So, I'll try and restate the topic subject to the question as to why the reader thinks Wittgenstein called Godel's Incompleteness Theorems, a logical trick?

What's your own understanding over Wittgenstein's comment about Godel's Incompleteness Theorems?

Sure, if all you wanted to point out was my misunderstanding of Godel's Incompleteness Theorems then you made your point. Rest assured your mockery of me is not something I would have thought that you would personalize your own authority over my ineptitude over the matter; but, carry on if you wish with your tirade about how your educated on the matter and I'm not. :lol:

What are the definitions of 'complete for a complexity class size' and 'consistent for a complexity class size' such that a logic can be complete and consistent for a complexity class size? — TonesInDeepFreeze

I don't mean to be snide; but, if you haven't acquainted yourself with the halting problem, then it would clarify any confusion about how definitions are stated and applied.

Wittgenstein's suggestion that 'The theory of knowledge is the philosophy of psychology' is an important statement. That is because the source human thinking is a central area for psychological investigation. This is at the core of the different models of psychology.. — Jack Cummins

I think that what one can figure from stating psychology in this way is that by having a body of knowledge upon which we can formulate bedrock beliefs or hinge propositions, one would be able to achieve the certainty that Wittgenstein sought in his own preponderance about psychology. After all, he wrote a whole book about certainty, which he needed for reasons only he would be able to explain.

As far as the idea of philosophy needing therapy, what this signifies is for a thinker to be more aware of the psychological basis of one's ideas and beliefs. Human motives and factors in socialisation are central to our philosophical understanding, alongside cultural beliefs. Being able to reflect on these aspects of one's beliefs and thoughts has an important place in philosophy. — Jack Cummins

Yes, socialization seems important; but, is it more important than individualization?

When I was undertaking some psychotherapy training, having therapy was seen as vital. That is because it enabled one to be aware of the 'blindspots' of thinking and one's beliefs. This is a significant area for philosophy, especially in self-knowledge, biases and becoming aware of one's own 'blindspots' , which can be a stumbling block to clear thinking. — Jack Cummins

I haven't encountered such a term as "blindspots" in therapy. I have heard about cognitive distortions or biases or thought patterns that are negative... Seems interesting to say that when philosophers engage in weltanschauung's or systems of thoughts one can fall into all sorts of mistaken beliefs or erroneous conclusions about how to perceive or "think about", as such.

He definitely pushed the experiment of the Tractatus—basically to only state what can be said with absolutely certainty—as far as he could, which demonstrated his intellect but also persistence to carry a line of thought all the way through, past where everyone else might rest on a first impression. Only such a thorough “mistake” (if we would even call it that) could lead to such a monumental revolution as the Investigations. — Antony Nickles

It was hardly a mistake, as some might think it was. Wittgenstein stated in the Investigations that many of his thoughts had been continued and expanded on from the Tractatus to the Investigations. I don't think he thought of the Tractatus as entirely a mistaken work; but, certain elements of it, such as the picture theory of meaning, were not adequate to answer the questions that occupied Wittgensteins mind.

Wittgenstein is looking at the mechanics of our interest and judgment through a concept—how it is identified, distinguished, satisfied. — Antony Nickles

Yes, although it would seem as though that the mechanics of what concepts are, are to this day a point in question. As I already stated, grammar seems to be the path to greater understanding rather than route logic which had been trying to solve as Wittgenstein sought out.

So one of the conclusions you are referring to is "incompleteness puts a hard limit on understanding the world"? — TonesInDeepFreeze

It is taken that incompleteness quashes Hilbert's program. — TonesInDeepFreeze

Well at the time Hilbert's program was one instance, as you say.

Are there any writers who you think are well paraphrased with that, and what writings of theirs do you have in mind? — TonesInDeepFreeze

I don't have any to provide.

Not only has it not been demonstrated that propositional logic is not the only logic adequate for that task, but it's overwhelmingly clear that propositional logic is not adequate for that task. — TonesInDeepFreeze

So, one may be able to do so in some other formal language?

What are complete and consistent, or incomplete or inconsistent are theories, not whatever "decidability for P v NP" is supposed to mean. — TonesInDeepFreeze

I'm of the understanding that for a complexity class size to be complete and consistent, such as P v NP, then everything within such a set constitutes a complete and formal theory.

