Rather, let me reword that last part:
“If A then C” and “If B then C” are faulty premises (if the conditional is to be interpreted as the simple material conditional). “If necessarily A, then C” or “Conditionalizing on A, then C” are more accurate premises.
Another way to look at the flaw is that it’s not precisely correct to state the argument as
"If we lose the battle, then it’s better to have less men, " and
“If we win the battle, then it’s better to have less men”
More correctly, it’s:
“It’s better to lose the battle with few men than to lose the battle with many men,” and
“It’s better to win the battle with few men than to win the battle with many men.”
Which leaves room for the statement “It’s better to win the battle with many men than to lose the battle with few men,” which is useful to include if you care about winning and losing, and if you believe that the odds of winning with many men are significantly better than the odds of winning with few men.
You beat me to it.
Quoth Indistinguishable:
OK, I’ll accept that resolution. I’m still a bit curious if this particular flavor of slipperiness of terms has a name.
Quoth Manduck:
I figured that was taken for granted. It’s still an interesting argument, regardless of its motivation.
Yeah; if the Angel of the LORD had appeared and said “Hi, Harry; nice prayers last night. In answer to which God has authorized me to miraculously transport another 50,000 men from England–fully equipped, trained, and, y’know, not exhausted and hungry and suffering from dysentery–what say you?”, for all we know, Henry would have taken him up on it in a heartbeat. As it was, Westmoreland was basically just whinging at that point, and the speech is fundamentally an emotional appeal to a bunch of heavily outnumbered men (exhausted, hungry, and beset with disease) in the middle of a hostile country.
I think it’s something of a mistake to over-conflate “Henry V, historical King of England”, and “Henry V, fictional character based on the foregoing historical person”. The real Henry at the real Battle of Agincourt was no doubt a cold and calculating tactician, and perhaps due to considerations of terrain and strategy really couldn’t have made effective use of more reinforcements–but I doubt he ever really said anything so stirring as Shakespeare’s Henry. Shakespeare goes so far as to have his (fictional) Henry V claim that the battle was won “without stratagem/But in plain shock and even play of battle”, which bears very little resemblance to the real Battle of Agincourt. Shakespeare’s Henry V isn’t about logic or the actual tactics and strategy and shape of the battlefield at the Battle of Agincourt; it’s about a bunch of stouthearted Englishmen defeating a vast horde of haughty cheese-eating Frenchmen in a stand-up fight because the English have God on their sides and any good Englishman* is worth worth ten of those Frenchies any day.
*Or Welshman.
There are not two premisses A and B; there is only A: “We will win the battle.”
The reasoning is:
A -> C
!A -> C
Tf. C. QED.
And C becomes a tautology.
Did Henry know this?
Having a look at the rest of the speecch though, I think Mr. Excellent has the right of it; Henry’s interest is more in the honour to be gained than the practicalities of winning while outnumbered:
Something to consider when volunteering (or remaining a-bed in England): is the C-in-C a loon?
A and B (= !A) aren’t the premises; it’s the lines A -> C and !A -> C which are premises. (Erroneous ones, in this case; what we actually have is better understood as A -> C and !A -> C)
Eh, what’s in a name? But if you insist, it’s been called “‘the’ modal fallacy” (see the discussion on Aristotle’s sea battle here).
Must every thread turn into a referendum on Iraq?
Sailboat
