A relationship between alcoholism and dental pathology (particularly missing teeth), has been reported in studies of male, inpatient alcoholics. The present exploratory study was undertaken to assess how readily these findings can be generalized to an unselected sample of male and female dental patients. Data on drinking behavior, alcohol-related problems, and risk factors for alcoholism were obtained through an interview and questionnaire. A dental chart review provided measures of dental pathology. The results showed that measures of dental pathology (including tooth loss, carious teeth, and periodontal disease) correlated significantly with alcohol-related indicators. The associations were more evident for males than for females, which is consistent with some studies of alcohol-related medical consequences. The results suggest that further analytic studies of alcohol consumption and dental pathology are warranted. Because the relationship between tooth loss and harmful drinking was clearest among males with a history of conduct problems, subsequent research would benefit from a focus on this high-risk group.
A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The 'revenge' problem is easily defused. The solution to the semantical paradoxes offered here revives the mediaeval cassatio approach, one that largely disappeared due to its incomprehending rejection by influential contemporary writers such as William Shyreswood and Thomas Bradwardine. The diagnosis readily extends to the set-theoretic paradoxes. Variations on FibonacciThe Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…. has many beautiful and fascinating properties. It is an infinite series of numbers in which each term is the sum of its two immediate predecessors: Fib[i] = Fib[i-2] + Fib[i-1]. Yablo's Paradox, which is a hard, or 'strengthened' version of the Liar, consists of an infinite sequence of sentences, each saying of all its successors that they are not true (Yablo 1985;1993). I hope to show that there is an interesting connection between the series and the sequence. There is nothing paradoxical about the series, but the sequence is paradoxical, and I want to claim that, once the connection is made, the paradox is swiftly solved. The solution, of course, carries over to simpler and standard versions of the Liar.Each member of the Fibonacci series 'remembers', and sums, its immediate two predecessors. Series constructed on the same general principle, but with better memories, are invariably less interesting than Fibonacci's original. In the 'total recall' series, where each member sums all of its predecessors, the first two members are identical and any member after that is simply twice its predecessor. One can also have 'soothsayer' or 'forward-looking' variants of Fibonacci. For example, the series in which each member is the sum of its immediate two successors is just the Fibonacci series in reverse.One way to manufacture an extremely boring variant of Fibonacci is to go Boolean, using a binary arithmetic in which addition ('+') is defined by the following matrix: is an infinite repetition of a three-digit pattern. From arithmetic to logic The Yablo sequenceFor a more far-reaching conclusion, we now turn to Yablo's sequence of sentences. It is a total foresight sequence, since each of the constituent sentences is about all of the subsequent ones:Y 1 : For all integers n>1, Y n is not true. is a class of functions {f: N N | f(n) = f(n-2) + f(n-1)}, no particular series but only the characterization of a generic series. Without the specification of values for at least two members, there is no grounding; no particular series is specified. Now, the Yablo sequence is a counterpart of the total foresight variant of the reverse Fibonacci -any member of the seq...
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