Spiritual Logicism

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04.07.2023 01:41PM

Spiritual logicism is my term for my philosophy of the universe. I hope to be able to get into some interesting discussions about it and the nature of reality generally here. There is a lot to unpack, so I suggest reading this a little bit at a time, and feel free to comment and specific parts of it without having read the whole thing. I don't want to bore you!

Spiritual logicism

Part 1: The basic idea.

Logicism is a pre-existing philosophy of mathematics. (We'll get back to reality in general momentarily.) I'm not going to define it here, but instead recommend reading this webpage for more information. The reason I omit the definition is that I would instead like to present my own version of logicism somewhat strengthened from even strong logicism: All of mathematics is an extension of logic. Not just certain fields, and not just mathematical truth, all of mathematics. This still isn't too radical of an idea, but spiritual logicism is, in my experience, basically unheard of. Here is my definition:

Spiritual logicism: The belief that spiritual truths about the universe can be understood as, and fundamentally are, an extension of abstract logic. An extension of logicism to the nature of reality.

Part 2: Why?

One could reasonably ask how on earth I would come to such a conclusion. As such, I don't just want to go straight to explaining the ramifications of such a belief system, but rather want to begin by explaining how I came to believe what I do. I have always wanted to understand the deeper truth about the universe, and having a mathematical/logical background I realized that to conclude anything, I would need at least one assumption. My goal, however, was to minimize assumptions. In the end, I settled on one and only one assumption, but it soon became clear just how vast the implications were. I present, the truth premise:

The truth premise: There is a valid and complete notion of truth.

Despite how short it is, there is a lot to unpack. First of all, there is an issue here: The truth premise asserts itself as true, before any sort of notion of truth has been established. My resolution to this: Ignore it. Performing some sort of bootstrap here is entirely necessary. We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of. Now let's break down what the truth premise really means. There are two key words: Valid and complete.

Valid: Consistent and sound.

Complete: Capable of assigning every objective and meaningful statement a truth value of true or false.

Consistent: Containing no contradiction. No statement is both true and false.

You may have noticed that I have omitted the definition of soundness. In logic, the soundness of a set of axioms means that they imply only true results. The issue here is that we are trying to obtain a notion of truth in the first place. Soundness as it is used here is to say that if there is any sort of underlying truth structure within the universe, this notion of truth is consistent not only with itself, but with this underlying truth structure. It is not clear what such a structure would be, but nonetheless it is an important precaution. Now, why should we accept the truth premise? Put simply: We need it. Without the truth premise, it is impossible to conclude anything. Let's suppose we put together some other set of assumptions that did not include the truth premise. Without the truth premise, an assertion of their truth wouldn't even be meaningful. We need a meaningful notion of truth as described in the truth premise. If someone wants to see it, I will explain why each assumption on the notion of truth is necessary for meaningful deductions to be made, but for now I will omit the specifics. Now, reasonably, we should be able to define binary functions (such as and, or, not, etc.) and have a meaningful notion of certain statements about them being true. Let's define f to be the or operation for an example. Then f(0,0) = 0, f(0, 1) = 1, f(1, 0) = 1, and f(1, 1) = 1. Reasonably, these should all by definition be true statements. This could be considered to fall under the soundness condition, where, for an example, f(0, 0) = 0 must be considered to be true, because the value of f(0, 0) is by definition 0. Replacing 0 and 1 with the truth values T and F we can rewrite these values as f(F, F) = F, f(F, T) = T, f(T, F) = T, f(T, T) = T. We now get propositional logic. We can show, for example, that P implies P or Q. (I can't type logical connectives, so I'll just use words.) We create a truth table:

P = F, Q = F: P or Q = F or F = F, P implies P or Q = F implies F = T.

P = T, Q = F: P or Q = T or F = T, P implies P or Q = T implies T = T.

P = F, Q = T: P or Q = F or T = T, P implies P or Q = F implies T = T.

P = T, Q = T: P or Q = T or T = T, P implies P or Q = T implies T = T.

