Some insights into Wittgensteinian hinges and Godel’s incompleteness theorems.

Extended Theory: Foundations of Knowledge and Formal Systems

1. Parallel Foundations

A. In Epistemological Systems:
• Hinge beliefs serve as unquestioned beliefs
• Pre-linguistic beliefs ground our knowledge
• Pre-linguistic beliefs enable the practice of justification

B. In Formal Mathematical Systems:
• Godel’s unprovable propositions function like hinges
• Some mathematical truths must be taken as bedrock
• Some mathematical statements are necessary for system operation but unprovable within the system

2. The Foundation Principle
• All systems whether epistemic or formal require unprovable foundations (hinges)
• Unprovable statements are not weaknesses but necessary features
• Hinges do not limit systematic knowledge but are a requirement for all systems of knowledge
• The attempt to prove every statement within a system leads to the following:
o Infinite regress
o Circular reasoning
o Foundational assumptions (hinges/axioms)

3. Unified Understanding of the Limitations of Systems
• Epistemological systems are built on hinges
• Formal systems have unprovable but necessary truths
• Both systems require the following:
o Statements that cannot be justified within the system
o Statements that are necessary for the system to function
o Statements that must be accepted rather than proved

4. Knowledge Implications

A. Mathematical Knowledge:
• Some mathematical propositions must function as hinges
• These are not problems for the system but features of formal systems
• The unprovability of certain mathematical propositions in a formal system mirrors the role of hinges in epistemic systems

B. Scientific Knowledge:
• Foundational assumptions are necessary for a scientific system
• These function like mathematical axioms and epistemological hinges
• They are necessary to scientific progress

5. Practical Applications:

A. In Mathematics:
• Recognizing certain mathematical propositions as hinge like
• There are limits to formal proofs
• Recognizing the role of bedrock statements

6. Philosophical Implications

A. For Knowledge
• Knowledge doesn’t need complete proof
• Systems are reliable despite having unprovable elements
• Foundational elements and proofs have different functions

B. For Truth:
• What we accept as true can exist independent of provability
• Some truths must be simply believed without proof
• What we accept as true is not always provable

7. Integrating Epistemological and Formal Systems

A. Common Features:
• Unprovable foundations are necessary
• Accept starting points
• Seeing limitations as enabling features

B. Differences:
• Understanding the properties of foundational elements
• Different methods of verification
• Different types of knowledge acquired

Understanding this integration suggests the following:

1. The limits Godel discovered in formal systems coincide with the role of hinges in epistemology
2. Mathematical and JTB necessitate unprovable foundations
3. These are features of these systems, not problems to be solved
4. Having a clear understanding of these systems helps to better understand both domains

As far as I know, no one has made this connection, viz., between hinges and Godel's incompleteness theorem.

:up:

:up:

What might an outline of a theory of knowledge look like in my interpretation of OC?

A Layered Theory of Epistemic Foundations

1. Foundation Layer: Pre-linguistic beliefs or certainties
• Consists of pre-linguistic or animal beliefs or certainties
• Pre-linguistic beliefs are manifested through action
• E.g’s include special awareness, object permanence, and bodily awareness
• These form the foundations of what makes the language games of knowledge possible
• Not subject to claims of truth or falsity because they precede such concepts
2. Framework Layer: Hinge Beliefs
• Built on top of pre-linguistic beliefs
• This is the riverbed of our system of JTB
• Differing levels of stability
o Bedrock hinges (nearly immutable, e.g., physical objects exist
o Cultural hinges (can change over time)
o Local hinges (depend on contexts or practices)
• Not justified by evidence or reasons but shown through our practices
• Makes the language games of justification and doubt possible

3. Operational Layer
• Built on the foundation of hinge propositions
• Requires:
o Meaningful doubt
o Methods of justification
o Context within language games
• Subject to verification and falsification
• They can be taught and demonstrated

Key Principles:
1. The Doubt Principle
• The language game of doubt requires a stable framework
• Not everything can be doubted
• There must be practical consequences to doubt
• Doubt is necessary for knowledge claims

2. The Justification Principle
• Operates within language games
• Different language games require different forms of justification
• Justification ends with hinge propositions
• Justification cannot have an infinite regression

