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By Martin Gardner

Martin Gardner is likely to be the wittiest, so much devastating unmasker of medical fraud and highbrow chicanery of our time. right here he muses on subject matters as various as numerology, New Age anthropology, and the past due Senator Claiborne Pell's obsession with UFOs, as he mines Americans' possible inexhaustible urge for food for undesirable technology. Gardner's humorous, brilliantly unsettling exposés of reflexology and urine treatment may be required studying for someone attracted to "alternative" drugs. In an international more and more tilted towards superstition, Did Adam and Eve Have Navels? will provide these folks who prize common sense and customary feel great solace and proposal. "Gardner is a countrywide treasure...I want [this] can be made obligatory interpreting in each excessive school—and in Congress."—Arthur C. Clarke "Nobody alive has performed greater than Gardner to unfold the knowledge and appreciation of arithmetic, and to dispel superstition."— The New Criterion, John Derbyshire

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10. II. 3rpVC(Tl \- C VC(T1 \- C == rp( C» == rp(C» Tl C T2 and Tl =f T2 VC(T2 \- C == rp(C» 3C(T2 \- C and T)CIT) T2 \- C T1lfC T2 \- rp( C) T \- rp(C) T s:: Tl Tl \- rp(C) Tl \- C assumption 3E ; 1 condition 2,3 3 5 5 4,6 T2 is a conservative extension of T; 8 condition 9,10 2,11 12. Contradiction. 13. Consequently, Tl is not an inessential extension of T. Now we shall use this lemma as a proof that HlffC is not an inessential extension of He. Let HlffC + be an extension of HlffC at the expense of an addition to the axiom schema 44 V.

Hintikka, I. Niiniluoto, and E. ), Essays on Mathematical and Philosophical Logic, 49-94. All Rights Reserved. Copyright © 1978 by D. Reidel Publishing Company, Dordrecht, Holland. •. , l k - 1 IS a numerical term (formula, function term). ) (iii) When X is a function term, and t a numerical term, then {x}(t) is a numerical term. (iv) If A and B are formulas, then so are -,A, (A V B), (A 1\ B), (A _ B), and (A ~ B). 3. l' 0 is freely generated from a set of 'initial constants ' (enumerated below) by the partially defined operations (i) - (vi) to be described.

Thus, instead of description fffxA(x, Yl> ... , Yn) it is possible to use a constant with indexes ayt , • • • , Yn' In this case different letters correspond to different descriptions. This method is developed in the book by Slupecki and Borkowski. This is another method of fixation of a description. Thus the system HfffC is equivalent to the system of natural deduction with the direct rule of elimination of the existential quantifier. Hence the system of natural deduction with the direct rule of elimination of the existential quantifier is not equivalent to the standard calculus of predicates, as is often stated.

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