## Does Deduction Necessitate Approximation and Vagueness?

What is the basis for reason? And mathematics?

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Eodnhoj7
Posts: 5883
Joined: Mon Mar 13, 2017 3:18 am

### Does Deduction Necessitate Approximation and Vagueness?

"A deduction is speech in which certain things have been supposed, something different from those supposed results because of necessity there being so" (Aristotle, Prior Analytics I.2, 24b 18-20).

The statement is a speech making a supposition, which is an "uncertain belief"(a) or an assumption. "The word supposition (Lat. suppositio ) originally meant substitution, and commonly indicates an assumption, hypothesis, or theory."(c) "In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something."(b) "Aristotle believes that only propositions are true or false."(b)

This is supposition claiming that suppositions differ by necessity, first resulting in the basic assumptions of true and false. This manifests into different types of suppositions which manifest as the laws of identity, non-contradiction, and excluded middle (which are not limited to but are inspired by aristotles writings). All laws and rules for suppositions are suppositions in themselves as statements of assertion

"Difference is because of necessity" or "necessity therefore difference" can be observed as corresponding suppositions, thus asserts assumptions.

Aristotle claims differentiation is necessary because "nothing new" stems from "one premise" (Stanford encyclopedia, 3.2, aristotle's logic). Necessity of differentiation is grounded in "newness".

This differentiation, observed by the law of excluded middle, however is a constant voiding of one assumption into many.

One example is Cat ---> (Cat exists. Cat does not exist.)

This observes difference as a constant state of assuming nothing, ie that each contextual identity assumed is effectively nothing in itself.

It is this "or" state of being (embodied by the law of excluded middle inherent within idenity) which is fundamentally assumed, much like difference, considering it requires observing a thetical and antithetical state of a phenomenon that is subject to the angle of the observer. This deduction of perspective is observed by the pyrhonists and neitzche as a deduction of the nature of supposition.

The angle of the observer, as both a point of assumption and assumption, varies considering it is subject to deduction itself.

Thus deduction results in the atomism of supposition and there corresponding perspectives, leading to an inherent multiplicity where one phenomenon is approximated through its parts.

Thus necessity leads to differentiation of one supposition into many as an approximation of it. Deduction results in vagueness as continual propositions, as categories, are made resulting in one core supposition existing in multiple states.

(a) https://www.bing.com/search?q=suppositi ... CA140579D1

(b) https://www.iep.utm.edu/aris-log/#H2

(c) https://www.encyclopedia.com/religion/e ... tion-logic
Last edited by Eodnhoj7 on Tue Sep 03, 2019 7:29 am, edited 1 time in total.

Impenitent
Posts: 2727
Joined: Wed Feb 10, 2010 2:04 pm

### kinda, sorta... maybe

-Imp

Eodnhoj7
Posts: 5883
Joined: Mon Mar 13, 2017 3:18 am

### Re: kinda, sorta... maybe

Impenitent wrote:
Thu Aug 29, 2019 9:54 pm
-Imp
You get it? Deducing deduction is vague thus deduction is vague.

Impenitent
Posts: 2727
Joined: Wed Feb 10, 2010 2:04 pm

### Re: Does Deduction Necessitate Approximation and Vagueness?

definitions and meanings of terms are vague
...
transferring immaterial labels to tangible things which are infinitely undefinable and then pronouncing them "truths" by deducing them from similarly mislabeled unidentifiable components of syllogistic rigidity is the trick...

or something like that...

-Imp

Scott Mayers
Posts: 1632
Joined: Wed Jul 08, 2015 1:53 am

### Re: Does Deduction Necessitate Approximation and Vagueness?

Eodnhoj7 wrote:
Thu Aug 29, 2019 9:46 pm
"A deduction is speech in which certain things have been supposed, something different from those supposed results because of necessity there being so" (Aristotle, Prior Analytics I.2, 24b 18-20).

The statement is a speech making a supposition, which is an "uncertain belief"(a) or an assumption. "The word supposition (Lat. suppositio ) originally meant substitution, and commonly indicates an assumption, hypothesis, or theory."(c) "In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something."(b) "Aristotle believes that only propositions are true or false."(b)

This is supposition claiming that suppositions differ by necessity, first resulting in the basic assumptions of true and false. This manifests into different types of suppositions which manifest as the laws of identity, non-contradiction, and excluded middle (which are not limited to but are inspired by aristotles writings). All laws and rules for suppositions are suppositions in themselves as statements of assertion

"Difference is because of necessity" or "necessity therefore difference" can be observed as corresponding suppositions, thus asserts assumptions.