Decidability for P verses NP, in computer science, is considered complete and consistent.

Not to disregard what you said; but, thank you for the clarification. I edited that post which you addressed because it was inaccurate.

Sure; well, I won't comment on the effect Godel had on logic and mathematics. There are intellectuals that still ponder about it to this day, since this is a fundamental problem of mathematics at the time when Godel made his discovery.
— Shawn

You referred to conclusions that were drawn. But you don't have any in particular to mention. — TonesInDeepFreeze

There are so many things various people have said about Godel's Incompleteness Theorems, which is telling about how mostly logicians and mathematicians have been influenced by Godel. What Godel said was so fundamental to the field of mathematics and how it was perceived by many as a hard limit on the ability to understand the world. I'm not a mathematician or logician, and am quite a novice at logic; but, I think that the implications of Godel on the future of computing hasn't really been addressed. My opinion about this is that as we advance our understanding of complexity class sizes in computing, then it seems possible that new ways of inference could be discovered. Logic has been a field most appreciated by computer scientists, along with the father of computing, Turing, describing Godel's Incompleteness Theorems as the halting problem.

An undecidable problem in logic is undecidable irrespective of how much time or memory you throw at the problem. The P versus NP issue only applies to problems that are at least logically decidable. — Tarskian

Yes; but, returning to what was said in the OP, then I believe that if logic is tautological, then the only constraints on systems of logic are the ways in which we try and change the principles of the formal system itself. So, I don't think we really know that the field of logic is over and there is nothing more to discover about it. We could always discover a way in which logic behaves in terms of differing terms defining how different formal systems interact. Given that physics and reality is composed of dimensions, I don't think it is farfetched to say that logic is not a field that can be described through one system like propositional logic, and as you said one could call propositional logic complete and even consistent for the complexity class size of P versus NP!

I'd like to add to my previous post, that the implications of incompleteness have been only demonstrated by incorporating new procedural rules into a system, which could not prove their use as consistent with regards to the principles of the formal system itself prior to adding the procedure. With that said, there could be formally complete systems that are consistent, which occupy their own logical space.

Now, everyone concluded that this was the end of the possibility of proving everything in logic, and even unifying logic with mathematics. I don't think this conclusion is the right one to draw. It would almost seem like the ad hoc ergo propter hoc fallacy.

One could always try and add new terms defining the formal system to add sophistication to the formal system itself to account for the new terms. It has not been demonstrated that propositional logic is the only logic that could accomplish the goals of unifying logic with mathematics or proving everything in logic alone.

The problem is logic itself: — Tarskian

I always thought the solution to the problem of certain logical systems needed to compute undecidable problems, is solved by appealing to greater complexity class sizes. This allows for other more sophisticated/robust systems of logic to be discovered instead of the inherent limitations of a formal system which is incapable of decidability.

This would imply that for every true statement about the physical universe, there exists a proof that can be derived from the supposedly canonical and categorical but unknown theory of the physical universe. — Tarskian

I do not like stating this in formal systems like Peano Arithmetic; but, rather in terms of decidability. By framing the question in terms of decidability, we do away with the problem of the inherent limitations of human intuition devising formal systems. This is a question model theorists might be able to prove, in my opinion.

I'm interested in your take according to the halting problem being avoided given the assumption that a sufficiently sophisticated computable logical system with the capacity to compute with an ever expanding alphabet, in hypothetical terms, would be able to simulate reality. Again, this is an ad hoc argument against incompleteness, if possible. I'd also like to mention that this is only true for completeness, not consistency given that there actually seem to be singularities in the fabric of spacetime, according to Einstein, Hawking, and Penrose.

No, Godel proved a meta-theorem regarding formal systems of a certain kind, including PA. The proof of that metatheorem can be done in various formal systems or done in ordinary informal mathematics, as is the case with Godel's original proof. — TonesInDeepFreeze

Yes, well I think you are referencing Rosner? Can you provide the reference?

