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)

## The Failure of Linear Logic?

- Arising_uk
**Posts:**9567**Joined:**Wed Oct 17, 2007 2:31 am

### Re: The Failure of Linear Logic?

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.

- Immanuel Can
**Posts:**3327**Joined:**Wed Sep 25, 2013 4:42 pm

### Re: The Failure of Linear Logic?

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?Eodnhoj7 wrote:The failure of linear logic (my brief argument)

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?

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.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.

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?

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.Immanuel Can wrote: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?Eodnhoj7 wrote:The failure of linear logic (my brief argument)

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?

- Immanuel Can
**Posts:**3327**Joined:**Wed Sep 25, 2013 4:42 pm

### Re: The Failure of Linear Logic?

Okay, fair enough.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.

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

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