Misconstruing Negative Vs Positive Condition

Martin (1992: 195-6):

Contingent relations make a distinction between conjunctions incorporating negative polarity (unless and lest) and those which don't.  The relevant proportionalities and relevant paradigm are as follows:

UNLESS : IF…NOT ::

LEST : SO THAT…WILL + NOT 

unless Ben plays you'll lose :

if Ben doesn't play you'll lose :: 

Ben'll play lest you lose :

Ben will play so that you won't lose

But the opposition between "positive" and "negative" values has a different meaning in the context of conditional relations from that in purposives.  With conditionals, the opposition is between exclusion and inclusion (or non-exclusive) to be precise).  Unless means 'if and only if not';  if on the hand does not preclude the possibility of additional modalised Causes:

EXCLUSIVE

[4:60]  Unless you go that way ['as long as you don't]

            you'll be there by six.

            (It's the only way you can go wrong.) 

INCLUSIVE

[4:61]  If you go that way

            you'll be there by six.

            (But you could also go the back way.)

Blogger Comment:

In SFL theory, as in formal logic, the logical meaning of positive condition is if P then Q and the logical meaning of negative condition is simply if not P then Q — not "if and only if not":

• If Ben doesn't play, you'll lose. 
• If you don't go that way, you'll be there by six.

The opposition of 'exclusive vs non-exclusive' is irrelevant to the logical opposition of positive and negative condition.

See also if and only if.