Aristotle claims differentiation is necessary because "nothing new" stems from "one premise" (Stanford encyclopedia, 3.2, aristotle's logic). Necessity of differentiation is grounded in "newness".

This differentiation, observed by the law of excluded middle, however is a constant voiding of one assumption into many.

One example is Cat ---> (Cat exists. Cat does not exist.)

This observes difference as a constant state of assuming nothing, ie that each contextual identity assumed is effectively nothing in itself.

It is this "or" state of being (embodied by the law of excluded middle inherent within idenity) which is fundamentally assumed, much like difference, considering it requires observing a thetical and antithetical state of a phenomenon that is subject to the angle of the observer. This deduction of perspective is observed by the pyrhonists and neitzche as a deduction of the nature of supposition.

The angle of the observer, as both a point of assumption and assumption, varies considering it is subject to deduction itself.

Thus deduction results in the atomism of supposition and there corresponding perspectives, leading to an inherent multiplicity where one phenomenon is approximated through its parts.

Thus necessity leads to differentiation of one supposition into many as an approximation of it. Deduction results in vagueness as continual propositions, as categories, are made resulting in one core supposition existing in multiple states.

(a) https://www.bing.com/search?q=suppositi ... CA140579D1

(b) https://www.iep.utm.edu/aris-log/#H2

(c) https://www.encyclopedia.com/religion/e ... tion-logic
The terms, "duct" and "duce" are the root terms of induction, deduction, and abduction. These mean "lead" ('duct' may be an old past tense of 'duce'). In logic, the means of HOW one leads or is led to a conclusion depends on whether the information supporting the conclusion is more certain or not. "de-duction" means "lead from" and for logic, defines the reasoning that has perfect closure or certainty depending upon the evidence. That is, the argument (verbal evidence claims) leads to the conclusion with direct certainty, like a pipe that forcefully directs water through a duct to a unique place.

"Induction" actually means that the conclusion is not lead directly to with certainty. This is still more how we learn through association but is not absolutely certain because it is about drawing conclusions as statistical popularity through patterns. For instance, if I said what follows, "1, 2, 3,.." is "4", this is not something rationally certain to be true but is a type of guess based upon patterns. For another instance, we induce that the sun rises and falls within every day by noticing the pattern of MOST days but not all.

A "deduction" then is a demonstration of how a conclusion MUST follow with certainty by the argument that leads to it. This too has one dependency: that all the evidence (input premises) used to suppor that conclusion is true. In essence, the whole argument with the conclusion is a hypothetical or conditional type of statement: If the given assumptions are true, then the conclusion is true.

The assumptions going in act as 'evidence' that imply the conclusion if true. As statements, these are called premises, because all lines may not be assumed but subconclusions or prior proven statements (theorems) from another argument outside of that one.

When we assume something true by directly witnessing it through our senses, this is a 'pose', just as this word is used today in contexts of some model freezing their stance. This root term defines many related ones that relate to logic: posit (pose it), post (posed), positive, position, proposition, opposition, preposition, supposition and more. If you spend some time on this you'll discover a very large range of words from this one root because everything we begin reasoning from begins from an initial observation (something the environment 'poses' to our senses). The position one holds does not mean other positions do not. A "supposition" is any claim UNDER the assumption of a POSITION. Thus, when we 'suppose' something, it doesn't have to be true.

I doen't understand your means of interpreting things. But deduction is certain UNDER those pro-posed claims of an argument that implies the conclusion. If the argument is false, then either one of the premises are false based upon those particular premises that assume/presume. Does this help?

Eodnhoj7
Posts: 5883
Joined: Mon Mar 13, 2017 3:18 am

### Re: Does Deduction Necessitate Approximation and Vagueness?

Scott Mayers wrote:
Wed Sep 04, 2019 3:22 am
Eodnhoj7 wrote:
Thu Aug 29, 2019 9:46 pm
"A deduction is speech in which certain things have been supposed, something different from those supposed results because of necessity there being so" (Aristotle, Prior Analytics I.2, 24b 18-20).

