Right.
655 is followed by:
- And one can not say that of the propositions that I am called L.W. Nor of the proposition that such-and-such people have calculated such-and-such a problem correctly.
What one cannot say about the proposition that I am called L.W. and the proposition that such-and-such people have calculated such-and-such a problem correctly is that they are hinges. You can, however, say that they are incontestable. His name is L.W. and people do calculate correctly.
So here is a draft taxonomy, produced in conversation with Claude.
We have a family of overlapping accounts of certainty, a classic family resemblance. In some the certainty is as it were internal to the game, at least in part constituting how one plays. In others, the certainty underpins the game, is taken as a given in order for the game to take place. In some the certainty is a result of our being compelled to act, in others we have a degree of choice. Some set forth the way things are, others set forth what are to do.
I’m not overly pleased with this result. I’m going to keep looking in to the structure of each, as I’m still enamoured with “counts as…”, an approach that sets out something common in the logic of at least some of these. Constitutive rules create the possibility of practice. Hinges and axis are clear examples of this process, bedrock perhaps the most difficult. I remain unconvinced that these cannot all be put in terms of constitutive rules.
Transcendental condition as the “logical structure” of hinges?
What are you asking?
A transcendental account has the structure: X; X only if Y; hence, Y.
A hinge might be understood as having such a structure. A hinge is constitutive of the very process of doubting;
OC §341: The questions that we raise and our doubts depend on the fact that some propositions are exempt from doubt, are as it were like hinges on which those turn.
We doubt; the only way we can doubt is if we hold Y firm; therefore, Y.
Note that here I am using “hinge” in a specific way, not as the general category of certainties, as recently adopted.
Where, in the writings of Wittgenstein, do you find a similar use of the “transcendent?”
I’m not engaged in explaining Wittgenstien. Not mere exegesis.
But given his approach, what can we make of the relation between his examples of the indubitable, and is there some common logic?
It is going to be difficult to locate his “approach” without such engagement.
If you do not really need him, why return to his writings?
Whatever.
With 20 extra characters.
I accept your surrender.
It’s a sadness that the responses here have been far less helpful than those of Claude.
The topic for this thread was set out fairly clearly. If you want to talk about something else, make a new thread.
When we construct a formal language, we begin with primitive expressions such as a, b, c… as individual constants, ~, ∧, ∨, ⊃ for connectives, …x, y, z for variables, and so on. We then define well-formed formulas as specific combinations of these. We define an interpretation as a relation between these symbols and a non-empty set, the domain of the model, assigning values to the variables and constants of our logic from that domain and truth in terms of that assignment.
Notice that each level constitutes the grounding for the level above it. So the question that suggests itself is: is there a similar dependence amongst the various forms of certainty?
Speculative, of course, but entertaining.
This is an interesting attempt, but I think the analogy doesn’t hold. In a formal language, you stipulate primitives, define well-formed formulas from them, and then define interpretations. The whole structure is built from the ground up, with each level deliberately constructed to support the next. The dependencies are explicit because someone put them there.
Witt’s picture is the opposite. Hinges aren’t stipulated. They aren’t constructed to support anything. They’re inherited, acted on, presupposed. The dependency runs in the other direction from formal systems. In a formal language you start with primitives and build up. In Witt’s picture you’re already inside the practices before you can identify what’s holding them up. The bedrock isn’t laid first and then built on. It’s discovered retrospectively as what was already in place.
There’s also another deeper problem. Formal systems have precise levels with defined relationships between them. Witt is deliberately resisting that kind of precision. OC 52 says there’s no sharp boundary between hypotheses and certainties. The metaphors he uses, riverbed, hinge, scaffolding, all resist formalization. Trying to map the structure of certainty onto the structure of a formal language imposes exactly the kind of clean structure that Witt thinks misrepresents how certainty actually functions.
That said, Banno’s instinct that there’s a dependency structure isn’t wrong. There is one. Bedrock hinges are prior to linguistic hinges, which are prior to epistemic practices. But the dependency is practical, not formal and stipulative. It’s closer to natural history than to model theory.
No need for all that. There is a dependency structure. That’ll do. The letter “a” counts as an item, “z” counts as a variable; we need these before we can say that “⊃” counts as a connective, “f” as a predicate and ∃ as a quantifier, and we need these before we can say that “a” counts as an individual and “f” as a property.
You are right that a formal structure is built on purpose. Notice that the purpose is there already—to formalise the practice. Logicians don’t begin by just shuffling letters; that’d get nowhere. Just as for natural languages, they also have the purpose of the formal system in mind at the start, as the goal. A syntax is set up with an interpretation in mind.
It’s trite, almost lazy, to simply assert that certainties resist formalisation. If a formal system can help us to see more clearly the difference between a hinge and a riverbed, that’ll do. We needn’t ask more of formalisation.
You presume that what is practical cannot be formalised. That’s not right - consider, addition, measurement, probability. You conflate formality and stipulation. Another muddle.
I suppose your resistance to a taxonomy of certainties rests on your problematic idea of unspeakable certainties. Those things of which we are certain can be stated, and our certainty shown. Leaving them as ineffable is not in the spirit of Philosophical Investigations.
I haven’t said that what is practical cannot be formalized. Addition, measurement, and probability are all formalizable, and I have no objection to that. What I’ve said is that the specific thing Witt is pointing to in OC resists formalization, and for a specific reason that Witt himself gives. OC 26 shows that any rule for when mistakes are excluded generates a regress, because you can go wrong in applying the rule. OC 27 says that if you tried to formulate such a rule it would have to contain the expression “in normal circumstances,” and we recognize normal circumstances but cannot precisely describe them. That’s not me being trite or lazy. That’s Witt making a point about the structure of our epistemic practices, a point that has a structural parallel with Gödel’s results about the limits of formal systems.
You say if a formal system can help us see more clearly the difference between a hinge and a riverbed, that’ll do. I agree. I’m not against using formal tools to clarify. I use the Gödel parallel myself for exactly that purpose. What I resist is the suggestion that the dependency structure between levels of certainty can be captured in a formal taxonomy without remainder, because the text repeatedly shows that the boundaries between levels aren’t sharp. OC 96-99 on the riverbed explicitly says there’s no sharp division between the movement of the waters and the shift of the bed. A formal taxonomy imposes sharp divisions. That’s what formal taxonomies do. Using one as an illuminating comparison is fine. Treating it as an adequate representation of the structure is where the distortion enters.
Your claim that my resistance to taxonomy rests on “unspeakable certainties” misrepresents what I’ve said. I haven’t called non-linguistic hinges unspeakable or ineffable. I’ve said repeatedly that we can describe them in language. What I’ve said is that they don’t require language to function. The dog navigating its environment acts with certainties that operate without propositions. We can describe those certainties propositionally, and when we do philosophy that’s exactly what we do. But the description is ours. The certainty was operative before the description and would be operative without it. That’s not ineffability. It’s the difference between a thing and its description. And it’s entirely in the spirit of the Investigations, where Witt says “don’t think, but look.” He’s constantly pointing us to what’s shown in practice rather than said in propositions.
