@kennethamy,
kennethamy;132908 wrote:I don't know what you mean by a "categorical argument". An argument consists of at least two statements. One of which is the conclusion. The other of which is the premise. And the premise is supposed to support the conclusion. Nowhere does the definition say how many premises there must be. I think you are thinking of the argument called, the syllogism. Now, a syllogism is defined as an argument with two premises and a conclusion. But a syllogism is, of course, only one kind of argument. Of course, in every valid deductive argument, there is nothing in the conclusion that is not already in the premises.
By the way, the converse of All apples are fruit is, All fruit are apples. And, of course, those two statements are not equivalent. In fact, the first is true, but the second is false. You are talking about what are called "immediate inferences". And, immediate inferences are arguments with just one premise. There is no second premise to mediate between the premise and the conclusion. Syllogisms are called "mediate inferences" for the opposite reason. Obversion and contraposition are both immediate inferences.
Which is why I made the point that different forms of Logic have different rules. Aristotle developed categorical logic with the use of the syllogism. You can't just converse any statement you wish, immediate inferences only produce equivalences when done to certain types of statements. To get an equivalent statement, conversion must be done to a universal negative or a particular affirmative statement. Other types of immediate inferences also have similar rules, however, an obversion can be done on any type of statement.
What you presented :
1. No dogs are snakes. Therefore, 2. No snakes are dogs
is not an syllogism in categorical logic. It is an immediate inference of a statement.
The reason I am speaking in terms of syllogisms is because that was the initial type of Logic which you proposed earlier with the argument:
All Italians are Europeans.
All Romans are Europeans
Therefore, all Romans are Italians.
This argument is a syllogism, so it must adhere to the rules of categorical logic. It must have three terms, the middle term must be distributed at least once, and a term must be distributed in the premises if it is distributed in the conclusion.
If you wish to discuss a different form of Logic we could do that, but by presenting this argument in the form of a syllogism, I assumed that was the Logic in which you were referring to.