So in all cases P implies P or Q is true. At this point, we have seen that any notion of truth as in the truth premise should include propositional logic, and thus that we can consider the axioms of propositional logic can be considered a part of our definition of truth. It is possible that this notion of truth, to satisfy completeness, needs to include other axioms. Recall that completeness requires that our notion of truth assigns true or false to every "meaningful and objective" statement. To uncover what this means for our notion of truth, let's take a quick detour to another belief. Some people hold the belief that they are imagining the entire universe, and that it is all within their head. While this doesn't seem particularly reasonable, we can't prove them wrong with empirical evidence. The key thing to realize is that in different contexts, there are different reasonable/useful assumptions. Another example would be mathematics, in which we (at least in most areas of math) assume the nine axioms of ZFC. In conclusion, the notion of truth described in the truth premise can be thought of as all possible extensions of propositional logic, where we must specify the context (which extension it is in reference to) of any non-tautological truth.

Part 3: Axiomatization and conceptualization.

We left off with the conclusion that truth can be viewed as all possible extensions of propositional logic. Namely, with certain additional axioms, we should be able to describe our own reality. This leads us to the axiomatization principle:

The axiomatization principle: The reality we live in can be entirely described by a set of axioms.

At this point, spiritual logicism is an obvious conclusion. So what are these mysterious axioms? Well, we don't know, but one could view science as the field which searches for this answer. Science attempts to find the laws by which the universe abides by studying it from the inside. Our best guess at the moment is probably M-theory. The laws of M-theory can be seen as a candidate for the set of axioms which define our universe. This notion of truth also has another critical implication. Concepts separate from reality are just as real as it, so long as they are well-defined. One such example is math. The reason math is an important example is that it also relates to our reality. This demonstrates how concepts separate from our reality being just as real as it could potentially have some very big implications. At this point, we approach the realm of more specific conclusions about the nature of reality, of which there are many, so I will leave it at this for now, as this has gone on long enough.

oromagi

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oromagi

04.07.2023 04:46PM

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@ebuc

ebuc made a baby!

Best.Korea

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Best.Korea

04.07.2023 05:43PM

Cute

b9_ntt

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b9_ntt

04.07.2023 06:45PM

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@Math_Enthusiast

Spiritual logicism: The belief that spiritual truths about the universe can be understood as, and fundamentally are, an extension of abstract logic.

What does spiritual mean to you? What is a spiritual truth?

... An extension of logicism to the nature of reality.
... with certain additional axioms, we should be able to describe our own reality.
... The reality we live in can be entirely described by a set of axioms.

Are you asserting that there is one reality for everyone? that everyone shares one and only one reality?

Debates: 22

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04.08.2023 07:42AM

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@Math_Enthusiast

Hmmmmm.

Everything is internal,

Externality is an assumption converted from incoming signalling.

Spirituality is a notable reaction to a specific stimuli.

Logic is how data is ordered.

And truth is determined by the self,

Or externally, truth is an indeterminate factor of what we assume.

Nonetheless, perhaps an actual human being will one day visit Mars.

Just as a few have visited the Moon, I think.

Such is the nature of what we might conclude to be reality.

Debates: 18

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04.08.2023 01:56PM

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@Math_Enthusiast

https://youtu.be/5hfYJsQAhl0

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04.09.2023 01:37PM

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@Math_Enthusiast

Spiritual logicism is my term for my philosophy of the universe. I hope to be able to get into some interesting discussions about it and the nature of reality generally here. There is a lot to unpack, so I suggest reading this a little bit at a time, and feel free to comment and specific parts of it without having read the whole thing. I don't want to bore you!

Going to do just that, my response toPart 1 follows, then I'm off to Helen Georgia for an Easter nature day in the mountains. Looking forward to coming back to this post later for that all too rare interesting discussion on this board.

Spiritual logicism

Part 1: The basic idea.

Logicism is a pre-existing philosophy of mathematics. (We'll get back to reality in general momentarily.) I'm not going to define it here, but instead recommend reading this webpage for more information. The reason I omit the definition is that I would instead like to present my own version of logicism somewhat strengthened from even strong logicism: All of mathematics is an extension of logic. Not just certain fields, and not just mathematical truth, all of mathematics.

