= ≠ ⇒
If you say “Microsoft Windows = bad” you are almost certainly making a false claim within your own beliefs. Not because Windows is not bad necessarily and not because I might think it is good, but because Windows = bad is likely to give rise to an absurdity within your own beliefs should I interrogate you on the matter. There is a difference. Consider also “Hitler = bad”. If you think that “Windows = bad” and “Hitler = bad” then you also think “Windows = Hitler”. I will expect you don’t believe “Windows = Hitler”.
What you likely intend instead is “Windows ⇒ bad”. You could read this as “Windows implies bad”. Now you are free to believe the following three statements without giving rise to an inconsistency in your belief:
- Windows ⇒ bad
- Hitler ⇒ bad
- Windows ≠ Hitler
Here is the truth table for implication:
P Q P⇒Q
0 0 1
0 1 1
1 0 0
1 1 1
Notice how ⇒ does not commute? Specifically, if you swap the propositions around you might get a different result. Bad ⇒ Windows is not the same as Windows ⇒ Bad — of course. This cannot be said for =. Bad = Windows is the same as Windows = bad.
You might wonder why I care so much. After all, if you said “Windows = bad” I’d know what you meant. But did you know what you meant and is this understanding universal each time you relax your discourse like this?
I have often observed a confusion between equivalence (also often called bi-implication) and implication in general discussion. Indeed, I hypothesise that this tendency to subvert a proposition in this manner is responsible for many failings in humanity’s general faculty of reason. I think we as a species would be better for it if we repair this failure of intellectual discipline (for what gain anyway?).
Therefore, I think that not only is this trivial correction important, but very much so. Thanks for listening.
December 13th, 2008 at 10:06 pm
“badness” is a property. it belongs to an object. it’s not on the same level as objects, in that regard.
you can’t do boolean logic with an object and a property, only with objects and objects, or properties and properties.
implication is just as wrong as equality.
December 14th, 2008 at 6:01 am
Wouldn’t it make even more sense to say:
Windows ∈ Bad Things
?
December 14th, 2008 at 7:26 pm
Or bad(Windows). In order for Windows ⇒ bad to make sense, Windows should be a proposition.
December 15th, 2008 at 6:38 pm
“Bad” is a subjective property assigned to an entity by a person, so I would model it as a mapping “(Person, Entity) => SubjectiveQuality”.
January 13th, 2009 at 8:15 am
It’s all about context.
Who told you that the rules of logic apply to the postulation “windows = bad”?
Nobody. You implied that from your context (you’re a programmer, …).
Other people (with other contexts) look at the postulation in a different way. They transform the ‘=’ to something that has more meaning to them (i.e. the word ‘is’). So the postulation becomes “windows is bad”. Yeah!
“Interpreting content” is not a function that just takes the input as a parameter and creates an output but it has an additional parameter named “context”.
“It’s in the eye of the beholder.”
It’s fun to think in the meta-level and put logic into it.
…and thereby being able to promote some out-of-the-box thinking.
January 14th, 2009 at 3:30 am
Yes, I don’t think you can use “implies” because none of the items you’re connecting are propositions. A proposition implies another. You could use, as pointed above, some set theory and logic:
((Windows belongs to Bad Things) and (Hitler belongs to Bad things)) does not imply (Windows is Hitler)
January 17th, 2009 at 1:21 am
This comment has been removed by the author since it not useful.