I don't see this as a problem so much as a part of the answer: it's not that some propositions are always hinges, but that in order to play a language game we must set aside doubt for some propositions.The problem is that what's basic in one context is not in another. — Sam26
"A right-hand glove could be put on a left hand if it could be turned round in four-dimensional space.". — frank
You can't see the obvious here? You want a debate without words? See ....why cannot there be a robust debate as to whether philosophy of language come prior or after formal epistemology? — schopenhauer1
Or perhaps you are reading Kant into Wittgenstein. I agree here with @Sam26; hinges are not just the now quite problematic notion of synthetic a priori, nor are there clear conclusions in On Certainty. I think you have missed quite a bit of what is going on here.Well, he isn’t saying it’s like Kant, and that’s the problem as it is… — schopenhauer1
I don't understand how.Its a logical footnote to prevent solipsism is all. — Philosophim
Didn't you want to use it in order to explain something about gloves?Best not to overanalyze it or elevate it to have any deeper meaning then that. — Philosophim
And once you represent it, it is the thing...Trying to figure anything more out about the thing in itself is pointless. You can't, you can only represent it. — Philosophim
So there's that. We can't know what a "thing in itself" is. But presumably we can know what the thing is. So what purpose is there in this philosophical construct, this phantasm, this thing-in-itself? You can't say anything about it, so the story goes - and yet the pages hereabouts are full of it.Generally, the debate is, "Can we know what a thing in itself is?" Can we know what reality is, apart from our interpretations of that reality? And the answer is "No". — Philosophim
How do you represent something unless that 'something' is there? — Philosophim
We need something 'in itself' to represent. — Philosophim
Well, not only you, and not in response to any particular post. I was just setting out a few thoughts regarding the direction of this thread. There's a slide from "here is a hand" not being known right down to a conclusion that hinges are non-propositional and preverbal. But I don't agree that if you get on one end of the slide, you must get off at the other.I assume this is directed toward me, so I'll respond. — Sam26
Ok. No, it isn't, but Ok.No, the relation is to a chosen reference. — frank
That an object is left-handed or right-handed is relational. You want to claim that the relation must be to an observer. I've pointed out that this is not so.And so you've joined the ranks of those to whom it's obvious that space doesn't have a left and right. — frank
What could that mean? That birds do not fly north for winter?It's just that directionality does not exist in the wild. — frank
A coordinate system is not an observer.Chiral objects and figures like hands exist, by definition of chirality, in two distinguishable forms that are mirror images of each other. But, being isometric, the two forms cannot be distinguished if we take only the metric into account. For the distinction of chiral objects we need more than just a metric, we need to introduce an orientation of the space in order to define reflections and mirror images, i.e. we need coordinates. — https://match.pmf.kg.ac.rs/electronic_versions/Match61/n1/match61n1_5-10.pdf
Your observer is reduced to a point. That is all that is needed.How can you have choosing going on with nobody to choose? — frank
Quadruped? That's my problem then. Not enough feet.Being in a quadruped body is the basis for the distinction. — frank
You reached it as a conclusion to some argument? This?Directionality is something we give to space. It doesn't have that on its own. Some responders to this thread have said that this is blatantly obvious, others like me, arrived at it intellectually... — frank
It's wrong. If the glove has a palm and a back then we can tell its chirality. If it does not have a palm and back then inserting an "observer" does not help. The judgement will depend on which side the glove is seen from, not on the fact of there being an observer. It's not necessary to "insert an observer" to settle the issue; simply choosing a point on this or that side of the glove will suffice.Consider a container in which a single glove is floating. Is it a right-handed glove or a left-handed glove? We can insert various new items into this space-container, e.g., an anorak, a scarf, a shoe, but only the insertion of a human observer into the space will permit an answer. — SEP on Leibniz
This looks to be a play on "use". Only conscious beings construct. But that tells us nothing about space.But only a conscious being can construct a point of origin or use. — Philosophim
Nuh. The river bed is silt, sand and rocks. It stays relatively fixed while the river flows past. If it didn't, we wouldn't have a river - we'd have a swamp or a delta or some such.The riverbed is bedrock. — Joshs
David Hilbert and Wilhelm Ackermann are often credited with formalizing the notion of soundness in their work on formal logic systems in the early 20th century. Their 1928 book "Grundzüge der theoretischen Logik" (Principles of Mathematical Logic) laid the groundwork for formal systems, including the notion that derivations in a formal system should correspond to semantic truths.
However, the soundness theorem is usually associated with Kurt Gödel, who in 1930 proved both the soundness and completeness of first-order logic (predicate logic) as part of his doctoral dissertation. This work demonstrated that if a formula is provable, it is also true in all models, and conversely, if it is true in all models, it is provable. The proof of soundness is typically straightforward compared to the proof of completeness, but both are key results in Gödel's work.
So while Hilbert and Ackermann helped define the formal system, it is Gödel's 1930 work that solidified the formal proof of soundness in the context of first-order logic. — ChatGPT
Soundness (if G |- P then G |= P). Proof is straightforward by induction on length of derivation. I don't know who first proved it. — TonesInDeepFreeze
...there are no sentences that are not about some thing, and so not true sentences that are not about some thing — Banno
I'm sorry you can't see how it answers the OP. It is at least a beginning. HenceHow would this be an answer to the OP? — Leontiskos
J apparently can see how it addresses the OPIt's a direct answer, certainly. — J
...which is too general, too glib. I might reply, in kind, that all (true) sentences can be parsed into propositional logic. "p". Therefore all true sentences are "formulable within formalism"....whether all true sentences are formulable within formalism, and it seems a foregone conclusion that they are not. — Leontiskos
We have both existential quantification and ∃!. And we have Tarski and all the ensuing work. These are concerted efforts to explore the grammar of truth and existence. First order logic shows that quantification is not a first order predicate, free logic shows the implications of treating existence as a first order predicate. Tarski explicitly makes truth a second order predicate ranging over propositions. Claiming that there is no explicit predication of existence or truth in formal logic is ignorant.Given that there is no explicit predication of existence (or, I think, truth) within formal logics... — Leontiskos
There is no suggestion that we limit ourselves to formal logic. But you might benefit from making at least some use of it. It seems we are repeating the problem seen in other threads, where a lack of literacy in formal languages leads to an inability to set out the issues clearly....how could this question possibly be answered by limiting ourselves to formal logics? — Leontiskos
Neither of us, nor I suspect anyone else here, have the background in intensional logic (with an "s", not a "t") that is required. I'll just leave here the intuition that more recent developments in treating intensions as algorithms reinforce treating intension as use, and leave it at that....intentional logic would seem to be a topic that is relevant to the thread. — Leontiskos
It does not pay to assume that a word must have an opposite, or one opposite, whether it is a 'positive' word like 'wilfully' or a 'negative word like 'inadvertently'. Rather, we should ask ourselves such questions as why there is no use for the adverb 'advertently'. For above all it will not do to assume that the 'positive' word must be around to wear the trousers; commonly enough the 'negative' (looking) word marks the (positive) abnormality while the 'positive' word, if it exists, merely serves to rule out
the suggestion of that abnormality. — Austin, Plea for excuses, Philosophical Papers, p. 192