But who shaves the barber?

As a math enthusiast, you know that Godel put a bullet right between the eyes of Logicism, it fell to the self-referential paradox, even after Russell’s do over with the Principia, the attempt to reduce mathematics to logic clearly failed.

Gödel proved that it is logically and scientifically impossible to devise a set of axioms from which all the phenomena of the external world can be deduced.

This still isn't too radical of an idea, but spiritual logicism is, in my experience, basically unheard of. Here is my definition:

Spiritual logicism: The belief that spiritual truths about the universe can be understood as, and fundamentally are, an extension of abstract logic. An extension of logicism to the nature of reality.

While Godel proved that you cannot extend logic to the nature of reality completely and consistently, but in doing so, he also provided a proof that stands logically in support of faith in a transcendent reality.

Kurt Gödel’s Incompleteness Theorem is analytically perfect and rigidly deductive and therefore it is conclusive as far as logic and science are concerned. The incompleteness theorem states categorically that no axiomatic system is, or can be, complete without reference to a higher system in which that system must be embedded. Therefore, the presumed ideal of science is impossible, it is logically and scientifically impossible to devise a set of axioms from which all the phenomena of the external world can be deduced.

Since any representation of logic and science as somehow complete systems, or statements that contend that logic and/or science constitute comprehensive representations of reality have been proven to be logically and scientifically incorrect. As far as Science and Logic are concerned then, faith in a transcendent reality is more true to reality than logic and science can be.

Faith is essentially belief in a higher system, it postulates a transcendent reality in which we live and move and have our being. Kurt Gödel provided a proof that the act of having faith in a greater reality in which the normal world of logic and science is embedded is a more logical and scientifically, a more true representation of reality.

Werner Heisenberg confirmed that uncertainty is a feature of reality with his own proof in the physical sciences. Each and every unified theory, which is to say every scientific attempt at unifying and completing physical theory, postulates other dimensions in which this reality is embedded, every one of them, as and perhaps because, Kurt Gödel logically proved that they must.

It follows that the common assertion of our spiritual detractors, that you can’t believe in a non-physical existence or a transcendent reality without proof has been “proven” by Kurt Gödel to be illogical and unscientific, it’s OK to do it, but it should be recognized as a faith-based assertion rather than a logical, rational, or scientific premise. When our spiritual detractors typically speak with certainty that faith is illogical and unscientific, that is more of a faith based religious belief than anything resembling a logical or scientific premise.

FLRW

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FLRW

04.09.2023 02:39PM

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@Sidewalker

Yes, Godel's theorem is about arithmetics. Metaphysics and a fortiori Reality are not reducible to arithmetics. I wish people stopped using science they don't understand to support every other ill-defined metaphysical claim they have.

Topic's author

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04.09.2023 10:41PM

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@oromagi

Please don't lure ebuc over here. I thought that I would get along well with them for obvious reasons, but no.

Topic's author

#10

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04.09.2023 11:11PM

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@b9_ntt

Spiritual logicism: The belief that spiritual truths about the universe can be understood as, and fundamentally are, an extension of abstract logic.
What does spiritual mean to you? What is a spiritual truth?

A good question. The answer is probably going to be somewhat disappointing: Nothing in particular. The reason I use it, is to emphasize that, as I will likely discuss in a later post, this position of everything being based upon logic, does not make the universe a "cold hard" place. It can actually lead us to some interesting conclusions about, for an example, what happens after death.

... An extension of logicism to the nature of reality.
... with certain additional axioms, we should be able to describe our own reality.

... The reality we live in can be entirely described by a set of axioms.
Are you asserting that there is one reality for everyone? that everyone shares one and only one reality?

I assume you would beg to differ. I'll grant you that there are certain things that are experienced in a particular way by exclusively one person, but in terms of objective reality, yes, I am asserting that. If you would like to propose an argument that we don't all share the same reality, I would be interested!

Topic's author

#11

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Posts: 184

04.10.2023 12:32AM

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@zedvictor4

Everything is internal,

Externality is an assumption converted from incoming signalling.

