## What are the achievements of Logic?

What is the basis for reason? And mathematics?

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Eodnhoj7
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### Re: What are the achievements of Logic?

A_Seagull wrote: Mon Mar 05, 2018 5:56 am
wtf wrote: Sun Mar 04, 2018 4:05 am
A_Seagull wrote: Sun Mar 04, 2018 2:19 am I wasn't trying to argue with you!
Oh ok my misunderstanding.
A_Seagull wrote: Sun Mar 04, 2018 2:19 am I was just making inferences from Godel's conclusion.
Incompleteness/undecidability are fantastically problematic They lead to many philosophical questions. Like, what is truth? If reason can't lead to truth then the Western project is doomed. That's why the postmodernists are winning these days. The societal rejection of reason comes straight from math itself.

* From non-Euclidean geometry we know that math can't tell us what's true. It depends on your axioms.
Then the synthesis of axioms is a mathematical truth, with synthesis dependent on a positive or negative...thesis or antithesis...hence we can observe the quantitative and qualitative foundation of logic/math as:

1)Positive "unity" through "1".
2)Negative absence as unity through the relation of units, through movement, as "2".
3)The synthesis of unity and unit as "3".

And we can observe that 1,2 and/or 3 provide the foundation for all further number.

* And ‎Gödel told us that even when we choose a set of axioms, we still can't know what's true!
It that itself an axiom? If so does that mean axioms are both constant and relative truth as a neutral median of synthesis?

What is true? Rationality cannot tell us. Western civilization is at risk. Pick up a newspaper. Intersectionality is in; rationality is out.
Is emotion truth then? If so, are the men who are emotionally involved within logic and math true then?

Tell me, what do you think of my thesis? That non-Euclidean geometry and Gödel's incompleteness theorem are the root cause of the contemporary labelling of rationality itself as a tool of social oppression rather than one of human liberation?

Considering that the axioms you observe are angles of awareness, we can observe intuitively that Euclidian geometry is the root of perspective and what we see as incomplete (hence contradiction) is merely an observation of our own limits...hence a constant truth in itself.
A_Seagull wrote: Sun Mar 04, 2018 2:19 am Would you like to comment on my conclusion?
Ok! You wrote:
A_Seagull wrote: Sun Mar 04, 2018 2:19 am If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely non-problematic.
It's terribly problematic. We can no longer rely on reason to know what's true. There's a straight line from Riemann and Gödel to the suppression of free speech by social justice warriors.

The entire Western tradition is at stake. Euclid's project has failed.

Godel's incompleteness theorem's only observe it is not finished, but are Godel's incompleteness theories really true when a point is always a point and a line is always a line? What if Euclid's project is only beginning?

And look here. I have a datapoint for you. It's from an alt-right website but there's no reason to believe the information is false. If you hate alt-right websites I'll stipulate to your objection and you can forget I mentioned it. But it's out there, it's apparently true, and it's pretty depressing if one is a rationalist.

Students enrolled in a Physics 101 course at Pomona College last semester were required to complete a "Decolonizing Physics" project by calling attention to issues like "implicit bias" and "microaggressions."

https://www.campusreform.org/?ID=10586

I say this is the result of the lost of faith in rationality due to non-Euclidean geometry and incompleteness.
The author Lovecraft metaphorically wrote about a city which was built upon non-euclidian geometry...the inhabitants of this city and all those who observed it went mad...it's a point that may give a very low-degree of justification to your point. But if reason leads to an absence of reason...is it reason at all?

It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.

For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
Is truth merely a symbol then?

So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.
wtf
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### Re: What are the achievements of Logic?

A_Seagull wrote: Mon Mar 05, 2018 5:56 am It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.
I haven't studied much philosophy so I can't say. But going back to Descartes's Meditations, it would seem to be the case that at least one aim of philosophy is to figure out how we can know what's true. We start by doubting everything, then we work our way up from that.

