This user has been deleted and all their posts removed.

This user has been deleted and all their posts removed.

This user has been deleted and all their posts removed.

what did Gödel believe in? The combined rules of reason, logic, and maths. Particular beliefs being consequences of applications of those rules. — tim wood

That is your description, written so as to support the point you're making. But it was not how Gödel understood it himself.

Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. — Rebecca Goldstein

Gödel’s view of mathematical intuition as a kind of perception echoes Plato’s claim that the soul has an eye suited to grasping the intelligible - the ‘eye of reason’. In the Republic, mathematics belongs to the level of dianoia—a faculty higher than belief, yet still dependent on symbols and hypotheses. Plato insists that geometrical and arithmetical truths do not belong to the world of becoming, but to a higher, stable, unchanging realm. Hence Gödel’s Platonism is not modern nostalgia, but a precise continuation of that classical outlook: mathematics is not invented, but discovered—seen by a faculty suited to such realities. And not a matter of belief, doxa or pistis, but insight into what is.

Hinge propositions correspond to non-logical axioms that correspond to presuppositions, rather than to undecidable sentences whose truth values are deferred - for to assume the truth of an undecidable sentence is to imply that the sentence has been decided through external considerations. In which case the the sentence is just another non-logical axiom.

The truths of undecidable sentences are to be decided - not through formal deduction by using the system but externally of the system, by either the user of the formal system who makes a decision as to their truth value (in which case they become promoted to the status of non-logical axioms) or through external but presently unknown matters of fact or by future censensual agreement if the formal system is used as an open language. Undecidable sentences are a subclass of the more general undecided sentences, namely those sentences which are not yet decided, but might be settled either internally by appying the system, or externally by extending the system.

- :up:

Would you allow an edit to, "Truth is the seeming adequacy of thought to apparent being"?

No, because it seems obvious that there is a difference between what is true and what merely appears to be true. Indeed, one cannot have a coherent appearance/reality distinction if there is "nothing but appearances." In that case, appearances just are reality, and we have something like Protagorean relativism.

This user has been deleted and all their posts removed.

Keeping in mind you have ruled out adequacy

I did?:chin:

Pretty sure that's the definition I gave. What exactly is the counterpoint, that thought cannot be adequate to being? Epistemic nihilism?

This user has been deleted and all their posts removed.

So, Tim Wood has departed the forum.

- A dramatic exit!

Yes, took me by surprise. We were debating the possibility of there being philosophical absolutes but it was hardly what you'd call a blazing row.

Incidentally, apropos of the Godel discussion in this thread, I heard John Vervaeke remark the other day that practically all postmodern philosophers are united in their hatred of Plato (whereas I have probably a rather naive admiration for Platonism.)

- I saw you say that! I found it interesting. It's something I will have to consider further.

- I wasn't following his posts very carefully, but my hunch is that it might be unrelated to the discussion itself. Maybe he just felt that he was spending too much time on TPF and made a strong decision to leave.

Maybe he just felt that he was spending too much time on TPF and made a strong decision to leave. — Leontiskos

I really do get that, and often consider it, although even if I decided to stop posting, I wouldn't have all my posts deleted.

I explained what happened in the Shoutbox.

One particular member began editing their posts to remove everything they had written, because they'd decided they didn't want to be a member of TPF any more. When I asked about it privately they asked me to delete their account and blank their posts in one fell swoop. — Jamal

The whole story:

Mystery member posted a new discussion that consisted of a book title, a link to the book, and basically nothing else except for some words to the effect of "here is a book" (not even anything concerning the book's content). I deleted it for low quality and neglected to tell mystery member why I did so. Mystery member began self-erasing, and the rest is history. — Jamal

Thanks, Jamal, appreciated. I did go looking for the explanation but overlooked that it had been made there.

If he comes to regret his departure he could always send an email to infoatthephilosophyforumdotcom, and I could send him an invitation.

Deleted User
0
This user has been deleted and all their posts removed. — Deleted User

@Jamal - so sorry to hear of this dramatic turn of events.
All of this and the way it has been handled is most unfortunate.
I would like to add my thoughts but this is not the place.

Could the posts concerning Deleted User ( Tim Wood) be moved to a more appropriate spot. Not the Shoutbox where only a few enter!

Is the Feedback category accessible without signing in? The loss of a long-term member is not easy to take on board or process...the loss of the posts and shared thoughts, poetry and music. Ouch!
Also, I think Tim might find it helpful to read...even if he might be needing a really, long break.

Deadnaming! :scream:

Drama Queen! :razz:

Is the Feedback category accessible without signing in? — Amity

Yes, feel free to start a thread there asking for clarification, and I'll respond with information I've so far scattered across various threads.