3. The Principle of Context
• Knowledge claims only make sense within the language games of epistemology
• Some propositions can be epistemological in one context and be a hinge in another

4. Principle of Practice
• Knowledge is demonstrated by practice and by our statements
• Actions are more fundamental than statements
• Learning involves the acquisition of explicit knowledge and implicit certainty
• Practice grounds theoretical knowledge

Methodological Implications:
1. Epistemology
• Understand how knowledge claims function in practice (language games)
• Examine the relationship between our actions and our certainties (beliefs)
• Study the many language games of justification across contexts
• Understand the importance of our background reality in knowledge

2. Scientific Knowledge
• Scientific methods rest on hinge certainties
• Paradigm shifts involve changes in hinges
• Understand the relationship between theory and observation

3. Everyday Knowledge
• Acknowledge the importance of practical knowledge
• Again, recognize the role of the inherited background
• Recognize the relationship between action and belief

This is a way of understanding knowledge within the context of some of Wittgenstein’s thinking in OC and the PI.

A lot more work needs to be done, but this is the beginning of how I think of epistemology using Wittgenstein as a catalyst for my thinking.

Key Themes of Thread:

1. Context and Purpose
• On Certainty is Wittgenstein’s response to G.E. Moore's papers Proof of an External World and A Defense of Common Sense.
• Wittgenstein challenges Moorean propositions (e.g. “Here is one hand”)
• As part of Wittgenstein’s critique he addresses skepticism and the nature of doubt

2. Hinge Propositions:
• Hinges are foundational beliefs that form the bedrock of our language games and knowledge claims
• They aren’t subject to traditional epistemological categories of justification and truth
• Examples include basic beliefs about having hands, the existence of objects, and other minds
• They are part of our inherited background or world picture
• There are a variety of different hinges, with some being more immutable than others


3. Knowledge and Certainty
• OC distinguishes between knowledge and subjective certainty (conviction)
• Moore’s claims are more akin to expressions of his convictions rather than knowledge claims
• Knowledge (JTB) requires truth, justification and the possibility of doubt
• Knowledge claims must be demonstrated rather than stated


4. Doubts Role
• Doubting is not always meaningful; some are logically excluded
• Doubt requires a framework and a context to make sense
• Universal doubting would undermine meaningful doubting
• Meaningful doubting must occur within a system where things are not doubted

5. Language games and Framework
• Certain propositions must be held fast within a language game (not questioned)
• Bedrock beliefs allow for the possibility of language and meaning
• Like the rules of chess, the pieces, and the board they provide the background for the game to be played

6. The Nature of Hinges
• They can be pre-linguistic or animal beliefs
• Hinges can be pre-linguistic rather than propositional
• They can change over time, although some are more permanent than others
• They can vary due to different systems of belief, though some core hinges are universal

7. Implications for Epistemology
• Challenges traditional epistemology that all beliefs within an epistemological framework require justification
• Some beliefs make justification possible
• Helps to understand the limits of knowledge and doubt
• Demonstrates how certainty is grounded in action rather than a specific theory

Thanks, I listened to most of it and there's not anything new there. There are many more interesting videos on the topic. I've been listening to Dr. Bernardo Kastrup.

It doesn't make any sense to me, but I'll delete them anyway.

I don't use LLMs to write my posts. I quoted the LLM's answer to a question. Isn't this like quoting a paper or book? Do you want me to delete the posts?

I think Grok 2 mini beta did a great job of answering these questions

deleted

deleted

deleted

deleted

deleted

deleted

Sorry, but I'm a bit burnt out when it comes to Wittgenstein. Good luck with your thread.

Ya, I'm familiar with him. I do believe we live other lives based just on what I've learned from NDEs.

Fair enough. As I've said many times in this thread, I think research into children with memories of previous lives is corroborative in some ways to NDE reports. Both indicate modes of being beyond physical birth and death. — Wayfarer

There is some evidence that supports previous lives, but I don't know how strong it is because I haven't studied it as closely as NDEs. In terms of numbers, it's not as common as NDEs.

It's a shame you can only see it through your pre-concieved notion of what a 'religious point of view' must be. — Wayfarer

It's not a preconceived notion, it's a conclusion arrived at through more than 45 years of study. I was very religious for years.

