By PK | 02/02/2023

The Swiss cheese paradox is as follows: 

„Swiss cheese has lots of holes. The more holes you have, the less cheese you have. And the more cheese you have, the more holes you have. Thus, the more cheese you have, the less cheese you have. Do you agree?“

The cheese paradox arises from the fact that the term more is used with two different meanings. First, more refers to the volume of the whole piece of cheese with holes, and then more refers to the relative volume of the cheese to the holes.

ChatGTP's answer was perplexing. It was correct though and it didn't fall for the paradox. It also explained very well how the cheese is prepared (see picture below). But it had not understood the problem: 

„No, I do not agree with the statement you have made about Swiss cheese,“ he replies convinced of the correctness of his answer. And then he solves the paradox: „The presence of these holes does not necessarily mean that there is less cheese. (…) Regardless of the size of the holes, the amount of cheese present in a piece of Swiss cheese is determined by its weight, not by the number of holes it contains.“ 

This is true, but he does not mention the fact that a piece of cheese that has more holes must be larger.    

„But you do agree that a piece of Swiss cheese with a lot of holes, assuming the size of the holes would be equal for all Swiss cheese, is larger than a piece of cheese with fewer holes?“

„No, I do not agree with the statement you have made about Swiss cheese.“

ChatGTP then refers in its answer only to the volume and weight of the cheese, which of course remains the same. But it can not imagine the piece of cheese, which is larger with more holes.

The size of a piece of cheese is determined by its weight and volume, not by the number of holes it contains.“

Of course, this is not entirely true and I point this out to ChatGTP:

„But the volume of a piece of Swiss cheese depends on the number of holes it contains. A cheese with more holes has more volume than a cheese with fewer holes if both have the same weight.“

 ChatGTP: „ I apologize for the misunderstanding. You are correct that the volume of a piece of Swiss cheese can be affected by the number of holes it contains. If two pieces of Swiss cheese have the same weight but one has more holes than the other, the piece with more holes will have a larger volume due to the presence of the additional air pockets.“

ChatGTP has understood it now. 

There is some doubt, however, over whether he has really recognized the problem in the last sentence:   

„It is also worth noting that the size and number of holes in Swiss cheese can vary, so it is not necessarily the case that all pieces of Swiss cheese with a lot of holes will have a larger volume than those with fewer holes.„

ChatGTP's answers are not wrong, but they are not based on an approach that any human would take, which is to imagine the piece of cheese pictorially. Thus a piece of cheese with many holes is bigger than a piece of cheese with few, small holes. For ChatGTP, a piece of cheese is an abstract object with properties of volume and weight. Then, of course, a piece of cheese does not get bigger by having more holes, since the volume and weight of the actual cheese remain the same. 

Swiss Cheese Paradox

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