Page 1 of 1

### The Failure of Linear Logic?

Posted: Mon Mar 27, 2017 9:31 pm
The failure of linear logic (my brief argument)

The issue with logic is it's dependence on self-evidence which requires a certain level of subjectivity. This level of subjectivity manifests as all axioms being possibilistic relative to the nature of the observer(s). Because of the possibility nature of all axioms, that manifests through the relativity of the observer, one axiom can have multiple logic chains composed of seperate axioms who in themselves are self evident and simultaneously are subjective in their reflectivity with other axioms.

All logical arguments are composed of interrelated axioms that:

A) exist on their own as primitives that cannot be reduced further.
B) manifest reflections between other axioms and the observer(s) which in turn manifests further definition.
C) unify with other axioms, through a synthesis, cancelling out the prior axioms and creating a new one.

Regardless of the order, these three aspects of "relativity", "reflectivity", and "unity/synthesis" exist in one degree or another through a treatise because these three components enable and manifest definition.

Also because of the inherent subjective nature of axioms a certain level of probabilism is involved as the observer through observation steers the course of how the axioms relate, reflect, unify with other axioms.

It is this subjective nature of axioms, that axioms take on the form of actual "curvature" (α) of logic. It is this actual curvature which exists relative to potential curvature (ω).

It is this relativity between actual and potential axioms that manifests the strict linear-ism required in most logic. The nature of relativity between actual and potential, as far as I understand, requires a linearism when it comes to logic.

ex: α∫ω = α <------> ω

ex: α ------> ω

However all axioms are propogative in proportional to the observer/observation that is inter-joined to them.

ex: α ------- α1 -------- α2 -------- α3 --------> ω

The issue occurs as the axioms are all beginning axioms (logic curvature) for further beginning axioms and relative to multiple observers the logic chain begins to spider web as each beginning angle
has multiple possibilities of extension when a separate observer is involved for the nature of the beginning axiom multiplies in degrees reflective of the number of observers (Φ).

ex: (α→αx)≜Φx
(ω→ωx)≜Φx

ex: α --- ψ(ω,ω1,ω2...∞)

ex: α ------- α1 -------- α2 -------- α3 --------> ω

α1 ------- b ------- b1 ------- b2 --------> ω
α3 ------- c ------- c1 ------- c2 --------> ω

So now where it was just the original beginning axiom, now there are several beginning axioms all with separate linear chains each ending with a number of possible potential axioms.

The failure of linear logic is it's ability to manifest to much definition. The increase in definition reflects a paradoxical decrease in understand the nature of the individual axioms as an increase in further axioms shifts the proportionality in observation to all the other axioms.

+(∂>Aα) ≡ -(Φ∝α)

∂(definition)= ψ*α
A (original)

### Re: The Failure of Linear Logic?

Posted: Thu Apr 20, 2017 8:59 am
Are you talking about Logic or instead Ideas or even Language. As what you say doesn't seem to make much sense applied to Logic because axioms are generally accepted to be proved true by empirical methods, not logically.

### Re: The Failure of Linear Logic?

Posted: Thu Apr 20, 2017 6:17 pm
Eodnhoj7 wrote:The failure of linear logic (my brief argument)
It's an interesting argument. But does it really reflect a deficiency in linear logic itself -- a formal or procedural imperfection, if you will -- or simply a realization that first axioms are not, in themselves, logico-deductive?

Since linear logic is predicated on given axioms, from where are those axioms "given," but from the inductive inferences of human beings?

In other words, the start of knowledge is induction. But after the first induction, the subsequent linear, logical process might be quite flawless. So should we indict the second-step deductive procedure (logic), when the real liability is in the primary induction?

And how will we frame out critique of logic without trusting the reliability of logic in order to do it?