But they're not synonyms - one is a state of a thing and one is the thing itself. But anyway, I suppose that's just a terminological issue (actually, I think it reflects the 'mind is the brain' view currently dominant, where it is consciousness that is what is distinctive about the brain, as opposed to there being a soul that has the consciousness). — Clearbury

I'm afraid I have to disagree with the dominant view. The mind as I use it is, for all practical purposes, is synonymous with consciousness. Although there may be differences in some contexts, especially if you're a materialist or physicalist. Also, I generally don't use the term soul in reference to that which survives death. I believe consciousness is more accurate.

There are two types of NDEs that you seem to be conflating. There are those that involve floating about in the room. Those are the ones that, supposedly, others can corroborate - though I think there's no hard evidence of such corroboration. Plus, just as we incorporate alarm sounds into dreams, nothing stops the same happening in these scenarios. — Clearbury

Actually, I'm not conflating anything. I've described three kinds of NDEs (category 1, 2, and 3) pointing out the differences between each of these NDEs. I don't know why you would say supposedly corroborate, the data on this is overwhelming. As I've pointed out it's the same data that a detective uses when trying to confirm or disconfirm testimony, you interview the people involved. It's not very difficult and it's done all the time. I find it a bit strange that people just dismiss this information. Although you did acknowledge it with some hesitation. I don't know what you mean by "hard evidence?" Maybe you mean scientific evidence, but this is something I've also addressed, viz., by pointing out that epistemology is not limited scientific evidence. This seems to be a common misunderstanding of many that post in this thread, and even when they do acknowledge it, they seem to forget just how powerful good testimonial evidence is.

I'm not saying there aren't some similarities between dreams and veridical experiences. I'm saying that we don't corroborate hallucinations, delusions, or dreams in the same way that we do veridical experiences. The way these terms (hallucinations, delusions, and dreams) are used in our everyday language clearly separates them in a significant way from veridical experiences. On the other hand, NDEs are being corroborated all the time, and if they can't, then I'm skeptical of them, or at least I set it aside. I'm not saying that all NDEs can be corroborated, but a significant number can.

Then there are the NDEs where people seem to have the experience of travelling to a different realm. Those are not corroborated. There's a similarity among these experiences, but there's a lot of similarity between dreams too, and the similarity does not seem significantly greater. — Clearbury

When we look at the testimonial evidence of NDEs we have to examine it the same way we would examine any testimonial evidence. First, again, is corroboration, which gives us an objective way to verify the testimony. Even NDEs that incorporate traveling through a tunnel, seeing loved ones, having a life review, have been corroborated. What I mean is that if you can objectively corroborate at least part of their story, then you can make an inference based on how consistent it is with other stories that see and hear generally the same things. So, although you can't corroborate some of the story that doesn't mean we don't have other means of testing the story. For example, let's say someone tells you of their trip to Alaska and part of their story can be corroborated and other parts can't, we generally would accept the testimony as accurate, especially if there are other stories that match with theirs. So, although we can't corroborate all of it, there is enough consistency with other stories that allows us to accept their story as truthful or veridical. Do people sometimes lie, of course, but are all these people lying? Analyzing testimonial evidence takes time and patience. It must be compared with a lot of data. I've spent a lot of time analyzing the testimonial evidence and I generally find it to be accurate. There're two main reasons that people reject these stories: First, they're wedded to a particular worldview. Second, they don't have all the facts/information.

So why don't they kill themselves and encourage others to do likewise? That is what we would typically do if we find a beautiful place - we try and revisit it and encourage others to do likewise. These people claim to know, in a way that the rest of us do not, what lies in wait for us the other side of death. And they claim it is wonderful. Yet they seem reluctant - more reluctant, if anything, than the general population - to go back there. That's very peculiar to me. — Clearbury

I've read over 5000 accounts of NDEs, and what you'll find is that many people who have an NDE don't want to come back to this life, but they're told they must return because their objectives for coming here aren't complete. What I've found is that we enter into some agreement before choosing to have these human experiences, and it's important that we finish our task. Also, those who commit suicide often find that they've made a huge mistake, i.e., they're just going to have to come back again and do it all over again. So, it's not as simple as you might think and killing yourself is not an escape.

