Working down my bucket list, I find myself at pages 351-352 of the Fawcett Gold Medal paperback edition of RAH's "The Number of the Beast" (heretofore "TNOTB"), in which Deety and the Reverend Doctor Charles Dodgson (aka "Lewis Carroll," the author under that name of "Alice in Wonderland" and under his own of "Symbolic Logic") engage in a six-statement game of sorites.
I've always been troubled that the six statements Deety comes up with fail to satisfy the definition RAH gives (page 351 of TNOTB: "statements incomplete in themselves but capable of intended to arrive at only one possible conclusion.").
Deety's six statements (the bottom half of page 352, TNOTB):
"1) Everything, not absolutely ugly, may be kept in a drawing room;
2) Nothing, that is encrusted with salt, is ever quite dry;
3) Nothing should be kept in a drawing room, unless it is free from damp;
4) Time-traveling machines are always kept near the sea;
5) Nothing, that is what you expect it to be, can be absolutely ugly;
6) Whatever is kept near the sea is encrusted by salt."
followed by (from Dodgson/Carroll): '"The conclusion is true?" he asked.
(Deety:) ' "Yes."
For the first time he stared openly at Gay Deceiver.
"That, then - I infer - is a 'time-travelling machine?' "
Yes.. although it does other things as well."
Ok, Members of the Massed Minds, I drew it out in Venn diagrams (which, from my travails in sixth grade, has been how I sort out statements in sequential logic unless coding in a programming language).
By statement 1,The set "Everything, not absolutely ugly" contains those things that may be kept "in a drawing room."
("may" is a permissive operator that does not confine "Everything, not absolutely ugly" to the inside of a drawing room);
Statements 2, 3, 4 annd 6 establish that Time-traveling machines are ALWAYS kept near the sea, are thus encrusted by salt, are never quite dry, and should, therefore, never be kept in a drawing room (by order of inclusion in successively nested logical sets).
Statement 5 is interesting. A new set, "things that are what you expect them to be," is introduced by Deety and placed inside the set of "Everything, not absolutely ugly."
But Deety uses the operators "may" and "should" to define the set of what is placed in a drawing room. You MAY keep "Everything, not absolutely ugly" in a drawing room but are not compelled to do so - the set "Everything, not absolutely ugly" includes the inside of a drawing room, not vice versa.
A little more controversial is the proposition "Nothing should be kept in a drawing room, unless it is free from damp" but by Victorian English conventions, I think we're intended to accept "should" as an absolute condition excluding damp items (like "time-traveling machines") from "in a drawing room."
My question - does the text actually lead Charles Dodgson/"Lewis Carroll" from those six statements to the true conclusion that Gay Deceiver is a time-traveling machine?
I don't think so, either from logic or an appreciation of the geography of south-central England. The rest of page 352 establishes that Dodgson and his three nieces are a day's walk from Christ Church College, Oxford, Oxfordshire, England. Having walked through Oxford University and the surrounding streets of Oxford with my wife and driven the roads of England between Oxford and the English seashore several counties away, I can testify Gay Deceiver was not "near the sea," either by road miles, as the crow flies, or in the frame of reference of someone who had to wake two young girls up and herd them and their sister Alice back home by foot.
Since (as Dodgson admits at the end of page 352) he had no logical grounds for expecting Gay Deceiver to be anything in particular, Statement 5 fails logically in any case.
But I'm open to any logical arguments I may have overlooked that Deety's statements don't lead to only one possible outcome, that being that Gay Deceiver is "a time-traveling machine." Honestly, the only outcome one can arrive at from rigorous logical analysis of those six statements is a two-fold one:
(a) Time-traveling machines should not be kept in a drawing room;
(b) Things that are what you expect them to be may be kept in a drawing room.
Nothing in Deety's six statements seems to me to connect the two folds of the outcome as I've stated it. I hope someone can show me where I went wrong on that analysis.
Vance P. Frickey
"I aim to misbehave." Captain Malcolm Reynolds, "Serenity"