If philosophy is nothing but word games for clever people, it wouldn't be important. Philosophy is literally about everything, right? What's true, how can we know what's true, how can we evaluate evidence, how should we live, what are right and wrong actions, etc. The big questions.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
But truth isn't an arbitrary label. In theory at least, truth is about what really is true. 2 + 2 is 4, snow is white, circles aren't square, etc. But I have no real disagreement with anything you've written so far.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.
Yes that is the formalist position. Math is a meaningless game played with marks on paper according to formal rules.

But then you are completely abandoning the role of math in the physical sciences. If math has no meaning outside itself, then physics must be nonsense, because it's based on math. But according to you, math can't have any meaning outside itself. 2 + 2 = 4 because we can prove it from the Peano axioms. But if a physicist claims that 2 planets plus 2 planets is 4 planets, they are NOT justified in making that claim. Because math is only true within its own formal system.

I think this is a problem for your thesis that math has no validity outside itself.

So your position seems to be rejecting physical science. Because you say math has no meaning outside itself. There go physics, chemistry, biology, and all the rest of the scientific tradition.

And when did this loss of faith in math as a tool for finding truth begin? With non-Euclidean geometry. Then relativity. Then the incompleteness theorems. My thesis.

Am I correctly understanding your point? That math has no meaning outside itself? Then what is the basis of believing anything in science?

Are you throwing your lot in with the postmodernists?
Eodnhoj7
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### Re: What are the achievements of Logic?

wtf wrote: Mon Mar 05, 2018 7:15 pm
A_Seagull wrote: Mon Mar 05, 2018 5:56 am It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.
I haven't studied much philosophy so I can't say. But going back to Descartes's Meditations, it would seem to be the case that at least one aim of philosophy is to figure out how we can know what's true. We start by doubting everything, then we work our way up from that.

If philosophy is nothing but word games for clever people, it wouldn't be important. Philosophy is literally about everything, right? What's true, how can we know what's true, how can we evaluate evidence, how should we live, what are right and wrong actions, etc. The big questions.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
But truth isn't an arbitrary label. In theory at least, truth is about what really is true. 2 + 2 is 4, snow is white, circles aren't square, etc. But I have no real disagreement with anything you've written so far.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.
Yes that is the formalist position. Math is a meaningless game played with marks on paper according to formal rules.

But then you are completely abandoning the role of math in the physical sciences. If math has no meaning outside itself, then physics must be nonsense, because it's based on math. But according to you, math can't have any meaning outside itself. 2 + 2 = 4 because we can prove it from the Peano axioms. But if a physicist claims that 2 planets plus 2 planets is 4 planets, they are NOT justified in making that claim. Because math is only true within its own formal system.

I think this is a problem for your thesis that math has no validity outside itself.

So your position seems to be rejecting physical science. Because you say math has no meaning outside itself. There go physics, chemistry, biology, and all the rest of the scientific tradition.

And when did this loss of faith in math as a tool for finding truth begin? With non-Euclidean geometry. Then relativity. Then the incompleteness theorems. My thesis.

Am I correctly understanding your point? That math has no meaning outside itself? Then what is the basis of believing anything in science?

Are you throwing your lot in with the postmodernists?
I second the above points mentioned ^^^^
A_Seagull
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### Re: What are the achievements of Logic?

wtf wrote: Mon Mar 05, 2018 7:15 pm
A_Seagull wrote: Mon Mar 05, 2018 5:56 am It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.
I haven't studied much philosophy so I can't say. But going back to Descartes's Meditations, it would seem to be the case that at least one aim of philosophy is to figure out how we can know what's true. We start by doubting everything, then we work our way up from that.

If philosophy is nothing but word games for clever people, it wouldn't be important. Philosophy is literally about everything, right? What's true, how can we know what's true, how can we evaluate evidence, how should we live, what are right and wrong actions, etc. The big questions.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
But truth isn't an arbitrary label. In theory at least, truth is about what really is true. 2 + 2 is 4, snow is white, circles aren't square, etc. But I have no real disagreement with anything you've written so far.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.
Yes that is the formalist position. Math is a meaningless game played with marks on paper according to formal rules.

