: it is an add-on connected to the WasonST because the 'three 
box' problem can be re-written in a Wason format _viz_.

Rule: If swan, then white. [= "All swans are white"].

Four cards, with a creature on one side and a colour on the other:

1. Swan   2. Black  3. White  4. Elephant

To check the rule we must turn 1. and 2. as these potentially falsify the rule. 

3. and 4. are logically irrelevant as they cannot disprove the rule.

This takes care of the white box.

The empty box case:-

Four cards, with a creature on one side and a colour on the other or blank on 
both sides (i.e. "empty).

1. Swan   2. Black  3. Blank  4. Blank

This, logically, is exactly the same as the white box case: 1. and 2. are 
logically relevant tests, 3. and 4. are not.


This state-of-affairs is connected with the fact that a 
UniversalGeneralisation/rule has no "existential import": i.e. "All swans are 
white" does not assert there are such things as swans or as whiteness - it 
merely asserts that if there are such things as swans then none of them will be 
non-white.

The negativist/falsificationist approach provides a solution to the "reen 
herring" of the so-called paradoxes of induction/confirming evidence: which are 
not genuine logical paradoxes for a falsificationist but in fact the upshot of 
a demonstrable theorem in the calculus of probability.

Consider:-

"All swans are white" = "There is no such thing as a non-white swan".

So what confirms one must equally confirm the other (i.e. as the two claims are 
logically equivalent the content of their supposed 'confirming instances' must 
be logically identical).

A white swan is a confirming instance of "All swans are white". Anything that 
is a not a "non-white swan" is a confirming instance of "There is no such thing 
as a non-white swan". 

This, given 'confirming instances' for one must logically give equal support to 
the other, means anything that is not a "non-white swan" (including 'empty' 
space) is just as much supporting evidence for "All swans are white" as is a 
white swan. So a red squirrel or a pink trombone confirms "All swans are white" 
just as much as a white swan does.

The paradox is only apparent since it rests on the false assumption that a 
positive instance of a UG/rule is _supporting evidence_ for the UG/rule. This 
is false insofar as _supporting evidence_ is understood in inductive or 
confirmatory terms. Positive instances are only supporting evidence in the 
sense that they constitute the absence of a counter-example. (And red 
squirrels, pink trombones and empty space are just as much absences of a 
counter-example as is the white swan, even though only the swan is a positive 
instance of the UG/rule).

These remarks also hold true even if we take confirming instance 
'probabilisticaly' - that is, as not confirming the truth of the UG/rule but as 
increasing the probability that the UG/rule is true.   

Donal
Not lost 
Not in the rain
Not in Juarez
And it's not Eastertime too




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[lit-ideas] Re: Negativity Can Pull You Through (was: Re: The Educational Value of Slips of the Whatever

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