Moreover, the proof make use of only finitistic, intuitionistically acceptable principles. — TonesInDeepFreeze

Yes, I would like to point out that I am not denying the logical validity of Godel's Incompleteness Theorems. I am only suggesting that the impact or the conclusions mathematicians reached at the time were too profound to the field of mathematics.

Incompleteness is a property of certain formal systems. I don't know what it means to say that nature is or is not complete. — TonesInDeepFreeze

Einstein had discussions with Gödel about how singularities and indeterminism could partake in physics and nature, which made him think nature was "incomplete," for lack of a better word.
— Shawn

Who used the word, for lack of a better one? And what is your source? — TonesInDeepFreeze

Well, at the time, many physicists were of the opinion that mathematics governs physics. So, I hypothesized that Einstein was aware of Godel's Incompleteness Theorems, since they had many discussions between each-other. I can only imagine that Einstein was interested in Godel's thoughts about physics according to Godel given his Incompleteness Theorems.

What "conclusions" do you have in mind? The incompleteness theorem is a mathematical theorem with mathematical corollaries. Of course, some people make philosophical inferences based on the theorem, but such inferences are not of the mathematical theorem itself. — TonesInDeepFreeze

Sure; well, I won't comment on the effect Godel had on logic and mathematics. There are intellectuals that still ponder about it to this day, since this is a fundamental problem of mathematics at the time when Godel made his discovery.

The defintion of 'formal language' includes that the language is countable. — TonesInDeepFreeze

There are potentially infinitely countable alphabets that could allow one to continuously expand the alphabet by including new terms in the formal system itself according to the principles of the formal system itself. Maybe model theory would be able to simulate reality with this possibility in mind. Regarding which:

4.01 [...] A proposition is a model of reality as we imagine it.

I'm not sure you know what that means, in a philosophical context. — Banno

Whatever works. I've seen this countless times of someone pointing out a logical fallacy and the other person just deflecting it. Anyway, thanks for the conversation.

I'm really not following any of this. — Banno

Well, you begged the question so many times about what are concepts, that I'm not surprised.

I think we can agree @Banno that concepts are human abstractions, yes?

I've no idea what that might mean. I'll leave you to it. — Banno

Here, I hope you can look at the article on ontological commitment entailed by universal quantification for "concepts":

https://plato.stanford.edu/entries/ontological-commitment/

I'll point out that if concepts are not things, then what would you identify them as? It seems that I am begging the question, now.

Concepts are not things! — Banno

...this is again nominalism
— Shawn

How? — Banno

If concepts are not things, then they do not have any ontology. The existence of a universal, which concepts would not have, according to what you are saying, would exclude concepts from having any ontology. Thus, one can think, from this, that concepts are criteria or identity features of human abstraction, which I don't really buy into.

I don;t see how one could disagree with universal quantification... — Banno

Yes, well, I will say that if concepts are truth-apt under universal quantification, then it would follow that concepts have the property of being a 'thing'.

No! That's not what it says. Rather, concepts are what we do. The difference is central. Concepts are not things! — Banno

Yes, well, this is where I agree with universal quantification and would subscribe to some form of ontology to what concepts are and how they derive their meaning.

Treat this as an example in which the malady is misunderstanding the notion of concept, and the treatment is to show that concepts are what we do, and not things. — Banno

Sure, this is again nominalism. So, if all there is to concepts is specific or stipulated use, then do we do away with universal quantification?

It is clear Wittgenstein is rejecting any notion of treating words as just names, and that concepts are about use, not just grammar. — Banno

Yes, concepts are used in different ways. The way we use words is largely defined by grammar, and that's just a factual definition. So, I don't understand the issue about grammar and use of words, if you may think there is one.

Midgley's plumbing metaphor might show the point better than Wittgenstein's therapy metaphor. — Banno

I think philosophy has a purpose, which, as she describes is of need towards other fields to reinterpret what progress those other fields attain. After all philosophy is probably as old as religion, and is valued for endowing other fields with meaning through its own activities.

So what sort of thing is a concept? — Banno

There's no need to beg the question. If you're looking for a specific answer, then go ahead, provide one.

What more is there to any given concept than what we do? — Banno

Sure; but, words aren't objects. I'm mostly interested in abstract concepts, which science has been elucidating, and providing us with knowledge about the world; but, since this thread is about the point or "need" for therapy, then I would like to return to the topic about whether you think philosophy has taken Wittgenstein's lesson to heart?