Spirituality is a notable reaction to a specific stimuli.

I'm honestly not sure what you are saying by any of this.

Logic is how data is ordered.

How so?

And truth is determined by the self,

How do you argue?

Or externally, truth is an indeterminate factor of what we assume.

Nonetheless, perhaps an actual human being will one day visit Mars.

Just as a few have visited the Moon, I think.

Such is the nature of what we might conclude to be reality.

I'm frankly a bit confused by the phrase "indeterminate factor of what we assume." Answer me this: Do you accept the truth premise as defined in my original post? If not, why not?

Topic's author

#12

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04.10.2023 12:41AM

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@PREZ-HILTON

I have to say, that was kind of funny, and it frankly made me happy. I wanted my ideas to be challenged, and I figured that they would be, so please do tell me some of your objections. At least answer me these two questions:

Do you accept the truth premise? (See my original post for a definition.)
Do you have any objections to my reasoning following the truth premise.

Of course I would like to hear your reasoning if you would care to offer it. If you have anything that you are confused on, or anything that you want me to clarify on, please tell me.

Topic's author

#13

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04.10.2023 12:46AM

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@Sidewalker

As a math enthusiast, you know that Godel put a bullet right between the eyes of Logicism, it fell to the self-referential paradox, even after Russell’s do over with the Principia, the attempt to reduce mathematics to logic clearly failed.

Gödel proved that it is logically and scientifically impossible to devise a set of axioms from which all the phenomena of the external world can be deduced.

I do know of Gödel's incompleteness theorem. It is commonly misunderstood. It says nothing about the external world. I suggest this website.

#14

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04.10.2023 01:53AM

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@Math_Enthusiast

P = F, Q = F: P or Q = F or F = F, P implies P or Q = F implies F = T.

P = T, Q = F: P or Q = T or F = T, P implies P or Q = T implies T = T.
P = F, Q = T: P or Q = F or T = T, P implies P or Q = F implies T = T.
P = T, Q = T: P or Q = T or T = T, P implies P or Q = T implies T = T.

This looks like gobbledygook to me. I kind of had to stop reading there.

Prior to that statement, it feels like you are using words in a confusing way and likely taking simple concepts and doing the opposite of what Richard Feynman did.

I will give the following example of something that bothered me before a gave up on trying to understand what sounded to me something similar to the word salad schizophrenics use. I listened to terrance Howard try to explain a math concept he invented where he explains 1+1 equals zero and it takes a similar tone as the post above.

The truth premise: There is a valid and complete notion of truth.

The statement above for example means nothing. There is also a valid and complete notion about what spaghetti is. Who cares. That's neither a statement of a position or really much of a position itself.

Now either the statement is gobbledygook or you are using a different definition for the words, particularly the word "truth" than the average lay person would use.

#15

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04.10.2023 01:56AM

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@Math_Enthusiast

Out of curiosity are you into Buckminster Fuller and his butchering of the English language like ebuc is. I know you said you guys don't get along but I was wondering if both of you are inspired by him which makes me not have the necessary background to make sense of your writing

#16

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04.10.2023 02:03AM

Reading the philosophy paper you linked now to see. If that helps me understand this.

Topic's author

#17

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04.10.2023 02:36AM

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@PREZ-HILTON

Post #14:

This looks like gobbledygook to me. I kind of had to stop reading there.

Unfortunately, this site does not have a feature to type math equations, or to make tables. This chunk of letters, equals signs, colons, and commas was intended to be a truth table. I understand your confusion though.

The truth premise: There is a valid and complete notion of truth.
The statement above for example means nothing. There is also a valid and complete notion about what spaghetti is. Who cares. That's neither a statement of a position or really much of a position itself.

You are correct in that on its own it is meaningless. This is why I went on to elaborate:

Despite how short it is, there is a lot to unpack. First of all, there is an issue here: The truth premise asserts itself as true, before any sort of notion of truth has been established. My resolution to this: Ignore it. Performing some sort of bootstrap here is entirely necessary. We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of. Now let's break down what the truth premise really means. There are two key words: Valid and complete.

