In a message dated 2/14/2016 5:04:28 A.M. Eastern Standard Time,
"What Popper claims is that the logic needed to evaluate the 'system of
scientific statements' is purely deductive (where evaluation is based in part
on understanding the deductive relations between statements). What Popper
nowhere suggests is that this 'system of scientific statements' is 'arrived
at' purely by deduction - far from it: no empirical statement can arrived
at purely by logical deduction. Thus the "process" by which we arrive at a
(provisional) 'system of scientific statements' is NOT a "PURELY deductive
process". As someone with some understanding of Popper's views, I am also
familiar with the frequent attempts by others to outline Popper's views and
with their frequent failure to get even the basics right."
Well, the same happened with Grice. Not all recognise he is a genius (I
think 95%, inductively, do)
"This frequent failure is hard to fully explain. Consider the above
example: it is fairly orthodox philosophically (and logically) to accept that
empirical statements cannot ever be 'arrived at' purely by deduction - for how
can we ever deduce, from deductive logic alone, anything that can only be
true given contingent (empirical/testable) facts? Therefore, it would seem
absurd to attribute to a first-rate logician and philosopher like Popper, a
position that denies this and which asserts, on the contrary, that "Science
in Popper's view is a PURELY deductive process". Yet this absurdity is
exactly what JLS attributes to Popper as "Popper's views". It is not even
close - it's a travesty of "Popper's views"."
I like the keyword 'travesty'. Obviously from the Italian, "travestire",
"to disguise," from Latin trans- "over" + vestire "to clothe". The Italians
(Venetians?) also gave Western civilisation the idea of a "transvestite"
(Venetians), defined, during the carnival season, as the "person with a
strong desire to dress in clothing of the opposite sex". Venetians claim the
custom comes from Ancient Rome -- they always adjudicate most customs to
Romans -- and Nero in particular -- who would hardly use his 'toga virilis'.
McEvoy: "No wonder people who are taken in by this kind of travesty also do
not take Popper's position as passing muster or as worthy of serious and
prolonged consideration. But some of us know different, and suggest Popper's
views (old and unfashionable as they might appear, like Bach's music or
Hume's attack on induction as a form of "logic") are worthy of such
One good critic seems to be Ivor Grattan-Guinness, in his "Karl Popper and
the 'The Problem of Induction': A Fresh Look at the Logic of Testing
Scientific Theories", in Erkenntnis, vol. 60.
Ivor Owen Grattan-Guinness is a historian of logic. Since Bartleby defines
Grice as a "British logician", we could, a fortiori, say that
Grattan-Guinness is a philosopher.
Grattan-Guinness was born in Bakewell, England.
(The town is famed for its cooks).
Grattan-Guinness's father was a mathematics teacher and educational
Grattan-Guinness gained his bachelor degree as a Mathematics Scholar at
Wadham and, more importantly from a Popperian point of view, an MSc (Econ)
in Mathematical Logic and the Philosophy of Science at the London School of
Grattan-Guinness gained both the doctorate (PhD) higher doctorate (D.Sc.)
in the History of Science at the University of London.
Grattan-Guinness is Emeritus Professor of the History of Logic at
Middlesex [not to be confused with Middle-Sex) University, and a Visiting
Associate at the London School of Economics.
Grattan-Guinness was awarded the Kenneth O. May Medal for services to the
History of Mathematics by the International Commission on the History of
Mathematics (ICHM) at Budapest, on the occasion of the 23rd International
Congress for the History of Science.
He was elected an Honorary Member of The Bertrand Russell Society, a club
to revere the well-known philosopher born in England or Wales.
Grattan-Guinness spent much of his career at Middlesex (not to be confused
He is a Fellow at the Institute for Advanced Study in Princeton, New
Jersey, USA, and a member of the International Academy of the History of
Grattan-Guinness is the editor of the history of science journal "Annals
In also founded the journal "History and Philosophy of Logic," which he
He was an associate editor of Historia Mathematica from its inception.
He acted as advisory editor to the editions of the writings of C.S. Peirce
and Bertrand Russell, and to several other journals and book series.
He is a member of the Executive Committee of the International Commission
on the History of Mathematics
Grattan-Guinness gave over 570 invited lectures to organisations and
societies, or to conferences and congresses -- some about Poppers, some not
("surely you can implicate that" -- Geary) in over 20 countries around the
These lectures include tours undertaken in Australia, New Zealand, Italy,
South Africa and Portugal.
Grattan-Guinness is the President of the British Society for the History
He was elected an effective member of the Académie Internationale
d'Histoire des Sciences.
He was the Associate Editor for mathematicians and statisticians for the
Oxford Dictionary of National Biography.
Grattan-Guinness took an interest in the phenomenon of coincidence and has
written on it for The Society For Psychical Research.