Are philosophers still in need of therapy?

But "And the question will then arise whether we are still willing to use the concept of 'calculating in the head' here—or whether in such circumstances it has lost its purpose, because the phenomena gravitate towards another paradigm." — Banno

Again, I am not interested in the complexity of the external aspect of a concept, this is something that Austin described with speech acts and stuff like that.

It seems you think a concept is something only in one's mind, a rule to be followed. Do you think Wittgenstein would agree? — Banno

No. One cannot speak a language without being taught about how to use words and phoneticize sounds for the words. It's a whole can of worms that I am not really interested in delving into at the moment.

So concepts have "internal" and "external" aspects? We might leave aside for now how it is possible to talk about these "internal" aspects, and suppose that the grammar, since it is shared, is "external". See PI §385. — Banno

Sure; but, if we're to talk about how Wittgenstein saw it, then I would like to mention his concern with how rules are followed and obeyed. I think that we can nowadays say that grammar and syntax are what define such "rules". So, I think, there is some internal aspect of how learning can at all take place...

What do you make of PI §381-2? This by way of addressing your "what other factors are associated with concepts apart from grammar?" — Banno

Are you alluding to qualities of concepts, which describe them? There are quite a few...

Consider the concept blue, the concept democracy, and the concept of cycling. What do these have in common such that we can call them all concepts? — Banno

Yes, well, every concept is defined by what rules govern their use in a language game. I don't think these rules exist outside the hypothetical realm of what constitutes what can be said, according to grammar.

Concepts are (perhaps) governed by grammar, but isn't something more involved? — Banno

Well, what is your take on the matter on what other factors are associated with concepts apart from grammar? If it is all about the externalities of the topic, then I'm only concerned with the internal aspect of how concepts are understood.

So you say sharing a common grammar makes it possible for us to understand concepts. — Banno

It sounds oversimplified, and there's much more to say; but, sure, by having a common grammar we are able to understand even concepts.

What are concepts? — Banno

From the inner aspect, they are governed by grammar. From the external aspect, they are determined by linguistic rules.

Is your next question going to be about what are "linguistic rules"?

What do you think a concept is? A thing in your head? — Banno

I never really approached this question the way others do. I've always held that by obeying the same grammar, which allows people to coherently formulate their thoughts in language, we are able to understand what Wittgenstein calls, "concepts as words."

Then how is it that you and I can be said to have the same concept? — Banno

I think it would be easier to frame this question in terms of syntax and grammar, as per the aforementioned.

About the passage of the Philosophical Investigations, I/§383, regarding "concepts as words" and Wittgensteins nominalism.

Is there a loophole in this rule regarding using Gemini? Gemini is Google's AI algorithm that condenses a search result to a paragraph or two.

Since Google is the standard and largest in scope of knowledge and information with Gemini, then would it pass?

Also, Gemini doesn't plagiarize output, as it is gathered from multiple open sources.

In comparison to the Tractatus, which, as you point out, held everything that could be said to make sense to a generalized standard for truth [...] — Antony Nickles

Yes, dare one say this approach was almost taken to "scientific" standards. Yet, I feel as though it was a work guided by sheer intelligence, to state what was said. Wittgenstein often complained in his letters that if only he had a greater intelligence, then his task of elucidations in philosophy would have been possible or achievable.

In your other post you ask “what is the difference here being made about 'phenomena' and 'concepts about phenomena'?” It is explaining his method, not a different approach to the world. He is not avoiding phenomena, but he is looking at what we say about something because that tells us how we judge it. — Antony Nickles

Yes, well let us start out with perhaps the only clue left in the Investigations about what it is all about:

'We are not analyzing a phenomenon (e.g. thought) but a concept (e.g. that of thinking), and therefore the use of a word. — (L. Wittgenstein Philosophical Investigations, I/§383)

So, how can a concept stand for a word? This strikes me as pragmaticism. Is this really an implicit reference to pragmatism in the Philosophical Investigations?

@Banno, may I kindly ask, what do you think?

