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I read this in Lewis Carroll once.

Basically the Raw Meat Paradox runs as follows:

  1. The meat that I eat at the table is the meat that I buy in the market.
  2. The meat that I buy in the market is raw meat.
  3. Therefore, the meat that I eat at the table is raw meat.

It's a "paradox" because p -> q , q -> r , p -> r is supposed to be a valid logical process, but the meat on your table will probably not be raw meat.

The paradox can be solved by making the logical system more complicated: incorporate an element of time and say that there is not enough information to deduce whether the meat is still raw by the time it reaches your plate.

(See also the Accident fallacy.)

Muke misstates the essence of the paradox. He says the three statements are of the form p ⇒ q, q ⇒ r, therefore p ⇒ r. In fact, there is no 'implies' in any of the three statements. They are more like "p is q", "q is r", "therefore, p is r". The problem lies not so much in the logic, as in the word 'is'. There are two interpretations of the word 'is', as it is used in the first statement: there's a purely logical interpretation, which is better expressed as 'is identical to', and there's the English-language interpretation, which I will write as 'is the same as', so the two can be distinguished. One thing can be said 'to be (the same as)' another thing if they are similar enough, or if they are related closely enough. If I have a wooden toy, painted red, then I paint it blue, I can say it 'is the same' toy as before, but I cannot say it 'is identical to' the way it was before. (Things are muddied further in that the 'is' of the second and third statements stand for 'has the property of being …'. This further distracts from the fact that the 'is' of the first statement can be interpreted either strictly or loosely.)

Reading the first sentence, there are two conflicting expectations. One expects the meat being eaten at the table to be cooked, (nearly) every time. One expects the word 'is' to mean 'is identical to', some of the time. For the sentence to make sense, it is easier to substitute a different (but still acceptable, and expectable) meaning for the word 'is' than it is to ignore the expectation on the state of the meat on the table. The sentence makes good sense with a different 'is' expectation, because the market meat gradually transforms into the table meat in a recognisable fashion. The sentence also makes some sense with a rather twisted table-meat expectation, but that expectation is more difficult to bend because one sees the word 'is' used in a loose way far more often than one sees raw meat eaten at a table. The assumption that only cooked meat is on the table is stronger than the assumption that the word 'is' means 'is identical to', and the stronger assumption bends the 'is' away from its pure logical meaning in order that the sentence makes sense. And once the meaning deviates from logical meaning, it is no longer appropriate to apply logic.

If one were to use logical terms to state the paradox, the flaw becomes clear:
1. The meat that I eat at the table is identical to the meat that I buy at the market.
2. The meat that I buy at the market has the property of being raw.
3. Therefore, the meat that I eat at the table has the property of being raw.
This no longer reads as a paradox. The 'is' of the first trio of statements allows for enough ambiguity that the assumption that the meat will be cooked when it is eaten is the overriding consideration in interpreting the sentence. The 'is identical to' of the second trio of statements does not allow for that ambiguity; the meat on the table not only 'is' the meat from the market in the previous sense, but it also has all the exact same properties as the meat from the market. Since this 'is' cannot be bent, the assumption of the meat on the table being cooked is the part of the paradox that must bend instead.

If one were to use logical terms to try and capture the paradox the other way, you get:
1. The meat that I eat at the table is the same as the meat that I buy at the market.
2. The meat that I buy at the market has the property of being raw.
3. Therefore, the meat that I eat at the table has the property of being raw.
Keeping in mind that 'is the same as' means the two things are closely related, but do not necessarily have all the same properties, the third statement does not necessarily follow. The property of meat being raw may be one of those things which is not covered by 'being the same as', like the property of a toy being painted a certain colour.

Another variation on this paradox is using the word 'is' to mean 'is an element of', or 'is a subset of' (in the set theory sense). X is an element/subset of Z. Y is an element/subset of Z. Therefore, X is Y (or, X is an element of Y, or, X is a subset of Y). Another approach is to use the indefinite article in a misleading form. X is an element of Y. An element of Y has the property of being Z. Therefore, X has the property of being Z. (This is good logic only if the second statement is replaced with "Every element of Y has the property of being Z", or perhaps if the first statement is replaced with "X is the only element of Y".)

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