Done. Perhaps all posts, irrelevant to the essay, can now be moved there, or deleted. Thanks.

https://thephilosophyforum.com/discussion/16007/deleted-user

Disclaimer: I can't comment on the comparison or parallel, due to the limits of my knowledge. I know how many cats I have to feed, what catfood costs and how far the store is. Beyond that, my encounters with arithmetic are few and brief; with mathematics, non-existent.

Rather than representing failures of reasoning, these ungrounded foundations serve as necessary conditions that make systematic inquiry possible. — Moliere

Does this systemic inquiry serve a practical purpose? Or is it more like Sudoku?

We often perform actions without hesitation, such as sitting on a chair or picking up a pencil, without questioning the existence of either. — Moliere

That's from experience. Chairs were made by people for people to sit on and pencils were made by people for people to write with: we've known these things from early childhood. A tentacled alien would not guess how to use them. As for questioning the existence of such mundane objects, Virtual Reality and holography have brought doubt back into play.
Humans made language long before they made philosophy and acquire language before the age of questioning. We have been living on this planet and using the things it provides since long before reasoning or justification. Couldn't do any reasoning or justifying without gravity, oxygen, and all that other necessary stuff we don't think about until they're absent.

For instance, the certainty that the ground will support us when we walk is a nonlinguistic hinge that enables movement without hesitation. Similarly, our unthinking confidence that objects will behave predictably, that chairs will hold our weight, that pencils will mark paper, represents this bedrock level of certainty. — Moliere

And yet, we can be wrong about those things. When the pencil point breaks, we fail to write; when a chair breaks, we fall down with a painful thump; when the ground is quicksand, we sink and suffocate to death. Cavemen, whose language consisted of gestures and vocalizations knew enough to test the reliability of physical objects by simple physical means.

Unlike nonlinguistic hinges, these can be spoken and seem propositional, yet they resist the usual patterns of justification and doubt. — Moliere

And that makes them dangerous, because of the exceptions, gaps, biases, delusion, misinterpretation and incorrect information. Much worse, our "language games" include fiction, deception, mis- and dis-information, which are all too easily internalized as foundational. Thus cultures become interwoven with false certainties and civilizations collapse.

I'm skipping the section on mathematics, by reason of skeptical ignorance.

Traditional approaches to knowledge often assume that proper justification requires tracing claims back to secure foundations that are themselves justified. This assumption generates the classical problem of infinite regress: any attempt to justify foundational elements through further reasoning creates an endless chain of justification that never reaches secure ground. — Moliere

Bedrock is not tested with logic; it's tested with a drill. It doesn't need justification, it just needs to be hard. Only direct testing can justify non-linguistic certainty and only practice can justify linguistic certainty.

Rather than representing failures or limitations, these unjustified foundations function as enabling conditions that make coherent thought and practice possible. — Moliere

I think acknowledging its failures and limitations improves cohesion of thought.

By recognizing this necessity, we can develop more nuanced approaches to foundational questions in epistemology, philosophy of mathematics, and potentially other domains where the relationship between systematic inquiry and its enabling conditions remains philosophically significant. — Moliere

To what end? This is a sincere question: What is it you hope to learn or achieve?

Response in 2 Parts
Part 1

This essay is heavy with dry theory. The author attempts a comparative analysis of foundational certainties. Structural parallels are explored: between Wittgenstein’s concept of hinges in ‘On Certainty’ (OC) and Gödel’s incompleteness theorems.

According to the author:

Both thinkers uncover fundamental limits to internal justification: Wittgenstein shows that epistemic systems rest on unjustified certainties embedded in our form of life, while Gödel proves that mathematical systems require axioms that cannot be demonstrated within the system itself […] Both reveal that the search for completely self-grounding systems is not merely difficult but misconceived

.
As a reader, I want to know what this means, how true it is and why it matters.
The author tells us it has:

implications for understanding certainty and knowledge… we can develop more nuanced approaches to foundational questions in epistemology, philosophy of mathematics, and potentially other domains where the relationship between systematic inquiry and its enabling conditions remains philosophically significant.

About theories:
Ray Monk quotes Wittgenstein:

‘Philosophy is not a theory but an activity.’ It strives, not after scientific truth, but after conceptual clarity.

From: https://www.prospectmagazine.co.uk/regulars/55561/wittgensteins-forgotten-lesson

The author writes:

In On Certainty, Wittgenstein introduces the idea of hinges as certainties that ground our epistemic practices. While Wittgenstein never explicitly distinguishes types of hinges, his examples suggest a distinction between non-linguistic and linguistic varieties, revealing different levels of fundamental certainties.
Non-linguistic hinges represent the most basic level of certainty,bedrock assumptions that ground our actions and interactions with the world. These are not expressed as propositions subject to justification or doubt but embodied in unreflective action.