Valid: Consistent and sound.

Complete: Capable of assigning every objective and meaningful statement a truth value of true or false.

Consistent: Containing no contradiction. No statement is both true and false.

You may have noticed that I have omitted the definition of soundness. In logic, the soundness of a set of axioms means that they imply only true results. The issue here is that we are trying to obtain a notion of truth in the first place. Soundness as it is used here is to say that if there is any sort of underlying truth structure within the universe, this notion of truth is consistent not only with itself, but with this underlying truth structure. It is not clear what such a structure would be, but nonetheless it is an important precaution.

Post #15:

I find ebuc just as difficult to read as you do. I was able to let it slide at first, but after a while ........//{this} kind ofthing gets pretty confusing.

Post #16:

Probably not. It was in response to Sidewalker's post, and was for the purpose of correcting misunderstandings on Gödel's incompleteness theorem.

Topic's author

#18

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04.10.2023 02:37AM

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@PREZ-HILTON

Whoops, sorry! I just realized that I also had a link in my original post, which is probably what you meant! Yes, that should help!

#19

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04.10.2023 07:08AM

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@Math_Enthusiast

Define the truth premise a little more clearly, so that it can be better appreciated by your audience.

Are you comparing truth with reality.

If so...Reality according to what?

Internal data processing, or immediate internally processed appreciations of external stimuli.

In both cases, simulated truths or realities.

Or perhaps just simulations

Math just converts to numbers.

But for the most part we have to convert back again to an understandable narrative or image.

Perhaps this is where A.I. will have the edge. (Alternative Intelligence)

What do you think?

#20

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Posts: 2,806

04.10.2023 09:30AM

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@Math_Enthusiast

We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of.

Why are you saying this? Why is this not written as follows.

We accept the truth premise as true

Why do you add

Within the valid and complete notion of truth.

Your truth premise almost sounds like you are just trying to say

The truth is true

To that ai would have to say obviously.

Let's check your definition again.

The truth premise: There is a valid and complete notion of truth.

Notion means - a belief about something

Valid means - true

So you are saying there is a true belief in complete truth.

Which also could be shortened to.

There is a belief in truth.

What exactly are you trying to get at here?

#21

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04.10.2023 09:31AM

Yes I agree with your truth premise that a belief exists that the truth is true. I think most people accept that axiom.

#22

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04.10.2023 09:35AM

I see you redefined valid below the statement but it doesn't help much with comprehension.

#23

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04.10.2023 10:50AM

It might take too much to get me to where you are. You might want to reconsider trying to teach me this. If you are patient though, than much appreciated

#24

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04.10.2023 11:53AM

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@PREZ-HILTON

One cannot believe that truth is true without casting doubt.

Which is not to say that one cannot believe that truth is true.

One can believe anything, wherein truth is unknowable and doubt is therefore built into the equation.

Topic's author

#25

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04.10.2023 01:24PM

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@zedvictor4

Define the truth premise a little more clearly, so that it can be better appreciated by your audience.

That is what the section of the post that I have quoted below is for. As I was saying to PREZ-HILTON, on it's own, my definition of the truth premise is entirely meaningless. It needs to be elaborated upon for it to be useful and meaningful.

Despite how short it is, there is a lot to unpack. First of all, there is an issue here: The truth premise asserts itself as true, before any sort of notion of truth has been established. My resolution to this: Ignore it. Performing some sort of bootstrap here is entirely necessary. We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of. Now let's break down what the truth premise really means. There are two key words: Valid and complete.

Valid: Consistent and sound.

Complete: Capable of assigning every objective and meaningful statement a truth value of true or false.

Consistent: Containing no contradiction. No statement is both true and false.

You may have noticed that I have omitted the definition of soundness. In logic, the soundness of a set of axioms means that they imply only true results. The issue here is that we are trying to obtain a notion of truth in the first place. Soundness as it is used here is to say that if there is any sort of underlying truth structure within the universe, this notion of truth is consistent not only with itself, but with this underlying truth structure. It is not clear what such a structure would be, but nonetheless it is an important precaution.

Are you comparing truth with reality.