### Re: The Failure of Linear Logic?

Posted: Sat Apr 22, 2017 4:53 pm
Arising_uk wrote:Are you talking about Logic or instead Ideas or even Language. As what you say doesn't seem to make much sense applied to Logic because axioms are generally accepted to be proved true by empirical methods, not logically.
Their is no empirical argument for empiricism without depending on an abstract concept. The continual flux of the physical observable universe does little to uphold empiricism other than to allow empiricism to be "the observation of flux". What is self-evident one day is not self-evident another, and the ratios between the observer and the physical world are often in constant flux.

The inability to manifest clear definition of the observable physical world puts many questions to empiricism.

As to what I am talking about, is strictly the failure of a strict "linear only" approach to all observations, and in this case logic because of the hidden number of angles and variable within each axiom that manifest further non-equal linear arguments/observations.

### Re: The Failure of Linear Logic?

Posted: Sat Apr 22, 2017 5:03 pm
Immanuel Can wrote:
Eodnhoj7 wrote:The failure of linear logic (my brief argument)
It's an interesting argument. But does it really reflect a deficiency in linear logic itself -- a formal or procedural imperfection, if you will -- or simply a realization that first axioms are not, in themselves, logico-deductive?

Since linear logic is predicated on given axioms, from where are those axioms "given," but from the inductive inferences of human beings?

All linear logic depends upon a "branching function" where at any given axiom 2 or more linear arguments/observations may manifest relative to the observer(s). Where linearism depends on arriving at "one" point of unity, this "branching function" can cause an increase in observable definition that is akin to randomness as multiple linear element branch to more linear elements, all of which intend to arrive at thier own individual unified interpretation of reality. Add in multiple observers and the process exponetiates.

The only what to deal with these expontentiation structures is to observe the reflective capacities between these "lines of interpretation" and this leads one away from linear and towards a necessary form of reflective reasoning that is similiar to circular reasoning. I am not intending to argue that all linearism is deficient, it is just deficient when take only on its own terms (linearism only.)

In other words, the start of knowledge is induction. But after the first induction, the subsequent linear, logical process might be quite flawless. So should we indict the second-step deductive procedure (logic), when the real liability is in the primary induction?

The process may provide definition, however because all linear observations instinctually require to a take on a one-dimensional approach, there is no reflective capacity with other linear arguments, so no linear statement has the capacity to self-reflect. Each linear statement seeks to reach a one-dimensional answer, however they branch out at different points (like a crack in a rock) when multiple observers are applied, lead to multiple linearist interpretations from one function, all simultaneously trying to reach a one dimensional answer irrespective of eachother.
And how will we frame out critique of logic without trusting the reliability of logic in order to do it?
However I have to emphasize this point again, I am not going against linearism...as it would be foolish to do so...I am point out its deficiencies when applied on its own terms. Linearism has an important place in philosophy, however, it is far from the be all end all.

### Re: The Failure of Linear Logic?

Posted: Sat Apr 22, 2017 6:49 pm
Eodnhoj7 wrote:However I have to emphasize this point again, I am not going against linearism...as it would be foolish to do so...I am point out its deficiencies when applied on its own terms. Linearism has an important place in philosophy, however, it is far from the be all end all.
Okay, fair enough.

Where do you want to go next? Why did this strike you as an important point to make at this time?

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 12:04 am
Immanuel Can wrote:
Sat Apr 22, 2017 6:49 pm
Eodnhoj7 wrote:However I have to emphasize this point again, I am not going against linearism...as it would be foolish to do so...I am point out its deficiencies when applied on its own terms. Linearism has an important place in philosophy, however, it is far from the be all end all.
Okay, fair enough.

Where do you want to go next? Why did this strike you as an important point to make at this time?
Circularity is unavoidable and an inherent structure of all arguments.

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 4:17 am
Eodnhoj7 wrote:
Sun Oct 29, 2017 12:04 am
Immanuel Can wrote:
Sat Apr 22, 2017 6:49 pm
Eodnhoj7 wrote:However I have to emphasize this point again, I am not going against linearism...as it would be foolish to do so...I am point out its deficiencies when applied on its own terms. Linearism has an important place in philosophy, however, it is far from the be all end all.
Okay, fair enough.