But then you are completely abandoning the role of math in the physical sciences. If math has no meaning outside itself, then physics must be nonsense, because it's based on math. But according to you, math can't have any meaning outside itself. 2 + 2 = 4 because we can prove it from the Peano axioms. But if a physicist claims that 2 planets plus 2 planets is 4 planets, they are NOT justified in making that claim. Because math is only true within its own formal system.

I think this is a problem for your thesis that math has no validity outside itself.

So your position seems to be rejecting physical science. Because you say math has no meaning outside itself. There go physics, chemistry, biology, and all the rest of the scientific tradition.

And when did this loss of faith in math as a tool for finding truth begin? With non-Euclidean geometry. Then relativity. Then the incompleteness theorems. My thesis.

Am I correctly understanding your point? That math has no meaning outside itself? Then what is the basis of believing anything in science?

Are you throwing your lot in with the postmodernists?
Rationalism can only take one or more concepts and generate another one. It cannot explain where original concepts come from.

In contrast, the process of pattern identification can explain where original concepts come from. And further it explains what a concept is and the relationship between words and concepts.(Words are labels for concepts).

Abstract logical systems (such as mathematics) have no meaning nor significance until a mapping is made between a concept and an element of that system. (ie. a concept is associated with a symbol of mathematics.)

The idea that there is an absolute truth which just has to be revealed or discovered is a fantasy (It has no rational basis). All one's knowledge of the world is no more than a model of the world. (ie the noumena is always unknown; all that one knows is the phenomena.)

All of physics is a model. Electrons, quarks, forces are all models. Physics uses mathematics by establishing a mapping by associating elements of the model with elements of mathematics. Even the claim that 2 cows + 2 cows = 4 cows requires a mapping between the concept of cows and elements of mathematics.

I discus these ideas in more detail in my book: "The Pattern Paradigm". ( I am currently working on the sequel.)
wtf
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### Re: What are the achievements of Logic?

A_Seagull wrote: Tue Mar 06, 2018 3:45 am Rationalism can only take one or more concepts and generate another one. It cannot explain where original concepts come from.
Yes, that is perfectly obvious today. But in the past, rationality in the form of math and logic were believed to be a way of knowing the truth.

Your original thesis was that Gödel's incompleteness theorem was inconsequential. But now you seem to be implicitly conceding your error. If rationality used to be regarded as a path to truth; and now we have come to see that it's not; how did that happen? Non-Euclidean geometry and Gödel's incompleteness theorem.

Right?

You're changing the topic and not engaging with me. Why?
A_Seagull wrote: Tue Mar 06, 2018 3:45 am In contrast, the process of pattern identification can explain where original concepts come from. And further it explains what a concept is and the relationship between words and concepts.(Words are labels for concepts).
What is "pattern identification" if not math and logic? Symmetry is a pattern. Group theory is the mathematics of symmetry. But you would say that group theory is nothing more than the formal working out of the consequences of the group axioms. You've tossed out the word "pattern" but you haven't made your case that it's anything other than math and logic.
A_Seagull wrote: Tue Mar 06, 2018 3:45 am Abstract logical systems (such as mathematics) have no meaning nor significance until a mapping is made between a concept and an element of that system. (ie. a concept is associated with a symbol of mathematics.)
Right. So how come math is so "unreasonably effective," as they say, in the natural sciences? Wigner asked that question and so have many others. But you seem to think it's a simple matter of assigning mappings. How do we know that science is making the right mappings? When Newton says F = ma, he's using math and mapping the symbols. But how did he map the symbols? Blind luck? How do we know when we've made the right mapping?
A_Seagull wrote: Tue Mar 06, 2018 3:45 am The idea that there is an absolute truth which just has to be revealed or discovered is a fantasy (It has no rational basis). All one's knowledge of the world is no more than a model of the world. (ie the noumena is always unknown; all that one knows is the phenomena.)
That's nihilism. You don't live your life that way. You drive cars, you fly in airplanes, you flip the light switch with every expectation that photons will start flowing copiously out of a nearby lightbulb, bounce off objects in the room, hit your retina causing an electrochemical signal to flow to your cerebral cortex and (somehow -- mechanism unknown) produce a sensory impression in your mind.

