A philosopher is defined as a blind man in an unlit cellar at midnight searching for a black cat that isn't there.
A theologian is identical in all respects save that he believes he has found the cat.
A lawyer, naturally, would smuggle the cat under his coat in order to brandish it theatrically when it best serves his purpose.
A scientist would accept the non-existence of the cat but be at pains to point out that it's non-existence could only ever be assumed; never proven.
A quantum physicist would say that the cat was both in the cellar and not in the cellar at the same time, and that it would remain both in and out of the cellar until someone spotted it.
An economist would hide the cat; bringing it out the following day, blaming the mouse on the interest rate hike; saying it was for the good of the group.
An engineer would briefly search for a cat and then employ his time more productively by constructing a superior cat replacement from the materials available in the cellar.
A soldier would shoot the cat to protect the liberty of the mouse, unless he was American in which case he would conduct a shock and awe campaign to win the heart and mind of the cat and (in the process) accidentally shoot the mouse.
A statistician finds the first creature with 4 +/- 0 legs and calls it a cat.
A logician proves that the cellar contains no cats. He also proves that the cat is white.
A psychologist psycho-analyses the cat's preference for dark cellars. Later, the cat sues him for implanting false memories about kittenhood abuse.
A debt collector seizes the cat, along with its kittens as interest.
A surrealist looks for the cat and finds an accordion.
A secret services operative disguises himself as another cat, infiltrates the cellar, gains the cat's trust and learns the whereabouts of other cats in return for a regular supply of sardines. After the assignment, he requires a flea-bath.
... A usenet top-poster would spend 3 days looking in the attic for the cat while everyone else was looking in the cellar.