Where do you want to go next? Why did this strike you as an important point to make at this time?
Circularity is unavoidable and an inherent structure of all arguments.
Well, it seems to me the most interesting point in your case is, "Their [sic] is no empirical argument for empiricism without depending on an abstract concept."

I think that part is definitely right, at the very least. Empiricism cannot be known to be right by empirical methods; firstly, because empiricism is a concept, not an empirical reality, and secondly, because empirical methods cannot be used as a way to justify empiricism without the prior assumption of empiricism being right. in other words, if you don't take empiricism for granted, then you can't be sure that any empirical result actually "proves" or "demonstrates" anything, and so you can't know it to be right.

The upshot of your observation, then, is that empiricism is a sort of "faith" stance, not an empirical one. And I think that's quite true.

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 7:17 am
Empiricism is not a faith stance because it based upon observation. Observation which is as objective as
possible. It is the foundation of the scientific method that is completely devoid of any faith whatsoever

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 4:06 pm
surreptitious57 wrote:
Sun Oct 29, 2017 7:17 am
Empiricism is not a faith stance because it based upon observation. Observation which is as objective as
possible. It is the foundation of the scientific method that is completely devoid of any faith whatsoever
The scientific method’s origins where in the axiom, with the hypothesis as an approximate of the axiom. In a separate respect, deduction is the observation of dimensions and their reflections and relations as a form of synthesis which simultaneously define themselves and its dual hypothetical nature.

The axiom in this respect synthesizes as a hypothesis and in this respect mathematics and logic may be equivalent to an abstract form of a natural "photo-synthesis" between reality and the observer through the axiom as the “flower”. It is within this nature of the axiom and the scientific method that a further degree of circularity can be observed as:

-"Develop General Theories"
-"Make Observations"
-"Think of Interesting Questions"
-"Formulate Hypotheses"
-"Develop Testable Predictions"
-"Gather Data to Test Prediction"
-"Refine, Alter, Expand, or Reject Hypotheses"
-"Develop Testable Predictions"
-"Gather Data to Test predictions"
-"Develop General Theories” (Garland)

Or broken down into the four fundamentals of:

“Characterizations (observations,definitions, and measurements of the subject of inquiry) (Ørsted)
Hypotheses (theoretical, hypothetical explanations of observations and measurements of the subject) (Feynman) (Born) (Ørsted)
Predictions (reasoning including deductive reasoning[68] from the hypothesis or theory) (Galileo)
Experiments (tests of all of the above)” (xxp)

It may simultaneously be inferred that the nature of metrology is the synthesis of dimensions as axioms of spatial elements and that axioms themselves are an innate “metrology” .

“It is clear they conceived number as the first principle (Greek: Arche), and that the substance of the entire universe is identified with numbers. Philolaos of Tarentum (ca. 475 BCE), in his book on Pythagorean Numbers states: "All things, at least those we know, contain Number; for it is evident that nothing whatever can either be thought or known without Number." (Leonessi)

Rand observed that “measurements exist, but are not specified. That measurements must exist is an essential part of the process. The principle is: the relevant measurements must exist in some quantity, but may exist in any quantity." (Rand, Introduction to Objectivist Epistemology (second ed.)) From this statement, and the observation of the Pythagorean perspective, it may be inferred that measurement is the observation of quantity, with all quantity being a form of symmetry.

The question occurs that if there is a degree of truth in this, how much more so for the letter, the word, or the sentence? Would numbers even constitute existence without language? “If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments. This seems to abolish logic, but does not do so.— It is one thing to describe methods of measurement, and another to obtain and state results of measurement. But what we call "measuring" is partly determined by a certain constancy in results of measurement” (philo invest) as a form of medianality of ratios.