Are you seriously trying to get me to believe that you think this is all random, that we can't really know that flipping the light switch completes an electrical circuit that includes the filament in the (old fashioned tungsten-based) bulb and the nearby power grid? You reject all that because it's not a knowable noumena?

I get the feeling you know a lot of words but haven't given these matters much thought.
A_Seagull wrote: Tue Mar 06, 2018 3:45 am All of physics is a model. Electrons, quarks, forces are all models. Physics uses mathematics by establishing a mapping by associating elements of the model with elements of mathematics. Even the claim that 2 cows + 2 cows = 4 cows requires a mapping between the concept of cows and elements of mathematics.
Yes and what is the process by which these mappings are made? How do we know we've made the right mappings?
A_Seagull wrote: Tue Mar 06, 2018 3:45 am I discus these ideas in more detail in my book: "The Pattern Paradigm". ( I am currently working on the sequel.)
I've read many of your posts and your thinking is quite fuzzy. Rather than promoting your book, you should strive to engage with the points I'm making right here. That would convince me that you might have something to say.
Dalek Prime
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### Re: What are the achievements of Logic?

wtf wrote: Sat Mar 03, 2018 11:49 pm
Dalek Prime wrote: Sat Mar 03, 2018 5:57 am
No. I just used it to wipe my butt. Tell Kurt to send it again.
ps -- Perhaps underneath that moronic response was a genuine curiosity about logicism.

From Wikipedia:

Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.

...

Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of first-order logic and those of higher-order logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on human-provided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept relies on the dubious notion that a system of proof based on man-made models is as authoritative as one based on the existence and properties of the natural numbers.

If you have any more questions as to why we now know that math is NOT reducible to logic, feel free to post about wiping your butt. It makes us all very impressed with your intelligence.
I find it humorous that you distinguish ''man-made models' as you say, from mathematical, which is also man-made. Both exist at our behest, much like philosophy itself. Indeed, every possible thought and consideration is man-made, and necessitates logical thought to be put together at all. So no, I shall continue to disagree by using the Godel dressing-down as bum wipe.

I know you are clearly smart enough to know that Peano used logic to explain numbers themselves. Whether through reduction, induction or deduction, we build or reverse engineer on logical premises. And that includes Kurt's methods for coming to his conclusions, based on premises he accepts.
Last edited by Dalek Prime on Wed Mar 07, 2018 5:19 pm, edited 1 time in total.
Dalek Prime
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### Re: What are the achievements of Logic?

Kurt Godel was correct on typed lambda calculus. It doesn't impact untyped, which Church had shown, Lisp being the operable result through McCarthy.
wtf
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### Re: What are the achievements of Logic?

Dalek Prime wrote: Wed Mar 07, 2018 3:13 am I find it humorous that you distinguish ''man-made models' as you say, from mathematical ..
I find it humorous that you claim I said something I never said, and never would say. I think you are quoting or remembering someone else. But feel free to wipe your butt, as soon as you learn how.
Dalek Prime
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### Re: What are the achievements of Logic?

wtf wrote: Wed Mar 07, 2018 6:27 pm
Dalek Prime wrote: Wed Mar 07, 2018 3:13 am I find it humorous that you distinguish ''man-made models' as you say, from mathematical ..
I find it humorous that you claim I said something I never said, and never would say. I think you are quoting or remembering someone else. But feel free to wipe your butt, as soon as you learn how.
Look back on your own post. I'm not going to spoon feed you.
Eodnhoj7
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### Re: What are the achievements of Logic?