With this distinction, the author goes further than Wittgenstein. There is no mention of non-linguistic hinges in OC. More of that later. Back to bedrock.
Bedrock is not the ground or foundation of belief.
From On Certainty:

110. But the end is not an ungrounded presupposition: it is an ungrounded way of acting.
166. The difficulty is to realize the groundlessness of our believing.

From the author:

Wittgenstein breaks with traditional epistemology here. Rather than viewing these certainties as beliefs requiring justification, he recognizes them as the ungrounded ground that makes justification itself possible. He notes, "There is no why. I simply do not. This is how I act" (OC 148). Doubting these hinges would collapse the very framework within which doubt makes sense, like attempting to saw off the branch on which one sits.

What happens when we reach bedrock?

In an article, ‘ Wittgenstein on Faith and Reason’, Duncan Pritchard says:

… ‘rational support’ in question, being inherently local in this way, is not really bona fide rational support at all, in virtue of being ultimately groundless. Wittgenstein was certainly alert to this worry, writing that the “difficulty is to realise the groundlessness of our believing.” (OC, §166) On his view the regress of reasons comes to an end, but it does not come to end with further reasons of a special foundational sort as we were expecting. Instead, when we reach bedrock we discover only a rationally groundless “animal” commitment (OC, §359), a kind of “primitive” trust (OC, §475)

: https://www.academia.edu/19857441/Wittgenstein_on_Faith_and_Reason_The_Influence_of_Newman

In On Certainty: https://prawfsblawg.blogs.com/files/wittgenstein-on-certainty.pdf
Wittgenstein writes:

475. I want to regard man here as an animal; as a primitive being to which one grants instinct but not ratiocination. As a creature in a primitive state. Any logic good enough for a primitive means of communication needs no apology from us. Language did not emerge from some kind of ratiocination [Raisonnement].

In this essay, the author writes that we often perform actions without hesitation. Examples are given of sitting on a chair or picking up a pencil. The unthinking action ‘illustrates Wittgenstein’s concept of a hinge proposition.’

I find this problematic. It is an example of the author’s theoretical ‘non-linguistic hinge’.

So many things will count as hinges. There is no doubt that there is a chair when I sit on it. But what is the hinge? The existence of chairs, this chair, that it will hold me, that the floor will hold the chair and the weight of me?
Even if we agree to everything that the author concludes. What of it?
Would we understand ourselves any better?
Non-theoretical understanding. Isn’t that what Wittgenstein pursued?

Response
Part 2

According to Ray Monk, Wittgenstein saw philosophy as ‘the understanding that consists in seeing connections.’ For him his philosophy is an activity not a body of doctrine.

From PI 122:

A main source of our failure to understand is that we don’t have an overview of the use of our words. - Our grammar is deficient in surveyability. A surveyable representation produces precisely that kind of understanding which consists in ‘seeing connections’. Hence the importance of finding and inventing intermediate links.

The concept of a surveyable representation is of fundamental significance for us. It characterizes the way we represent things, how we look at matters. (Is this a ‘Weltanschauung’?)

A worldview. That of an individual or a collective? Both? Interacting. Linking. It is how we come to know by sharing thoughts and images.

As a collection of notes, On Certainty is thought-provoking with an imaginative use of metaphors. Some rigid pictures are painted, like hard ‘hinges’, structures. Others are soft and fluctuating like rivers.

Wittgenstein calls his/our picture of the world its inherited background. We don’t get this by looking at its correctness or because we are satisfied with it. (OC 94).
This is one example of how Wittgenstein replaces the need for grounds and foundations. Others can be found with movement around an axis (OC 152), community (OC 298) and system (OC142).

The inherited background is like the river-bed. However, cultural concepts change. Different generations see things differently but some things stay the same. The river-bed may shift (OC 97).

This ‘bedrock’ is not about justification of knowledge. Justification comes to an end. The river-bed ‘channels’ thought.

The movement of the water (day-to-day thinking)) interacts with the river-bed structures. The flow of thoughts can change the shape of the river’s bank and course. There is not a sharp division (OC 97). We can change the world or our picture of it and vice versa.

Ungrounded grounds and ungrounded foundations are not a necessary condition.
Instead of grounds, ungrounded or otherwise, Wittgenstein points to 152, 94, 298, 142 and probably other passages. No mention of foundations. He rejects that model.

The author is correct regarding Wittgenstein's break with traditional epistemology. He moved away from old views about establishing foundations, a solid base on which to build knowledge. Wittgenstein believes that our understanding of knowledge is found in how we live, our beliefs and practices. Our certainty is practical rather than theoretical.

It is philosophy as a way of life. Not just for academics but for all.

The essay addresses the important philosophical questions of knowledge, certainty and foundations. However, the author's theoretical interpretation of W. is open to doubt. Some might say incorrect. There are several things that have been pointed out that are contrary to what is claimed in the essay.

Finally, what matters lies in the connection and activity. Sharing the challenge to improve understanding.

