0

I have two fallacious arguments written propositionally:

If P, then Q If P, then R Therefore: If Q, then R

And

If P, then Q If R, then Q Therefore: If P, then R

However, if these particular propositions were interpreted as being connected not by a conditional sign but by an "=" (identity) sign, wouldn't we have examples of the transitive property (i.e. P=Q, P=R, so Q=R using the rule of identity elimination in Fitch calculus)? However, neither conditional/biconditional introduction/elimination in Fitch would be able to prove this -- hence it being a fallacy. The Fitch rules to which I'm referring are these:

https://www.ocf.berkeley.edu/~brianwc/courses/logic/rulesummary.html

Is what I'm implying by using "=" that P, Q, R are the exact same proposition?

David Marlowe
  • 209

1 Answers1

0

If the statements did use an equality to connect the propositions, then the propositions would be equal.

That's obvious, but counterfactual.   The statements do not do so, so the propositions need not be equal.

While a counterexample will falsify an universal statement, a single example will not prove one.

tl/dr Look for a counterexample, rather than an example.

Graham Kemp
  • 129,094