Yes, you could say that. They are two sides of the same coin. Truth should describe reality, and reality should contain that which truly is. I don't think I worded that too well, so let me elaborate. It is true that 1 + 1 = 2, so 1 + 1 = 2 in reality. Similarly, 1 + 1 = 2 in reality, so it is true that 1 + 1 = 2.

If so...Reality according to what?

Reality according to truth! One of the ideas that is central to my entire concept is that to identify what reality really is, we first need to identify what it really means for something to be true.

Internal data processing, or immediate internally processed appreciations of external stimuli.

In both cases, simulated truths or realities.

Or perhaps just simulations

What? I don't follow. Is this something to do with the simulation hypothesis?

Math just converts to numbers.

Perhaps from the math you have encountered it converts to numbers, but not everything in math is about numbers. Topology, abstract algebra, set theory, category theory, and proof theory are not about numbers.

But for the most part we have to convert back again to an understandable narrative or image.

Yes, like logic.

Perhaps this is where A.I. will have the edge. (Alternative Intelligence)

I'm not sure what you mean here.

Topic's author

#26

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04.10.2023 01:45PM

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@PREZ-HILTON

We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of.

Why are you saying this? Why is this not written as follows.

We accept the truth premise as true
Why do you add

Within the valid and complete notion of truth.

At this point in the post, I was just establishing that truth is even meaningful, so if I didn't say "within the valid and complete notion of truth," this would just be meaningless. Let me give an example: A relativist may agree with me that something is true in some subjective manner, but they would be less likely to agree that it was true within this particular notion of truth.

Notion means - a belief about something

Valid means - true

So you are saying there is a true belief in complete truth.

Which also could be shortened to.

There is a belief in truth.

What exactly are you trying to get at here?

"Notion," "valid," and "complete" are not to be interpreted as usual here. They are being used as terminology for this particular purpose, because I don't want to have to write a whole paragraph every time I want to talk a bit about one of these concepts. Elaboration upon what is meant by "valid," and "complete" can be found in the below quote. I never said much about "notion," but I basically just meant "concept of."

Despite how short it is, there is a lot to unpack. First of all, there is an issue here: The truth premise asserts itself as true, before any sort of notion of truth has been established. My resolution to this: Ignore it. Performing some sort of bootstrap here is entirely necessary. We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of. Now let's break down what the truth premise really means. There are two key words: Valid and complete.

Valid: Consistent and sound.

Complete: Capable of assigning every objective and meaningful statement a truth value of true or false.

Consistent: Containing no contradiction. No statement is both true and false.

You may have noticed that I have omitted the definition of soundness. In logic, the soundness of a set of axioms means that they imply only true results. The issue here is that we are trying to obtain a notion of truth in the first place. Soundness as it is used here is to say that if there is any sort of underlying truth structure within the universe, this notion of truth is consistent not only with itself, but with this underlying truth structure. It is not clear what such a structure would be, but nonetheless it is an important precaution.

#27

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Posts: 2,070

04.10.2023 02:10PM

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@Math_Enthusiast

As a math enthusiast, you know that Godel put a bullet right between the eyes of Logicism, it fell to the self-referential paradox, even after Russell’s do over with the Principia, the attempt to reduce mathematics to logic clearly failed.

Gödel proved that it is logically and scientifically impossible to devise a set of axioms from which all the phenomena of the external world can be deduced.
I do know of Gödel's incompleteness theorem. It is commonly misunderstood. It says nothing about the external world. I suggest this website.

You don't need to explain Godel to me, the incompleteness theorem speaks directly to "logicism" and your so called "truth premise", hence it explicitly applies as used.

It only "says nothing about the external world" if you accept that logicism says nothing about the real world, you are refuting your own argument.

#28

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04.10.2023 02:41PM

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@Math_Enthusiast

Part 2: Why?

One could reasonably ask how on earth I would come to such a conclusion. As such, I don't just want to go straight to explaining the ramifications of such a belief system, but rather want to begin by explaining how I came to believe what I do. I have always wanted to understand the deeper truth about the universe, and having a mathematical/logical background I realized that to conclude anything, I would need at least one assumption. My goal, however, was to minimize assumptions. In the end, I settled on one and only one assumption, but it soon became clear just how vast the implications were. I present, the truth premise:

The truth premise: There is a valid and complete notion of truth.

