Paradox of Emmenthaler cheese
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This paradox is wrongfully known under the appelation paradox of Gruyere, which ruffled suceptibility of the amateurs of emmental (the Gruyere does not have holes with the difference, inter alia, of the emmental). Also we will remain neutral while speaking about cheese (with holes). It is stated then:
* The more there is cheese, the more there are holes;
* however the more there are holes, the less there is cheese;
* thus more there is cheese, less there is cheese.
It is most famous of the paradoxes builds according to a mode of syllogism called Barbara (or syllogism in A-A-A). It highlights that the application without understanding of the syllogism causes aberration.
Actually, it takes place here a subtle semantic slip between the average terms of the two premises; what prohibits the conclusion. This slip is due to a contextual difference. indeed, for each premise, there is an implied context which makes possible the acceptance of the premise as a truth. However these implicit contexts are opposed and invalidated the syllogism.
Concretely, one can schematize the thing by considering the volume of cheese (packed, i.e., holes included/understood) and the density of the cheese (the matter ratio/volume).
Terms
Major premise major means context
more there is cheese more there are holes increase in volume - constant density
however?
Minor premise means minor context
more there are holes less there is cheese constant volume - reduction in the density
thus?
Conclusion minor major confusion of the contexts
more there is cheese less there is cheese
But, there-A-you it not average to conclude?
Yes; if one adopts the point of view of mathematical logic. It is then necessary to consider the context as an axiom. The conclusion is then a theorem relating to axiomatic necessarily containing the conjunction of the contexts. Thus, it is deduced here that, when volume and density of cheese are constant, one has well ?more there is cheese, less there is cheese?. What can be reduced to an idiotic truism: ?as much there is cheese, as much there is cheese?.
See too
?Gruyere and Emmenthaler cheese? in the collection of howlers
Recovered of ?
http://fr.wikipedia.org/wiki/Paradoxe_de_l%27emmenthal?
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