A_Seagull wrote: Tue Mar 06, 2018 3:45 am
wtf wrote: Mon Mar 05, 2018 7:15 pm
A_Seagull wrote: Mon Mar 05, 2018 5:56 am It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.
I haven't studied much philosophy so I can't say. But going back to Descartes's Meditations, it would seem to be the case that at least one aim of philosophy is to figure out how we can know what's true. We start by doubting everything, then we work our way up from that.

If philosophy is nothing but word games for clever people, it wouldn't be important. Philosophy is literally about everything, right? What's true, how can we know what's true, how can we evaluate evidence, how should we live, what are right and wrong actions, etc. The big questions.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
But truth isn't an arbitrary label. In theory at least, truth is about what really is true. 2 + 2 is 4, snow is white, circles aren't square, etc. But I have no real disagreement with anything you've written so far.
A_Seagull wrote: Mon Mar 05, 2018 5:56 am So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.
Yes that is the formalist position. Math is a meaningless game played with marks on paper according to formal rules.

But then you are completely abandoning the role of math in the physical sciences. If math has no meaning outside itself, then physics must be nonsense, because it's based on math. But according to you, math can't have any meaning outside itself. 2 + 2 = 4 because we can prove it from the Peano axioms. But if a physicist claims that 2 planets plus 2 planets is 4 planets, they are NOT justified in making that claim. Because math is only true within its own formal system.

I think this is a problem for your thesis that math has no validity outside itself.

So your position seems to be rejecting physical science. Because you say math has no meaning outside itself. There go physics, chemistry, biology, and all the rest of the scientific tradition.

And when did this loss of faith in math as a tool for finding truth begin? With non-Euclidean geometry. Then relativity. Then the incompleteness theorems. My thesis.

All of which are dependent upon the axioms of Euclidian space in order to exist. The curvature of non-euclidian geometry and relativity can be observed as approximations of angles through frequencies, and what makes Euclidian geometry what it is, is strictly the "angle" through which lines and points exist. All curvature can be observed as frequencies of quantum angles, and approximation of that said angle, hence curvature is "relativistic" in nature because it is dependent upon an approximation through distance.

The incompleteness theorems also observe, to some degree, an inherent loop nature dependent for definition, hence what we can understand of as truth through math and space may be dependent upon alternation in some degree or another.

What we understand of as symmetry may isomorphic alternation as the approximation of unity, through movement. In these respects math may be incomplete along with logic, through its inherent nature of definition, however the altneration is always present as loops within loops, we all loops being no different from one grand loop, with the only difference being how the loops relate as "unit" being an approximation of "unity".

Am I correctly understanding your point? That math has no meaning outside itself? Then what is the basis of believing anything in science?

Are you throwing your lot in with the postmodernists?
Rationalism can only take one or more concepts and generate another one. It cannot explain where original concepts come from.

To explain the origin of concepts, by applying a continual set of definitions, would result in a simultaneous form of circular and linear reasoning, hence what we can understand as a foundation stone (of which like many foundation stone's the structure is not limited to) can be observed in the spatial format through which the means of definition takes place. In these respects one foundation for the nature of what constructs a concept is "space" or geometry.

In contrast, the process of pattern identification can explain where original concepts come from. And further it explains what a concept is and the relationship between words and concepts.(Words are labels for concepts).

Patterns are dependent upon spatial relations where the positive dimension defines itself to other positive dimensions, and simultaneously defines the background dimensions as negative that give definition in themselves. Much in the same manner a drawing of birds require acts a postive space, while the background (or negative dimension of the drawing) simultaneously gives it pattern.

Abstract logical systems (such as mathematics) have no meaning nor significance until a mapping is made between a concept and an element of that system. (ie. a concept is associated with a symbol of mathematics.)

That "mapping" or the connection of dimensions is an abstract dimension in itself in the respect the connect is conducive strictly to a "form" one of which is inseperable from space.

The idea that there is an absolute truth which just has to be revealed or discovered is a fantasy (It has no rational basis). All one's knowledge of the world is no more than a model of the world. (ie the noumena is always unknown; all that one knows is the phenomena.)