Grattan-Guinness claimes to have a recurrent affinity with one particular
number, namely the square of 15 (225), even recounting one occasion when a
car was in front of him with the number plate IGG225, i.e. his very
initials and that number.
The work of Grattan-Guinness touches on all historical periods, but he
specialised in the development of the calculus and mathematical analysis, and
their applications to mechanics and mathematical physics, and in the rise of
set theory and mathematical logic.
He also is fascinated by Popper's attacks on inductivism.
Grattan-Guiness is especially interested in characterising how past
thinkers, far removed from us in time, view their findings differently from the
way we see them now (for example, Euclid).
Like Geary, Grattan-Guiness has emphasised the importance of "ignorance"
as an epistemological notion in this task (vide Socrates).
Grattan-Guiness did extensive research with original sources both published
and unpublished, thanks to his reading and spoken knowledge of the main
languages of Europe.
He is the author of "The Development of the Foundations of Mathematical
Analysis from Euler to Riemann". MIT Press; 'Joseph Fourier, 1768–1830' (In
collaboration with J.R. Ravetz). MIT Press, "Dear Russell—Dear Jourdain: a
Commentary on Russell's Logic, Based on His Correspondence with Philip
Jourdain", Duckworth; :From the Calculus to Set Theory, 1630–1910: An
Introductory History, Duckworth; Psychical Research: A Guide to Its History,
Principles & Practices - in celebration of 100 years of the Society for
Research, Aquarian Press; Convolutions in French Mathematics, 1800–1840' in
3 Vols. Birkhauser.
1997. The Rainbow of Mathematics: A History of the Mathematical Sciences.
Fontana; From the Calculus to Set Theory 1630–1910: An Introductory
History; The Search for Mathematical Roots, 1870–1940: Logics, Set Theories,
the Foundations of Mathematics from Cantor through Russell to Gödel.
Princeton University Press (For research on this book he held a Leverhulme
Fellowship from 1995 to 1997); Routes of Learning: Highways, Pathways, and
in the History of Mathematics. Johns Hopkins University Press. W.H. and
G.C. Young, The theory of sets of points, 2nd edition (ed., New York:
Chelsea). [Introduction and appendix.] E.L. Post, ‘The modern paradoxes’,
and philosophy of logic, 11; Philip E. B. Jourdain, Selected essays on the
history of set theory and logics (1906–1918) (Bologna: CLUEB), xlii + 352
pages. George Boole, Selected manuscripts on logic and its philosophy (ed.
with G. Bornet, Basel: Birkhäuser),
"The Search for Mathematical Roots 1870–1940" is a sweeping study of the
rise of mathematical logic during that critical period.
The central theme of the book is the rise of logicism, thanks to the
efforts of Frege, Bertrand Russell, and Alfred Whitehead, and its demise due to
Gödel and indifference.
Whole chapters are devoted to the emergence of algebraic logic in the 19th
century UK, Cantor and the emergence of set theory, the emergence of
mathematical logic in Germany told in a way that downplays Frege's importance,
and to Peano and his followers.
There follow four chapters devoted to the ideas of the young Bertrand
Russell, the writing of both The Principles of Mathematics and Principia
Mathematica, and to the mixed reception the ideas and methods encountered over
the period 1910–40.
The book touches on the rise of model theory as well as proof theory, and
on the emergence of American research on the foundation of mathematics,
especially in the hands of E. H. Moore and his students, of the postulate
theorists, and of Quine.
While Polish logic is often mentioned, it is not covered systematically.
Grattan-Guinness's essay is a contribution to the history of philosophy as
well as of mathematics.
He has also edited Companion Encyclopedia of the History and Philosophy of
the Mathematical Sciences, 2 vols. Johns Hopkins University Press,
Landmark Writings in Western Mathematics. Elsevier.
Among his many essays, including the crucial attack on Popper's simplistic
views on inductivism, include:
Christianity and Mathematics: Kinds of Link and the Rare Occurrences after
1750." Physis: Rivista Internazionale di Storia della Scienza XXXVII. Nuova
Serie. Fasc. 2.
"Manifestations of Mathematics in and around the Christianities: Some
Examples and Issues." Historia Scientiarum 11-1.
A Sideways Look at Hilbert's Twenty-Three Problems of 1900, Notices of the
American Mathematical Society 47:
"Foundations of Mathematics and Logicism," in Michel Weber and Will Desmond
(eds.), Handbook of Whiteheadian Process Thought, Frankfurt / Lancaster,
Ontos Verlag: 97-104.
Cf. Michel Weber, « Ivor Grattan-Guinness, "Algebras, Projective Geometry,
Mathematical Logic, and Constructing the World. Intersections in the
Philosophy of Mathematics of A.N. Whitehead", Historia Mathematica 29, N°
427-462 », Zentralblatt MATH, European Mathematical Society,
Fachinformationszentrum Karlsruhe & Springer-Verlag, 1046.00003.
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