Exercise problem involving validity of arguments

Question

I was recently working from a textbook, doing practice problems. Based on the text, an argument is considered valid "if there is no logically possible situation in which the premises are true and the conclusion is false," logically possible meaning a situation that entails no contradiction. I take this to mean that there is some imaginable situation, not necessarily an actual situation, just a coherent one, where the conclusion can be false at the same time all the premises are true. Using those definitions, why would the following argument be considered invalid? In what logically possible situation would the conclusion be false at the same time the premise is true?

Biden is heavier than Obama.
Fatima cannot lift Obama.
So there is no way she can lift Biden.

Answer 1

The argument, as written, allows for some additional factor besides weight. Maybe Fatima cannot lift Obama for some reason besides weight. Maybe that reason applies to Obama, but not to Biden. On those new assumptions, both original premises could be true and the conclusion false.

The argument needs a premise that defines the universe more precisely. "If Fatima cannot lift Object A, then she cannot lift anything heavier than A, regardless of any other quality the second Object might have."

Answer 2

Mark Andrews is in the right direction. I add some rudimentary idea from FOL(first order logic) model theory to make the answer more compelling. In a model theory, validity is defined as follows: all models that make the premises true make the conclusion true. So to show that the above argument is invalid, all you need to do is to come up with a model under which the premises are true, but the conclusion is false.

Biden is heavier than Obama.

Fatima cannot lift Obama.

So there is no way she can lift Biden.

A model provides an interpretation for every (non-logical) term in the language. The following are the non-logical terms that need interpretation:

Biden, Obama, Fatima, is heavier than, can lift.

If the interpretation corresponds to the ordinary usage of the words, then a model that satisfies the premises indeed does satisfy the conclusion.

Now, let Biden and Obama be interpreted in the following way (leaving the rest of the non-logical terms intact):

Under this interpretation, both of the premises are true: Biden (120 lb weight) is heavier than Obama (70 lb bed frame), and Fatima cannot lift Obama due to the shape of the bed frame. However, Fatima can lift Biden (the 120 lbs weight) .

Answer 3

Maybe it is easier for Fatima to lift heavier objects. The relation between Fatima's ability to lift an item and it's particular weight is contingent unless specified and can, therefore, vary between possible worlds. Then missing premise here is that 'If Fatima cannot lift an object, she also cannot lift an item heavier than it'. Throw that in there and you fix Fatima's 'liftability' relation between possible worlds.

Answer 4

There is no evidence showing that the reason Fatima cannot lift Obama is because Obama is heavy. Actually, there is no link between weight and the ability to be lifted.

To show that this is an invalid statement, let's replace the objects.

(P1) A fridge is heavier than a motorcycle. (P2) A carrier cannot lift a motorcycle. (C) A carrier cannot lift a fridge.

The conclusion is clearly false, as a carrier can list a fridge, while he cannot lift a motorcycle because a motorcycle is not an ergonomical object to be lifted by a man.

So, maybe Fatima can lift Biden because even though Biden is heavier than Obama, he might be more ergonomic than Obama.

So, in order to make this a valid argument, it should contain at least one more premise.

P3: Fatima cannot lift anything heavier than something she cannot lifts.