In a simultaneous respect, a subjective logic is possible, as a synthesis of Nietzsche’s Perspectivism, which claims "that no evaluation of objectivity can transcend cultural formations or subjective designations (Mautner)". A paradox occurs as what is perceived objectively determines cultural formations and subjective designations in a simultaneous and different respect. The subjectivity of the axioms, through the "self", reflects and relates to the "objectivity" of axioms as "evidence". It is this duality of subjectivity, “our own mental activity is the only unquestionable fact of our experience” (Richardson) which formulates all measurements (Hay) as mental properties (Merlo) and belief (Cox) and objectivism, (Insert more objectivity notes), that manifests the "axiom" as "self-evidence" is a synthesis of "the subjective self" and "objective proportions of space" as an irreducible "synthesis as cause". It can be further argued that "rules (i.e., those of philosophy, the scientific method, etc.) are constantly reassessed according to the circumstances of individual perspectives (Schacht)" as subjectivity is a continual flux of "Relationalism". In a separate respect these “rules” simultaneously manifest a stability through the "limits of belief" as a logistics dimension. It is this flux and stability of the axiom through “rules” that is imaged fully through the “symbol”.

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 5:54 pm
surreptitious57 wrote:
Sun Oct 29, 2017 7:17 am
Empiricism is not a faith stance because it based upon observation. Observation which is as objective as
possible. It is the foundation of the scientific method that is completely devoid of any faith whatsoever
Actually, it is a faith stance. Consider this:

How did you learn about the empirical method? Did you discover it yourself? No? I'm not surprised. It took until the 17th Century for someone to do that, and even then, it was only Francis Bacon. And I'm pretty sure neither of us is him.

So how did you learn it? I'll warrant that it was from some guy in a lab coat. Or maybe it was a teacher. Or a textbook told you, and you believed it. Or perhaps a friend told you about it. But whomever it was, it was not empirically discovered. Rather, you inherited your knowledge of it from another person, and then believed them. You had faith that maybe, just maybe they were telling the truth.

When you tried the method, you found that it worked in the way it promised; and for the limited purposes it served, it worked very, very well. Eureka. But you never knew if it was the ONLY method, nor if it was capable of dealign with ALL existent things. You were to discover that there were things upon which the empirical method does not appear to work (aesthetics, morality, identity, interpersonal relationality, and so on), or for which it rendered only equivocal or reductional answers, but not complete and satisfying ones. But that was fine: for what it was, it did what it could do. And hopefully, you didn't expect it to do more.

However, maybe you did. And to move forward from that position, you had to take on faith that it would work for things upon which you had never yet used it. After all, you had not performed all possible experiments yourself. Nor had anyone. So you had to take on faith that the method would continue to work, and that it would work for applications that had not yet even been tried by anyone. And probably, you did take that on faith.

Or, if you were circumspect, perhaps you didn't entirely take that on faith, but remained somewhat skeptical of the comprehensive utility of the empirical method. But most people are not quite that circumspect. But your skepticism, if you retained any, reflected that you knew the method itself could not empirically confirm its own universal efficacy. You sensed you would be trusting it in faith, if you believed it did things that had not yet been empirically demonstrated.

In any case, it was never until AFTER you trusted the method that you found any confirmation for it at all. You believed first, tried, found it worked, and believed more. And to this day, perhaps you're not even sure how far the range of the method extends...but you continue to trust it anyway.

The whole process of learning and practicing the empirical method is thus infused with incidents of pure trust, faith and belief. Confirmation, when it comes, only comes afterward. First you believe, then you come to know...inasmuch as you can know anything.

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 6:45 pm
surreptitious57 wrote:
Sun Oct 29, 2017 7:17 am
Empiricism is not a faith stance because it based upon observation.
This is circular. Since empiricism IS observation, you're just saying that observation is not a faith stance because it is based on observation.

All science is theory-laden. It depends upon a multitude of unstated and unexamined theories and premises to justify itself. BUT, science works. If it ever stopped working, then maybe we'd have to examine those presuppositions and theories that like the turtles go all the way down.