It isn’tvalid to just declare truth, especially when your declaration of truth is self-referential,and particularly when there is a valid “proof” that explicitly refutes it.

Despite how short it is, there is a lot to unpack. First of all, there is an issue here: The truth premise asserts itself as true, before any sort of notion of truth has been established. My resolution to this: Ignore it.

Whenyou have truth by proclamation, and you simply ignore contradiction, it isn’t alogical argument anymore.

Performing some sort of bootstrap here is entirely necessary. We effectively just accept the truth premise as if it has already been established as true within the valid and complete notion of truth that it assures the existence of. Now let's break down what the truth premise really means. There are two key words: Valid and complete.

Thatisn’t what any sort of bootstrap means.

Valid: Consistent and sound.

Complete: Capable of assigning every objective and meaningful statement a truth value of true or false.

Consistent: Containing no contradiction. No statement is both true and false.

Godel’sincompleteness theorem proves that no axiomatic system can be both consistentand complete.

You may have noticed that I have omitted the definition of soundness. In logic, the soundness of a set of axioms means that they imply only true results. The issue here is that we are trying to obtain a notion of truth in the first place. Soundness as it is used here is to say that if there is any sort of underlying truth structure within the universe, this notion of truth is consistent not only with itself, but with this underlying truth structure.

The universe isn't true or false, it just is. Truth is a matter of propositional language, perhaps the propositions can be about the universe, but the universe itself does not have a "truth structure".

It is not clear what such a structure would be, but nonetheless it is an important precaution. Now, why should we accept the truth premise? Put simply: We need it. Without the truth premise, it is impossible to conclude anything.

It is impossible to reach concusions without making up truth and ignoring contradictions? That isn't how logic works.

Let's suppose we put together some other set of assumptions that did not include the truth premise. Without the truth premise, an assertion of their truth wouldn't even be meaningful. We need a meaningful notion of truth as described in the truth premise. If someone wants to see it, I will explain why each assumption on the notion of truth is necessary for meaningful deductions to be made, but for now I will omit the specifics.

If you are going to completely redefine logic and truth, maybe it would be best if you do include the specifics, minimally you should tell us what universe this logic comes from.

Now, reasonably, we should be able to define binary functions (such as and, or, not, etc.) and have a meaningful notion of certain statements about them being true. Let's define f to be the or operation for an example. Then f(0,0) = 0, f(0, 1) = 1, f(1, 0) = 1, and f(1, 1) = 1. Reasonably, these should all by definition be true statements. This could be considered to fall under the soundness condition, where, for an example, f(0, 0) = 0 must be considered to be true, because the value of f(0, 0) is by definition 0. Replacing 0 and 1 with the truth values T and F we can rewrite these values as f(F, F) = F, f(F, T) = T, f(T, F) = T, f(T, T) = T. We now get propositional logic. We can show, for example, that P implies P or Q. (I can't type logical connectives, so I'll just use words.) We create a truth table:

P = F, Q = F: P or Q = F or F = F, P implies P or Q = F implies F = T.
P = T, Q = F: P or Q = T or F = T, P implies P or Q = T implies T = T.
P = F, Q = T: P or Q = F or T = T, P implies P or Q = F implies T = T.
P = T, Q = T: P or Q = T or T = T, P implies P or Q = T implies T = T.

So in all cases P implies P or Q is true. At this point, we have seen that any notion of truth as in the truth premise should include propositional logic, and thus that we can consider the axioms of propositional logic can be considered a part of our definition of truth. It is possible that this notion of truth, to satisfy completeness, needs to include other axioms. Recall that completeness requires that our notion of truth assigns true or false to every "meaningful and objective" statement. To uncover what this means for our notion of truth, let's take a quick detour to another belief. Some people hold the belief that they are imagining the entire universe, and that it is all within their head. While this doesn't seem particularly reasonable, we can't prove them wrong with empirical evidence.

