wheresrhys

Further discussion on the logic functions with my good friend Matt, specifically regarding what they could mean, has landed on the idea that a value of, say, 2 or 3 for the truth of a statement X could equate to “X is sooooo true”.

Bearing this in mind, Matt wasn’t happy with the shape of the graph of =>, and further thought has led to the following necessary conditions for a function =>(x,y) (I’ll call it f from now on for ease of typing) which works well with the notion that something can be soooo true:

• f(x,1) –> 0.5 as x –> infinityx (so if something very true implies something else is true to a normal level, this means the implication is less a preserver of truth: more a diluter (though I set the asymptote as 0.5 as we thought it shouldn’t get closer to falsity than to truth)
• f(x,0) < 0 for all x > 1 (if x gets more true but y is still not true, then teh implication is, again, less of a truth preserver, though this is debatable. Maybe eqality with zero would be more appropriate.)
• f(1,y) –> infinity as y –> infinty (similar to the case where x varies and y = 1,  if 1 is immensely true despite x only being a little bit true then the implication is very strongly true)
• f(0,y) = 1/y for all y > 1 (the thinking here being that if y contiinues to get more and more true, despite no change in x, then the link between y and x should accordingly be weakened)