Grammar, empirical fact and value aren't three independent things.
— sime
What does this mean? — Agustino
I am saying that they are not dichotomous domains, but inseparable aspects of a single cognition or application of language, for Wittgenstein did not accept the analytic-synthetic distinction, and he drew attention to grammar, i.e. his personal thinking process, only by way of empirical examples, and stressed how the meaning of empirical propositions depends upon regularities in acts of measurement, agreements in human judgement and normative principles pertaining to human behaviour within a custom.
This is false, since language is social and collective, not individual. — Agustino
You can
define language that way if you wish, but you miss Wittgenstein's aim of philosophical investigations, which was to demolish Cartesian phenomenology and dissolve mind-body problems, as opposed to giving any supposed 'factual content' pertaining to linguistics, or even indeed to philosophy. His remarks are
logical remarks pertaining to
his definitions, not
factual remarks.
Wittgenstein's remarks concerning language were just a special case of more general considerations of what it means to say that one is "following a rule", which for Wittgenstein boil down to external criteria of assertion such that it only makes
logical sense to speak of "following a "rule" when there are independent means of checking whether or not one is following the rule independent of one's definition of it within an appropriately normative context where talk of obeying or breaking rules is motivated. Hence Wittgenstein preempts Searle's Chinese Room Argument attack on functionalist metaphysical approaches to AI that presume it is meaningful to speak of following rules in an Cartesian and cultural-independent context.
In the supposed "private language argument" passages Wittgenstein did not say that "one cannot invent a private terminology for expressing one's immediate sensations and use it meaningfully without public guidance" for that would contradict PI $109 you just quoted and constitute a substantial philosophical thesis, and not to mention fly in the face of what we intuitively do ubiquitously in our aesthetic lives, when we express ourselves.
Rather Wittgenstein merely implied that a speaker's utterances cannot be understood as "following a rule", "conveying a message" and so forth, until the speaker's utterances are correlated to external states of affairs within a normative context that motivates talk of "obeying and disobeying rules".
In the "sensation diary" passages Wittgenstein's chief preoccupation was to understand
what it means to "name" particulars by acquaintance, to which he concludes that it is meaningless to speak of someone as
referring to or
representing a particular by way of a universal , unless it is meaningful to speak of correct and incorrect application of one's 'naming rule', which in turn demands that criteria for correct naming is independent of the intuition of the person defining the naming rule.
See for example his manometer passage, where the "private-linguist" believes he is 'naming' a novel private sensation with the letter 'S' , and then later discovers that his use of 'S' predicts whether his blood pressure is rising. So 'S' can now be said to mean that "his blood pressure is rising", and we can now understand what the private-linguist is saying by 'S', i.e. he can now be said to infer something public.
Hence Wittgenstein had nothing against what "private linguists" i.e. philosophers,
express when they colloquially speak of inventing and using language in reference to their own sensations, rather Wittgenstein's point is that one cannot speak of
inferring anything from or
conveying anything with verbal expressions precipitated by immediate sensations, unless that is to say, a correlation of verbal behaviour to external matters of fact can be established and confirmed independently of the immediate mental contents in the minds of the speakers.