Wittgenstein and no Private Language (from Andrew Pessin's book, Uncommon Sense, Rowman and Littlefield Publishers, Ltd, 2012)
Definition of Private Language:
One that contains words referring to "immediate private sensations" (or more generally, private mental states), and insofar as these sensations and states are "private" to the individual experiencing them, no one else could be said, strictly speaking, to understand those words.
To appreciate Wittgenstein's rejection of the possibility of such a language, then, we need some background on the nature of me gal states and sensations and of the ordinary language terms that concern them.
Two Extreme Views about Mental States and Mental Language
Cartesianism: an individual's mind is like a private inner space to which only that individual has access. If I believe I am in pain, then I am in pain. As for mental language, a word such as "pain" gets its meaning by referring to that private inner sensation. So described, Cartesianism is perhaps not far removed from common sense.
In contrast, according to behaviorism, the words we use for our mental states refer not to our private inner sensation but instead refer, indirectly, to our publicly observable behaviors. To say that Fred is in "pain" is to refer not to what is occurring privately inside him but indirectly to the observable fact, say, that he has just stepped on a nail and is screaming.
Wittgenstein Rejects Both Extremes
In ordinary circumstance, there's no problem for us to understand and know others when they say they are in pain. If Cartesianism suggests otherwise, so much the worse for Cartesianism. More important, if Cartesianism were right, then we could never learn to understand and speak mental language.
While behaviorism may avoid these problems---if mental language refers to observable behaviors---it suffers from others.
(i) It seems that we know clearly what we mean when we say Fred is in pain even when we cannot state explicitly all the possible behaviors that would be deemed "painful behaving." This suggests that "Fred is in pain" means more than merely that Fred is exhibiting some such behaviors
(Ii) While Cartesianism wrongly suggested that knowledge of other people's mental states should be impossible, behaviorism seems wrongly to go the opposite extreme: if your behaviors are as accessible to anyone else as to you, there should be no difference between your access to your mental states and that enjoyed by others. Yet, sure there is. Wittgenstein states that, " other people very often know when I am in pain---, Yes, but all the same not with the certainty with which I know myself (#246 Philosophical Investigations).
So neither Cartesianism nor behaviorism gives an adequate amount of mental states and mental language. It's in the quest for some alternative view, that Wittgenstein enters into the private language argument.
The First Premise: Words, Meanings, and Rules
As noted earlier, it's not possible to "point out" one's inner mental states to someone else nor to "point" at someone else's. But that raises the question of whether we can "point out" our own inner states to ourselves, and so develop a private language.
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