### Re: The Failure of Linear Logic?

Posted: Sun Oct 29, 2017 7:48 pm
Immanuel Can wrote:
The whole process of learning and practicing the empirical method is thus infused with incidents of pure trust
faith and belief. Confirmation when it comes only comes afterward. First you believe then you come to know
I do not use the same terminology that you do so I do not believe in anything at all. For something that may or may not be true I simply wait until a testable hypothesis can determine which it is. No faith position is required. For something that cannot be determined by a testable hypothesis I merely retain an open mind. Again no faith position is required. One can make assumptions based upon pre existing knowledge but that is not the same as a faith position. I see no justification for believing anything without evidence because that belief could be false. But even if something is true it still cannot be regarded as such without actual evidence to demonstrate it. For nothing that I know or think is true is based upon any faith

### Re: The Failure of Linear Logic?

Posted: Mon Oct 30, 2017 12:32 pm
surreptitious57 wrote:
Sun Oct 29, 2017 7:48 pm
I do not use the same terminology that you do so I do not believe in anything at all.
But avoiding a particular word will not change the reality that word attempts to articulate. Call it "faith," "belief," "thinking-without-knowing-for-sure," "trusting," "hoping," "anticipating," or whatever you choose...the case will still be that that word describes the situation.

If you think about it carefully, you probably realize that you can't know what the "test" is, or what the "empirical method" is without trusting the personal reliability of your science teacher. Even after performing an experiment yourself -- or, say 100 of them -- you cannot know for certain that test 101, 1001, or 1,000,001 won't turn up the anomalous result that will falsify your entire hypothesis. You just have to trust that you've done enough tests that your leap of faith is warranted. As for the trust we all put in science textbooks and papers, how do we know that the person who wrote them was not errant, dishonest or incompetent? We don't, for sure; but we think ourselves adequately confident in trusting most -- if not all -- of what they say to us, provided their claims are not outrageous...

That's how we all learned science. There is no other way to do it. Certainly no "empirical" way.
I see no justification for believing anything without evidence
Nor do I. But it's good for both of us that science is not "without evidence." It never has all the evidence; but we hope it has enough evidence, in a given case, to justify our faith in it. And often, it does.

But sometimes it does not. For example, at one time it was scientific orthodoxy to believe that the smallest particle was an "atom." Now we know that is not so. However, scientists still believed it, and acted as if it were so. When it was falsified, so was their faith in the irreducibility of the atom. And that sort of process has been repeated throughout scientific history. It's not even unusual. If it were, science itself would have reached a final state on such questions, and would not need to seek any more answers at all.

### Re: The Failure of Linear Logic?

Posted: Tue Oct 31, 2017 5:37 pm
I would have to agree with Immanuel's stance about Empiricism being a faith stance, however I will argue it from a seperate but equally valid angle.

1) Empiricism requires the "axiom" for both itself and its foundations.

2) The axioms as "self-evidence" manifests a dual role of "subjectivity" through the "self" and "objectivity) through the "evidence" (for all evidence is strictly "ratios" or "structural symmetry").

3) The inevitable portion of subjectivity within the axiom points to a degree of randomness or absence of structure.

4) This "absence" of structure inevitably results in "force", with "force" being synonymous to "flux" or "movement".

5) Belief, although founded up and founding "structure", is in itself an absence of "structure" in the respect that it can be viewed strictly as a "force" or "movement".

6) In this respect, Empiricism, is strictly a philosophy of movement (further relating to the fact it studies matter, or perpetual flux) and not a thing itself.

7) Empiricism exists if and only if their is stability in more abstract philosophies, or it is exists in relation to other philosophies of movement such as solipisism.

a) The second point results a circular form of reasoning where one philosophy is used to justified the other which contradicts these philosophies by their own linear formatting they require (ie, circular reasoning is considering a contradiction under these philosophies generally speaking).