Why we can't show the following argument to be valid in SL:

Duff is taller than Ryckman.

Therefore, at least one thing is taller than Ryckman.

 

• From the perspective of SL, the argument has a sentence letter, say A, for a premise and another sentence letter, say B, for a conclusion.
• One can prove that there is no SD derivation from A to B--hence the argument will not be SD-valid--is not syntactically valid from SL's perspective.
• In addition, since the sentence letters of SL are truth-functionally independent of one another, there is no contradiction entailed by the assertion that there is a truth-value assignment on which A is true and on which B is false. From this it follows that the argument from A to B is not truth-functionally valid--is not semantically valid from the perspective of SL.
• Since these are the only kinds of validity captured by SL, it follows that, from SL's perspective, the argument is not valid.