If all truth is dependent on a map or model, what seperates that from absolute statement, considering the mapping or model is striclty the observation of a form?

All of physics is a model. Electrons, quarks, forces are all models. Physics uses mathematics by establishing a mapping by associating elements of the model with elements of mathematics. Even the claim that 2 cows + 2 cows = 4 cows requires a mapping between the concept of cows and elements of mathematics.

Would the cows exist without the mapping however considering the ratio of cows to resources is dependent on the mapping process? If too many cows are put in a field with not enough grass, the cows would die because of an absence of "mapping".

I discus these ideas in more detail in my book: "The Pattern Paradigm". ( I am currently working on the sequel.)
Patterns fundamentally are dependent on positive and negative space, whose median is a neutral degree of space as "both" and "neither" positive and/or negative. We can see a basic example of this in the yin/yang. In these respects the nature of space can be observed as having a four fold nature through three (positive, negative, postive-neutral, negative-neutral) with the three (positive, negative, neutral) extending from 1 as only being, qualitatively speaking, exists.

wtf
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### Re: What are the achievements of Logic?

Dalek Prime wrote: Wed Mar 07, 2018 6:34 pm Look back on your own post. I'm not going to spoon feed you.
You're confusing my words with Seagull's. Or somebody's. I did not say what you claim I said. It's not language I would have used.

Have a nice day. And don't forget to wipe your butt like your mom taught you. Or did she?
Dalek Prime
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### Re: What are the achievements of Logic?

wtf wrote: Wed Mar 07, 2018 9:17 pm
Dalek Prime wrote: Wed Mar 07, 2018 6:34 pm Look back on your own post. I'm not going to spoon feed you.
You're confusing my words with Seagull's. Or somebody's. I did not say what you claim I said. It's not language I would have used.

Have a nice day. And don't forget to wipe your butt like your mom taught you. Or did she?
You did. Have a better one.
Dalek Prime
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### Re: What are the achievements of Logic?

wtf wrote: Sat Mar 03, 2018 7:46 pm
Dalek Prime wrote: Sat Mar 03, 2018 5:57 am No. I just used it to wipe my butt. Tell Kurt to send it again.
So you're ignorant and proud of it? I don't follow your logic or rhetorical style. The incompleteness theorem destroyed the logicist program in 1931.
I didn't see this post wtf, but again, I reiterate what I said about lamda calculus earlier. It did impact typed, but not untyped.
Arising_uk
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### Re: What are the achievements of Logic?

Hopefully you can help me wtf as I find it very hard to believe that propositional logic can produce a true result that it can't prove? So is it that Gödel's result only applies to a specific kind of axiomatic system.

I found your stuff about truth and the success of postmodernism interesting as to me Gödel's theorem is like Einstein's relativity in that it comes into common thought and gets abused out of all recognition.
wtf
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### Re: What are the achievements of Logic?

Arising_uk wrote: Thu Mar 08, 2018 2:21 am Hopefully you can help me wtf as I find it very hard to believe that propositional logic can produce a true result that it can't prove? So is it that Gödel's result only applies to a specific kind of axiomatic system.
Predicate logic, the logic of mathematics. This is the logic that includes the "for all" and "there exist" quantifiers.

The first incompleteness theorem simply says that given a consistent set of axioms sufficiently powerful to do mathematical induction, there are propositions that can neither be proved nor disproved. So no set of axioms can tell you everything that's true. There are always truths that lie beyond the power of any consistent set of axioms.
Arising_uk wrote: Thu Mar 08, 2018 2:21 am I found your stuff about truth and the success of postmodernism interesting as to me Gödel's theorem is like Einstein's relativity in that it comes into common thought and gets abused out of all recognition.
Thank you. There's a book by Morris Kline called Mathematics and the Loss of Certainty that's all about this. How we formerly believed that math was a path to truth; and how we found out that it's not.