McEvoy on a different thread notes:
““The cat is on the mat” is simpler in many ways than “e = mc2” but it has less
i. The cat sat on the mat.
I seem to prefer this version. Admittedly, it is more difficult (or less
‘simple’, or more ‘complex’) to formalise, since we need time indexes (“sat” is
the past tense of ‘sit’) – but it has a triple rhyme that attracts me – and I
think it’s the phrase that was used to teach to read and write in elementary
schools (Toulmin uses it in a philosophical context).
“e = mc2” seems perfectly transparent to Einstein. But I’m not sure what he’d
do with (i). Let’s suppose we try to formalise it. We have two occurrences of
the last ‘formal device’ (in its vulgar counterpart, as Grice prefers) of the
iota operator, or definite descriptor (‘the’, (ix)). The utterance refers to an
event in the past, so we need temporal indexes (t2 < t1). We have a phrase,
‘on the mat’. The cat did not just _sit_, but she did it “on the mat”. Should
we treat, qua philosophical logicians, “sit-on-the-mat” as just ONE predicate,
or should we ‘de-compose’ it? I would de-compose it. The choices would be
reflected in the formalization:
ii. S((ix)C, (ix)M) (t2<t1)
Here, “S” stands for a dyadic predicate “sit on”. “C” stands for ‘cat’, and “M”
for ‘mat’. “e = mc2” sounds transparent, but if we add that this is
Schroedinger’s cat, (ii) triggers all sorts of implicatures. It may be argued
that “Schroedinger’s cat” is a misnomer, since it’s actually more than one cat,
so we would need a formalisation of the plural “cats” (“Schroedinger’s cats sat
on the mat.”). This may be the entailment behind McEvoy’s arguing that “The cat
[sat] on the mat” has “less falsifiability” than Einstein’s adage.
So we may argue that ‘The cat sat on the mat’ may not be _that_ simple (McEvoy
grants that “it _is_ [emphasis mine – Speranza] simpler in MANY WAYS,”
suggesting it may be NOT simpler in OTHER, perhaps fewer (seems to be the
implicature) ways, than Einstein’s adage.
McEvoy gives the illustration, ‘The cat [sat] on the mat,’ as a counter-example
to the precis of Popper’s as per the link given, equating simplicity with
falsifiability. The past tense ‘sat’ possibly complicates things.
Surely if we are sticking with the present tense, ‘The cat sits on the mat’ is
VERIFIABLE by, well, looking at the cat sitting on the mat (‘The cat sits on
the mat’ has been VERIFIED). If the cat does NOT sit on the mat, ‘The cat sits
on the mat’ has been FALSIFIED. In the past tense, the ‘method of verification’
iii. A: The cat sat on the mat!
B: How can you be so sure?
A: There’s hair all over it!
The presence of hair on the mat is an ‘index,’ as Peirce would have it, that
has led the utterer of A to BELIEVE that the cat sat on the mat. It’s not a
totally reliable index, of course – and Schiffer would find plenty of
counter-examples to test A’s ‘certainty’. The occurrence of ‘… believes …’
invites an exploration into the _sense_ of “The cat sat on the mat,” as uttered
by A (Physicians don’t seem to bother WHO utters “e = mc2” but that seems to be
THEIR problem). For, for A to BELIEVE that the cat sat on the mat, A has to
have SENSED that the cat sat on the mat – by SENSING that there is hair on the
mat. And so on.
This exploration onto A’s beliefs seems to distinguish “The cat sat on the mat”
with “e = mc2,” where we assume that Einstein has established, as per a
‘semantic postulate’ alla Carnap, how to define “e”, “m”, “c”, “2” and “=”.
“Cat” seems, by default, to refer to ‘Felis domesticus’ – a natural kind. But
we are not to assume that utterer A has a knowledge of DNA material that makes
a creature a member of the ‘Felis domesticus’ – a phrase coined, incidentally,
by Erxleben in 1777. “Mat” we may assume that is an item that belongs to the
‘common ground’ between A and his co-conversationalist B – it’s not a ‘rug,’
say. It is not a natural kind but notably an ‘artificial’ kind – of sorts.
The fact that there is hair on the mat poses the ‘falsifiability’ question as
to whether the cat merely SAT there, or perhaps she ‘LAID’ on the mat. Do cats
‘sit’? It may be argued that ‘sat’ was chosen by the writer of the elementary
‘reader’ because it rhymes with ‘cat’ and ‘mat’. It may be argued that you can
only ‘sit’ on something like a chair. On a mat, you rather lie. And so on.
Grice, H. P. “Actions and Events,” Pacific Philosophical Quarterly.