Ancien Membre de la Société des Bibliophiles.
Béthune, July 31. 1850.
P.S.--The Query (Vol. i., p. 185.) concerning the name of the Alost,
Louvain, and Antwerp printer, _Martens_ or _Mertens_, is settled in the
note, p. 68., of _Recherches sur la Vie et les Editions de Thierry
Martens (Martinus, Martens)_, par J. De Gand, 8vo. Alost, 1845. I am
ready to send a copy of the note if it is required.
[We have also received a reply to MR. CORNEY'S Query from MR. ASHER of
Berlin, who refers for particulars of this interesting collection to
Tieck's Preface to his _Alt-Deutsche Theater_. We propose shortly
returning to the curious fact of English comedians performing in Germany
at the close of the sixteenth and commencement of the seventeenth
centuries: a subject which has several times been discussed and
illustrated in the columns of our valuable contemporary _The Athenæum_.]
* * * * *
ACHILLES AND THE TORTOISE.
(Vol. ii., p. 154.)
This paradox, whilst one of the oldest on record (being attributed by
Aristotle to Zeus Eleates, B.C. 500), is one of the most perplexing,
upon first presentation to the mind, that can be selected {186} from the
most ample list. Its professed object was to disprove the phenomenon of
motion; but its real one, to embarrass an opponent. It has always
attracted the attention of logicians; and even to them it has often
proved embarrassing enough. The difficulty does not lie in proving that
the conclusion is absurd, but in _showing where the fallacy lies_. From
not knowing the precise kind of information required by [Greek:
Idiotaes], I am unwilling to trespass on your valuable space by any
irrelevant discussion, and confine myself to copying a very judicious
note from Dr. Whateley's _Logic_, 9th edit. p. 373.
"This is one of the sophistical puzzles noticed by Aldrich, but
he is not happy in his attempt at a solution. He proposes to
remove the difficulty by demonstrating that in a certain given
time, Achilles _would_ overtake the tortoise; as if any one had
ever doubted _that_. The very problem proposed, is to surmount
the difficulty of a seeming demonstration of a thing palpably
impossible; to show that _it is_ palpably impossible, is no
solution of the problem.
"I have heard the present example adduced as a proof that the
pretensions of logic are futile, since (it was said) the most
perfect logical demonstration may lead from true premises to an
absurd conclusion. The reverse is the truth; the example before
us furnishes a confirmation of the utility of an acquaintance
with the syllogistic form, _in which form the pretended
demonstration in question cannot be exhibited_. An attempt to do
so will evince the utter want of connection between the premises
and the conclusion."
What the Archbishop says is true, and it disposes of the question as one
of "Formal Logic:" but yet the form of the sophism is so plausible, that
it imposes with equal force on the "common sense" of all those who
repose their conclusions upon the operations of that faculty. With them
a different procedure is necessary; and I suspect that if any one of the
most obstinate advocates of the sufficiency of common sense for the
"balancing of evidence" were to attempt the explanation of a hundred
fallacies that could be presented to him, he would be compelled to admit
that a more powerful and a more accurate machine would be of advantage
to him in accomplishing his task. This machine the syllogism supplies.
The discussion of Gregory St. Vincent will be found at pages 101-3. of
his _Opus Geometricum_, Antw., 1647 fol. The principle is the same as
that which Aldrich afterwards gave, as above referred to by Dr.
Whateley. I can only speak from memory of the discussion of Leibnitz,
not having his works at hand; but I am clear in this, that his principle
again is the same. [Greek: Idiotaes] is in error, however, in calling
St. Vincent's "a geometrical treatment" of it. He indeed uses lines to
represent the spaces passed over; and their discussion occurs in a
chapter on what is universally (but very absurdly) called "geometrical
proportion." It is yet no more _geometrical_ than our school-day problem
of the basket and the hundred eggs in Francis Walkinghame. Mere names do
not bestow character, however much _philosophers as well as legislators_
may think so. All attempts of the kind have been, and must be, purely
numerical.