From a philosophical perspective, it might be instructive to consider the Buddhist view — Wayfarer

I have found that nothing gives us as clear a picture as NDEs. The evidence is much stronger than any religious point of view. I find that most religious have it generally incorrect. There are interesting ideas in the Buddhist tradition, but, again, if you want some answers about the afterlife, then NDEs give the most information.

Although I believe in life after death, I think NDEs are not good evidence for it. They seem better explained as dreams. — Clearbury

I'll answer this question first. I've written a lot about why I think NDEs give us good testimonial evidence, and why they're different from hallucinations, dreams, delusions, or any other purely subjective experience. The main difference is that they can be corroborated by others who were there. In other words, doctors, nurses, family, friends, and any other person at the scene can corroborate or invalidate what the NDEr is claiming to have experienced (seen, heard, etc). So, if others who were at the scene affirm one's claims, then that puts the experience into the realm of objective reality. This is what separates the NDE from hallucinations, delusions, or dreams. We can't corroborate what you see or hear in a dream. I can't go to your friend who was in your dream and ask if he said X, Y, or Z. The way we generally know that an experience is veridical is that others are having the same experience, or generally the same experience. Corroboration is one of the ways we use to examine whether or not testimony is reliable. This is seen in good detective work and even in good science.

'consciousness' survives death, rather than 'the person' or 'the mind' survives death? I am not a consciousness. i am a person. I am conscious a lot of the time (though unconscious some of it). When I am unconscious I am not non-existent. I exist, but I am just not conscious. So 'consciousness' and 'a person' are not equivalent. My quibble, then, is that it is persons or minds (I use the terms interchangeably) who survive death, not 'consciousness' (consiousness is something persons have, but it is not what a person 'is'). — Clearbury

Consciousness is much broader in scope than just being a person, although it's true that I'm referring mainly to persons. I believe that there is some element of consciousness in most if not all living things. I also believe that consciousness is at the heart of reality and that all of us ultimately come from this core consciousness. Death simply returns us to where we reside. What makes you who you are, are the memories and experiences that attach to your specific conscious awareness. For you to survive death I believe that your specific conscious awareness with all the memories and experiences that attach to you must survive, and I believe it does.

When you're unconscious you still exist, you're just not aware for a while, or you're vaguely aware as in a dream. Being unconscious seems to be something specific to this body, or more specifically, to the brain.

I also generally use the terms consciousness and mind as synonyms.

An interesting take on the argument of materialism vs idealism by Bernardo Kastrup.

Bernardo Kastrup | Refuting Materialism: full lecture

https://www.youtube.com/watch?v=cPCvQQQrZwU&t=2164s

An interesting podcast on consciousness.

Two AI's Discuss: The Quantum Physics of Consciousness - Roger Penrose Deep Dive Podcast

https://www.youtube.com/watch?v=-isq40ARB9g

Clearly, you haven't understood a thing I've said. I question your ability to interpret not only what I've communicated over and over again, but your ability to interpret OC. I find it a waste of my time trying to explain myself to you. You either don't take the time to read or you have a bottle of vodka next to you, maybe it's the latter. I don't know which.

It's not at all a leap in the dark, no more than accepting the Earth is more than 100 years old is a leap in the dark, or that I have hands is a leap in the dark.

And maybe life itself leaps forward with unreasonable confidence. — frank

It's not reasonable or unreasonable it just is the framework we have to work with.

It is justified within the system. — Fooloso4

To say that hinges are justified in any epistemic sense is to miss the main thrust of OC. It would be to "...grant you [Moore] all the rest (OC 1)." Hinge propositions are not subject to verification or falsification (the doubt) within the system, they allow all our talk of epistemic justification and doubting to take root. In other words, they are the ungrounded linguistic framework that allows the door to swing (the door of epistemology). This is why justification ends with basic beliefs, and why it solves the infinite regress problem. They form the bedrock of how epistemic language gets off the ground in the first place.

My interpretation of Wittgenstein and hinge propositions is that hinges are neither true nor false, i.e., hinges have a role similar to the rules of a game. I’m specifically referring to the use of true and false as something verified by facts, i.e., something justified within an epistemological system. “If the true is what is grounded, then the ground is not true, nor yet false. If someone asked us ‘but is that true?’ we might say ‘yes’ to him; and if he demanded grounds we might say ‘I can’t give you any grounds, but if you learn more you too will think the same (OC 205, 206).” One can use “true,” but note it’s not an epistemic use of the concept as justified true belief. Rational discourse requires that there be these basic beliefs for rational discourse to function.