I'll start by answering a pertinent question from @Vera Mont.

To what end? This is a sincere question: What is it you hope to learn or achieve? — Vera Mont

The paper explores why we can know things at all by connecting two big ideas: Wittgenstein’s notion that our knowledge rests on unquestioned "hinges" (like assuming the ground will hold when we walk) and Gödel’s discovery that even math has true statements it can’t prove within its own rules. The goal isn’t to solve a practical problem like building a bridge, but to understand the foundations of how we think and reason, whether in everyday life or in fields like math and science. By demonstrating that both knowledge and mathematics depend on unprovable starting points, the paper reveals a universal idea, viz., that our systems of understanding require ungrounded foundations to function. This matters because it helps us appreciate the limits and strengths of human reasoning, encouraging a bit of humility about what we can justify and confidence in the systems despite these limits. It’s like mapping the bedrock of thought, not to change how we live day-to-day, but to deepen our grasp of what makes knowledge possible, which can inspire clearer thinking in any field, from philosophy to science to ethics.

Thanks,
Sam26

Thank you for this well-presented OP. While I agree that Godel’s incompleteness theorems can lend themselves to the assumption of groundless grounds akin to Wittgenstein ‘hinges’, I don’t believe Godel would have been comfortable with such a relativistic, pragmatist conclusion. He considered himself a mathematical platonist. As Roger Penrose says about Godel:

Godel, himself, was a very strong Platonist…
The notion of mathematical truth goes beyond the whole concept of formalism. There is something absolute and "God-given' about mathematical truth. This is what mathematical Platonism, as discussed at the end of the last chapter, is about. Any particular formal system has a provisional and 'man-made' quality about it. Such systems indeed have very valuable roles to play in mathematical discussions, but they can supply only a partial (or approximate) guide to truth. Real mathematical truth goes beyond mere manmade constructions. (The Emperor’s New Mind) — Joshs

Thank you for your response and for highlighting Gödel’s Platonism, which is a crucial aspect of his philosophical framework. I agree that Gödel, as a mathematical Platonist, believed in the absolute, objective reality of mathematical truths, existing independently of human constructions or formal systems, as Penrose notes. This view contrasts with a more contingent, practice-enabled nature of Wittgenstein’s hinges, which are grounded in our form of life and seem to carry a relativistic or pragmatist flavor. However, the parallel I propose between Gödel’s unprovable statements and Wittgenstein’s hinges focuses on the structural similarity as opposed to a complete philosophical alignment.

The key connection is how both thinkers reveal the necessity of ungrounded foundations within their respective systems. Gödel’s incompleteness theorems show that any consistent formal system of arithmetic requires axioms or truths that cannot be proven within that system, pointing to a limit of internal justification. Similarly, Wittgenstein’s hinges are basic beliefs that lie beyond justification or doubt, enabling our epistemic practices. While Gödel might have resisted the idea that these mathematical grounds are merely pragmatic or contingent (as hinges might appear in Wittgenstein’s framework), the structural parallel holds: both systems depend on foundational elements that are not internally justifiable but are necessary for the system to function.

Gödel’s Platonism suggests that unprovable truths, like the consistency of a system, exist in a realm of absolute mathematical reality, accessible perhaps through intuition or external perspectives (e.g., a stronger system). Wittgenstein, by contrast, sees hinges as embedded in our lived practices, not as absolute truths but as practical certainties that make inquiry possible. The paper doesn’t claim Gödel would endorse Wittgenstein’s pragmatism but argues that the incompleteness theorems and hinge propositions both expose a universal feature of systematic thought: the need for ungrounded starting points. This structural necessity persists whether one views those foundations as “God-given” (Gödel) or as contingent features of human practice (Wittgenstein).

In short, while Gödel’s Platonism might make him somewhat wary of relativistic or pragmatist readings, the parallel with Wittgenstein’s hinges highlights a shared insight into the limits of formal and epistemic systems. This comparison enriches our understanding of foundational certainties, showing how they function across domains, even if their metaphysical status differs.

This response acknowledges Gödel’s Platonism and the critic’s concern, clarifying that the paper’s parallel is structural, not ontological. It defends the comparison by emphasizing the shared necessity of ungrounded foundations, while respecting the philosophical differences between Gödel and Wittgenstein, thus engaging the critique constructively without conceding the paper’s core argument.

Thanks for your response @Josh

By demonstrating that both knowledge and mathematics depend on unprovable starting points, the paper reveals a universal idea, viz., that our systems of understanding require ungrounded foundations to function. — Sam26

Yes, that's the part I didn't get: 'ungrounded foundations' seemed to me a contradiction in terms. I assumed unquestioned assumptions were formed either through empirical testing or specialized faith.
But if it's a study in how humans think about lofty matters, I can see a purpose to the exercise.