Here is the quoted passage from the Investigations on what, seemingly, Wittgenstein continued in his methodology between his earlier period and latter period:

'We are not analyzing a phenomenon (e.g. thought) but a concept (e.g. that of thinking), and therefore the use of a word. So it may look as if what we were doing were Nominalism. Nominalists make the mistake of interpreting all words as names, and so of not really describing their use, but only, so to speak, giving a paper draft on such a description'. — (L. Wittgenstein Philosophical Investigations, I/§383)

Here's an old thread of mine.

https://thephilosophyforum.com/discussion/2452/wittgenstein-and-nominalism

Wittgenstein starts with this kind of singular logical standard in the Tractatus, what he later will call purity, and then in the Investigations he realizes that each different thing has its own criteria. — Antony Nickles

What do you mean by "its own criteria"?

I view it as methodological nominalism, which the Investigations appealed to.

133. It is not our aim to refine or complete the system of rules for
the use of our words in unheard-of ways.
For the clarity that we are aiming at is indeed complete clarity. But
this simply means that the philosophical problems should completely
disappear. — Philosophical Investigations

I believe that what Wittgenstein was alluding to, in modern terminology, was the study of syntax and linguistics. In those fields, what Wittgenstein said in the quote, do rules in language make any sense. Had Wittgenstein been alive today, do you think he would have been interested in syntax and linguistics? Noam Chomsky's greatest idol was Bertrand Russell after all, as was Russell the closest friend to Wittgenstein.

Yes, I was using "philosophy" and "philosophers" rather interchangeably. I was rather highlighting the contrast between philosophy being in need of therapy (as if something was wrong with philosophy) and the philosophical process being akin to therapy. I was stressing the second idea although Wittgenstein might very well have meant it both ways. — Pierre-Normand

I believe he meant it both ways at the time. Although people consider the first analytic philosopher as Bertrand Russell, I think the logical positivists were actually the first, and hence Wittgenstein the chief logical positivist of them all, as they themselves would credit to him. I say this because at the time there was very little of the study of logic, which both Bertrand Russell and Wittgenstein were logicians. So, it seems pertinent to point out that Wittgenstein thought that the field of philosophy was leading him into mental cramps, and the process of education wasn't leading anywhere in his mind. It might be sad to say that Wittgenstein may have been an unhappy man upon his death.

Didn't W simply mean that philosophy clarified conceptual issues for philosophical problems in much the same way that therapy is meant to provide insight into life challenges?

This only holds true if you believe that a lack of conceptual clarity is causing you harm. As someone who views truth and reality as either largely out of reach or contingent human constructs, I find that there’s only so much clarification I am interested in. — Tom Storm

I think, with what you said in mind, Wittgenstein was very strict, in the Tractatus, about drawing a line between science and philosophy, for reasons related to mostly ethics. This demarcation left out the field of psychology, as I understand it. What Wittgenstein did do was something, to me, ridiculous. He set up the study of psychology (remember, in those days, psychology was treated as the study of the human soul, which Wittgenstein actually talks about also in the Tractatus) to the field of epistemology, and thus denies the existence of a "soul". It would almost seem that the only purpose of any person would be the development of one's knowledge to discover who they are, as does the whole purpose of education should be about, which Wittgenstein harshly criticized education itself, even though he was a teacher himself.

I had interpreted Wittgenstein's claim about philosophy and therapy (there may be more than one?) not so much as a claim that philosophers are in need of therapy than a claim that achieving conceptual clarity in philosophy is akin to therapy. — Pierre-Normand

I think that the practice of philosophy and the philosopher are one and the same, according to Wittgenstein's ethos.

The reason for this is that philosophers confronts conceptual puzzles that stem from their deeply ingrained habits of thinking (many of them arising from subtle misuses of ordinary language). — Pierre-Normand

Yes, well the bewitchment of our intelligence by the misuse of language, according to the latter Wittgenstein of the Investigations, is due to what, in your opinion?

Does an all good being like evil? — Leontiskos

Did the conspiracy between good and evil against Job make any sense to you?

June Alice Morelli (University of Venice) ‘The Mark of the Dispositional: Broad, Ramsey and Wittgenstein’ — Antony Nickles

Ooo, a Stoic slant on Wittgenstein...

Thanks for this.