L. Helm and D. McEvoy were referring to Occam’s razor. McEvoy refers to the
‘equation’ that one can draw from Popper’s “The Logic of Scientific Discovery,”
to wit: “Popper [a]rgues that simplicity = empirical content = falsifiability.”
McEvoy makes three critical points. “First, “[t]he [double] equation is
somewhat misleading. Not *all* [emphasis Speranza’s] forms of "simplicity"
equate with "empirical content" or "falsifiability", and Popper does not argue
otherwise. What [Popper] argues in [The Logic of Scientific Discovery] is along
the following lines. A theory like [Einstein’s]:”
i. e = mc²
“is, in its formulation, better from a scientific point of view, than a theory
like:”
ii. e = mc² except on Ash Wednesday, or when energy is
sluggish, or when mass behaves in unmass-like ways.
“etc. (i) being "better" by comparison, from a scientific point of view, is
because from a scientific point of view it has no get-out clauses etc. - and so
is more falsifiable and has greater empirical content. Popper argues that it is
in this crucial sense [or way – Speranza] also "simpler" than an alternative
with get-out clauses etc., and, further, that this is the sense [or ‘usage’ –
Speranza] of "simplicity" that is important as a value in scientific
explanation. The value of "simplicity", in this sense [or ‘usage’], is
correlated with how (i) is an adjunct to increased "falsifiability/empirical
content" - i.e. this sense [or usage – Speranza] of "simplicity" is derived
from considerations aiming at increased "falsifiability/empirical content" and
not the other way round. So Popper does not argue that whatever we call
"simplicity" helps us increase "falsifiability": that would be wrong, for
iii. The cat is on the mat.
is *simpler* [emphasis Speranza’s] in many ways than (i) but (iii) has less
falsifiability. Rather [Popper] argues that what most increases falsifiability,
in the formulation of theories, will correlate with a form of logical
"simplicity" in the formulation. Second, given [the above point], we can see
how Popper also argues that reductivism as an approach within scientific
explanation is contradictory to reductivism as a philosophical approach.
'Scientific reductivism', such as taking an area explained by a combination of
chemical and physical theories and reducing that combination to an explanation
solely in terms of one theory of physics, is a worthwhile aim - because it
increases the falsifiability of the theories under test i.e. the one theory
will be more falsifiable than the combination it replaces. Whereas
'philosophical reductivism', such as denying the existence of mental events on
the basis it would [be] *simpler* [emphasis Speranza’s] to say these are
unnecessary because everything can be explained in terms of physics, lessens
"falsifiability" by denying _on untestable grounds_ the existence of a class of
entities (e.g. mental events) that would otherwise constitute potential
falsifiers (e.g. their existence would of course falsify the claim that only
physical events exist). Even though they are logically in contradiction from
the point of view of increasing falsifiability, the confusion between
'scientific reductivism' and 'philosophical reductivism' is still widespread.
Many flawed arguments are based on the confusion. This confusion lies at the
heart of many attempts to defend 'physicalism', especially 'physicalism' as an
answer to the mind-body problem i.e. to claim the solution is that there is no
mind, or mental event, just bodily or physical events, such as physical brain
events (which we mistake for distinct mental events when this is [to echo
Occam] "beyond necessity"). Third, given the previous two points, we can
understand why in "Objective Knowledge" Popper gets to the crux of what is
debatable about Occam's Razor when he asks on what grounds are we to decide
what is "beyond necessity" (nevermind guess what Occam had in mind)? E.g. What
entities should we admit as possible (from the point of view of further
investigation) and which we should disregard? If we admit an entity as possible
and worthy of further investigation (e.g. distinct mental events), surely that
event cannot validly be discarded as "beyond necessity"?”
Thanks for the clarification. I guess the bibliography should add the
“Objective Knowledge” reference, which in a way, echoes Grice when he says in
1967: “I would like to propose for acceptance a PRINCIPLE [emphasis mine –
Speranza] which I might call Modified Occam’s Razor: Senses are not to be
multiplied beyond necessity. Like many REGULATIVE [emphasis mine – Speranza]
principles, it would be a near platitude [Implicature: but not a
platitude-platitude – Speranza] and all would depend on what was counted as
“necessity.” Still, like other regulative principles, it may guide.” Only that
Popper would have “mis-guide,” rather!
