When it comes to the logical analysis of everyday language statements, the word “but” is treated as equivalent to the word “and”. In practical terms, this means that where:
P = My mother is Italian.
Q = My father is German.
The following two statements:
“My mother is Italian and my father is German.”
“My mother is Italian but my father is German.”
Are analysed in exactly the same way, i.e. as:
(P & Q)
But how can this be? Don’t sentences that include the term “but” draw attention to a distinction (in the case of our example above, a distinction between one ethnicity/nationality and another) whereas sentences that include the term “and” do not draw attention to any such distinction?
The reason that logicians treat “but” as equivalent to “and” is that in logic we are interested in the truth-conditions of statements and the conditions under which “but” statements are true/false are exactly the same as those under which equivalent “and” statements are true. Consider our two examples again:
“My mother is Italian and my father is German.”
“My mother is Italian but my father is German.”
The first sentence is true if and only if my mother is actually Italian and my father is actually German. And the second second is true if and only if my mother is actually Italian and my father is actually German. This means that as far as logic is concerned, the two sentence mean exactly the same thing.