I’m noteven sure what this gobbledegook is supposed to be, it is masquerading as a deductiveargument, but that is not what it is by any stretch of the imagination.

The key thing to realize is that in different contexts, there are different reasonable/useful assumptions. Another example would be mathematics, in which we (at least in most areas of math) assume the nine axioms of ZFC.

Wedon’t just “assume” axioms, they must be established, accepted, orself-evidently true.

In conclusion, the notion of truth described in the truth premise can be thought of as all possible extensions of propositional logic, where we must specify the context (which extension it is in reference to) of any non-tautological truth.

Regarding this entire argument, all Ican do is quote Wolfgang Pauli, “it isn’t even wrong”.

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#29

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Posts: 184

04.11.2023 02:38AM

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@Sidewalker

You don't need to explain Godel to me, the incompleteness theorem speaks directly to "logicism" and your so called "truth premise", hence it explicitly applies as used.

It only "says nothing about the external world" if you accept that logicism says nothing about the real world, you are refuting your own argument.

Clearly I do need to explain Gödel to you, given that you don't seem to realize that a formal system being incomplete just means you can't prove every true statement. We can't prove every true statement about reality. So what? We'll just have to get used to it. Maybe read that website I linked, as Gödel's incompleteness theorem, just might say something other than what you think it says.

The universe isn't true or false, it just is. Truth is a matter of propositional language, perhaps the propositions can be about the universe, but the universe itself does not have a "truth structure".

First of all, when did I say that the universe was true or false? What on earth is that even supposed to mean? Secondly, I agree. The universe does not have any sort of "truth structure," I was just considering that possibility so that all of my bases were covered.

It isn’tvalid to just declare truth, especially when your declaration of truth is self-referential,and particularly when there is a valid “proof” that explicitly refutes it.

We need to make at least one assumption or else we can't deduce anything. Also, what proof refutes it? Please don't tell me you're still talking about your confused interpretation of Gödel's incompleteness theorem.

It is impossible to reach concusions without making up truth and ignoring contradictions? That isn't how logic works.

What? That's not what I said! I'm saying that we have two choices: Either reject the concept of truth itself, or accept the truth premise. Also, what contradictions? Name one.

If you are going to completely redefine logic and truth, maybe it would be best if you do include the specifics, minimally you should tell us what universe this logic comes from.

When did I do that exactly? The quote that you used here is basically just me saying "truth is a thing that exists, and that is itself true." Do you reject the existence of truth? That's really all I was talking about here. I'm not sure what you thought I was saying, but I certainly wasn't redefining or even plain old defining anything. I was just discussing the validity of the concept of truth.

I’m noteven sure what this gobbledegook is supposed to be, it is masquerading as a deductiveargument, but that is not what it is by any stretch of the imagination.

It's propositional logic. Also, it's not supposed to be a deductive argument, it is supposed to be a truth table, (if you click that link you will see that that is not something I made up) but there is not option to make a table on this website, so I did what I could. I also had to replace symbols with words, because there is no option to type math symbols on this website. You're not the first to be confused by that. It is important to realize that what I wrote there is literally just how modern propositional logic works, not some random thing I made up. Unless you want to rip out the foundations of modern mathematics, propositional logic wouldn't be the thing to call gobbledegook.

Wedon’t just “assume” axioms, they must be established, accepted, orself-evidently true.

They are never established, then they would be theorems. They are generally accepted or self-evidently true, that is why I said "reasonable assumptions." They are however, most certainly assumed. That is how all of modern mathematics works. As I have said many times now, you cannot draw any conclusions without at least one assumption.

Regarding this entire argument, all Ican do is quote Wolfgang Pauli, “it isn’t even wrong”.

This is one of my favorite quotes. It is possible that many ideas of the modern world fall under this description, and the flaws have yet to be spotted. Before math was formalized, our concept of set theory "wasn't even wrong." Russel was the first to show the world this, and he was also a major contributor to our modern version of set theory. Perhaps you will convince me that my idea "isn't even wrong," but you have yet to do so.

#30

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