McEvoy: “nevermind guess what Occam had in mind.” Well, there are linguistic
issues involved. Quine thought that Occam’s razor was meant to cut Plato’s
beard – but Schiffer came out with an “aftershave” which he thinks is pretty
effective!
McEvoy’s focus is on Occam’s complete phrase, “beyond necessity” – “præter
necessitatem”. The thing was first formulated as a “novacula occami,” but
surely not by Occam himself. The formulation “Non sunt multiplicanda entia sine
necessitate” is apparently not Occam’s.
For the record, the ‘simplicity’ entry in the Stanford encyclopedia
Baker, Alan, "Simplicity", The Stanford Encyclopedia of Philosophy (Winter 2016
Edition), Edward N. Zalta (ed.), URL =
<https://plato.stanford.edu/archives/win2016/entries/simplicity/>.
makes quite a bit of Popper 1959:
Baker notes: “Philosophically influential early work in this direction [i.e.
probabilistic/statistical justifications of simplicity – section 5 in the
entry] was done … by Popper, both of whom tried to analyze simplicity in
probabilistic terms.”
“Popper [in “The Logic of Scientific Discovery”] points out that Jeffreys'
proposal, as it stands, contradicts the axioms of probability.”
“Every member of the set LIN, of linear equations (of the form “y = a + bx”) --
is also a member of PAR, the set of parabolic equations (of the form “y = a +
bx + cx²”) -- where the coefficient, c, is set to 0.”
“Hence:”
iv. Law, L, is a member of LIN.
entails
v. Law, L, is a member of PAR.
“Yet, Popper notes, Jeffreys’s approach assigns higher probability to (iv) than
to (v).”
“But it follows from the axioms of probability that when A entails B, the
probability of B is greater than or equal to the probability of A.”
“Popper argues, [contra] Jeffreys, that the set LIN of linear equations has
lower prior probability than the set PAR of parabolic equations.”
“Hence the set LIN of linear equations is—in Popper's sense [or usage of this
adjective – emphasis Speranza’s]—more “falsifiable,” [quotations Speranza’s]
and hence should be preferred as the default hypothesis.”
“One response to Popper's objection is to amend Jeffrey's proposal and restrict
members of the set PAR of parabolic equations to equations where c≠ 0.”
An ad hoc to an ad absurdum – sounds right to me and it should please Occam and
the scholastic in Helm!
I loved McEvoy’s example (iii), ‘The cat is on the mat’. Apparently Toulmin
used this because it is ‘reading material’ – i.e. a rhyming sentence,
‘cat’/‘mat’ – used in elementary books to teach how to read (and write). And
thus NOT to be taken too seriously. It is still one of my favourite utterances
to illustrate the use of the definite descriptor (‘the cat,’ ‘the mat’), the
subject-predicate format –, Grice’s Causal Theory of Perception – where Grice
would prefer, “The cat seems to be on the mat”, and Grice’s idea of a
propositional complex (not a proposition), where ‘the cat’ needs to be reduced
to the ‘sense-content’ associated with the phrase, as ‘to be on the mat’ would.
C. A. B. Peacocke, once professor of metaphysical philosophy at Oxford, would
consider ‘The cat is on the mat,’ _pace_ Toulmin, as one of the most complex
utterances ever heard. I once tested its literalness and relied on the rather
poor and sexist Longman Dictionary of English. It gave for ‘cat’ a figurative
usage (“a nasty person”) as it did to “being on the mat” (fig. “being punished)
– which turns the propositional complex into something, to echo Alice
Hargreaves, ‘complexer and complexer…’ Note that for Grice propositional
complexes are _analysable_ (or as Popper would prefer, dialysable). Grice only
coined ‘propositional complex’ to challenge R. Grandy and R. Warner (in PGRICE,
Philosophical Grounds of Rationality) that Grice seems to commit himself to the
idea of a proposition (“Propositional complex,” rather being his terse answer –
vide: “Prejudices and Predilections, which become the life and opinions of Paul
Grice,” by Paul Grice.
Cheers,
Speranza