If someone asked, someone who is just learning chess, “Is it true that bishops move diagonally?” I would answer “Yes.” And if they further asked, “How do you know (an epistemological question)?” I might respond “It’s just one of the rules of the game.” In this case, the use of true is not justified, it’s just accepted as a basic belief without any grounding.

“But it isn’t that the situation is like this: We just can’t investigate everything, and for that reason we are forced to rest content with assumption. If I want the door to turn, the hinges must stay put (OC 343).”

Not only do hinges make it possible for rational discourse, but they also set the limits of what can be reasonably doubted.

We're never going to come to a consensus on OC, that's clear. There will always be some interpretation that someone has that you'll disagree with. What's important is that Witt established that there are some very basic beliefs about the world (call them hinges, foundations, Moorean propositions, call them what you like) that are starting points for language games, a place where there is no need for justification.

I think this idea has ramifications beyond epistemology. I think it solves the problem posed by Godel's two theorems. These hinge beliefs seem to exist in any system where proofs are required, whether epistemological or mathematical. This of course goes beyond anything Witt talked about in OC, but I think it has merit.

My view is that Moore's assertion, "I know this is a hand," amounts to an expression of subjective certainty, i.e., akin to a conviction (which Witt points out) that he is certain without justification (although Moore thinks he's justified). The reason I add the subjective is that there is a use of certainty as a synonym for know, i.e., objective certainty.

There's always going to be a certain amount of cultural relativism.

Just as there is no fixed point from which we can observe the motion of the universe, there is no fixed foundation for our knowing. — Fooloso4

There is no fixed point, but there are fixed points within given contexts. You seem to add things not part of what I'm contending.

Anti-foundational foundations? — Fooloso4

Yes, if what you mean by anti-foundationalism, is traditional foundationalism. His presentation of a foundation is nothing like traditional foundationalism. It's a different way of thinking about the foundation. It's outside epistemological constructs, i.e., it supports and gives life to epistemology.

It's interesting to note that different language games reflect different endpoints. However, it seems to me that some endpoints are not really hinges, and the way we can see this is by asking if it makes sense to doubt one's endpoint. For e.g., I've listened to some philosophers who want to place belief in God in the same category as Witt's hinges, so within their language game, it's a given, in the same way, this is a hand is a given. However, there is an important test to see if your hinge is proper, viz., does it make sense to doubt that proposition? Compare this is a hand and belief in God, it's much more natural to doubt the latter. There is an exception, let's say you had a veridical encounter with God, then in that case it could be considered a hinge. However, trying to prove your experience would be very difficult indeed.

...but... — Sam26

The "but" wasn't meant to be a disagreement but an additional point.

I agree with you that our actions are an important part of all this, they reflect something very important. We cannot forget about what we do! Our forms of life reflect this.

"Doesn't this mean: I shall proceed according to this belief unconditionally, and not let anything confuse me?

"But it isn't just that I believe in this way that I have two hands, but that every reasonable person does.

"At the foundation of well-founded belief lies belief that is not founded (OC 251, 252, and 253)."

Again, these endpoints seem to be foundational.

They are foundational in regard to what we do with them. Their meaning is their use in a language agme. — Banno

Yes, but there is a sense where we are also forced into a foundational position if we want to play the game, whatever that game may be. However, this doesn't mean the foundation can't change, at least in some contexts.

"'Here I have arrived at a foundation of all my beliefs (OC 246)." This passage plays off of OC 245.

So, the analogy I use over and over again is to think of foundational in the same way that the rules of chess, the board, and the pieces are foundational. One doesn't need to justify these components they are just there as part of the background needed to play the game. The games rest on these components, i.e., they're foundational to the game. You can also think of language games in the same way, viz., resting on certain implicit and explicit rules within our forms of life.

:grin: No, it's a concept that has various uses in different contexts. I don't see how anyone can read OC and not see a foundational component to what Witt is saying. I've read quite a few papers on this subject and it comes up time and time again, so it's not unique to me.