... Then I need to construct a truth-table for the conditional corresponding to the argument before determining whether this argument is tautologically valid?
I'm not sure exactly what you mean when you say 'tautologically valid'. All valid arguments can be restated as tautologies - that is, necessarily true conditional statements in which the antecedent is the conjunction of the premises and the consequent is the conclusion. Such conditional is the corresponding material conditional
to which you refer. But if there is any distinction between 'tautologically valid' and just plain 'valid', I have no idea what it is. It seems to me that they are the same.
So let's say
A=In an hour, a man's heart throws out more blood than his own weight
B=Blood flows only outward from the heart
C=The heart creates more blood in an hour than the weight of a man
D=Blood circulates through the body and reenters the heart
I agree with your interpretation that the semantics of the sentence 'But this
is impossible' is such that 'this
' refers only to the consequent of the proceeding conditional. Namely, the intended meaning is to convey a claim that 'the heart creates more blood in an hour than the weight of a man'
is what is impossible, rather than the proceeding conditional in its entirety. It is a bit of a sticky wicket, and could be interpreted to mean the negation of the proceeding conditional in its entirety. Note that the choice of interpretation changes the truth values.
Given the above, I interpret the argument as follows:
P2: If (A & B) then C
P4: If A then D
C: ~B & D
P2: (A & B) -> C
P4 A -> D
C: ~B & D
The argument is valid. The corresponding conditional is:
[(A & ((A & B) -> C)) & (~C & (A -> D))] -> (~B & D)
So, that is the statement to use in order to create a truth table for the corresponding conditional.