The statement is a speech making a supposition, which is an "uncertain belief"(a) or an assumption. "The word supposition (Lat. suppositio ) originally meant substitution, and commonly indicates an assumption, hypothesis, or theory."(c) "In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something."(b) "Aristotle believes that only propositions are true or false."(b)

This is supposition claiming that suppositions differ by necessity, first resulting in the basic assumptions of true and false. This manifests into different types of suppositions which manifest as the laws of identity, non-contradiction, and excluded middle (which are not limited to but are inspired by aristotles writings). All laws and rules for suppositions are suppositions in themselves as statements of assertion

"Difference is because of necessity" or "necessity therefore difference" can be observed as corresponding suppositions, thus asserts assumptions.

Aristotle claims differentiation is necessary because "nothing new" stems from "one premise" (Stanford encyclopedia, 3.2, aristotle's logic). Necessity of differentiation is grounded in "newness".

This differentiation, observed by the law of excluded middle, however is a constant voiding of one assumption into many.

One example is Cat ---> (Cat exists. Cat does not exist.)

This observes difference as a constant state of assuming nothing, ie that each contextual identity assumed is effectively nothing in itself.

It is this "or" state of being (embodied by the law of excluded middle inherent within idenity) which is fundamentally assumed, much like difference, considering it requires observing a thetical and antithetical state of a phenomenon that is subject to the angle of the observer. This deduction of perspective is observed by the pyrhonists and neitzche as a deduction of the nature of supposition.

The angle of the observer, as both a point of assumption and assumption, varies considering it is subject to deduction itself.

Thus deduction results in the atomism of supposition and there corresponding perspectives, leading to an inherent multiplicity where one phenomenon is approximated through its parts.

Thus necessity leads to differentiation of one supposition into many as an approximation of it. Deduction results in vagueness as continual propositions, as categories, are made resulting in one core supposition existing in multiple states.

(a) https://www.bing.com/search?q=suppositi ... CA140579D1

(b) https://www.iep.utm.edu/aris-log/#H2

(c) https://www.encyclopedia.com/religion/e ... tion-logic
The terms, "duct" and "duce" are the root terms of induction, deduction, and abduction. These mean "lead" ('duct' may be an old past tense of 'duce'). In logic, the means of HOW one leads or is led to a conclusion depends on whether the information supporting the conclusion is more certain or not. "de-duction" means "lead from" and for logic, defines the reasoning that has perfect closure or certainty depending upon the evidence. That is, the argument (verbal evidence claims) leads to the conclusion with direct certainty, like a pipe that forcefully directs water through a duct to a unique place.

"Induction" actually means that the conclusion is not lead directly to with certainty. This is still more how we learn through association but is not absolutely certain because it is about drawing conclusions as statistical popularity through patterns. For instance, if I said what follows, "1, 2, 3,.." is "4", this is not something rationally certain to be true but is a type of guess based upon patterns. For another instance, we induce that the sun rises and falls within every day by noticing the pattern of MOST days but not all.

A "deduction" then is a demonstration of how a conclusion MUST follow with certainty by the argument that leads to it. This too has one dependency: that all the evidence (input premises) used to suppor that conclusion is true. In essence, the whole argument with the conclusion is a hypothetical or conditional type of statement: If the given assumptions are true, then the conclusion is true.

The assumptions going in act as 'evidence' that imply the conclusion if true. As statements, these are called premises, because all lines may not be assumed but subconclusions or prior proven statements (theorems) from another argument outside of that one.

When we assume something true by directly witnessing it through our senses, this is a 'pose', just as this word is used today in contexts of some model freezing their stance. This root term defines many related ones that relate to logic: posit (pose it), post (posed), positive, position, proposition, opposition, preposition, supposition and more. If you spend some time on this you'll discover a very large range of words from this one root because everything we begin reasoning from begins from an initial observation (something the environment 'poses' to our senses). The position one holds does not mean other positions do not. A "supposition" is any claim UNDER the assumption of a POSITION. Thus, when we 'suppose' something, it doesn't have to be true.

I doen't understand your means of interpreting things. But deduction is certain UNDER those pro-posed claims of an argument that implies the conclusion. If the argument is false, then either one of the premises are false based upon those particular premises that assume/presume. Does this help?
Help? Duct/duce as meaning "lead" necessitates logic (language by default) as having inherent directional qualities in which it is grounded...which I have been arguing all along.

Yeah it helps, it provides a deeper layer of patterns to understanding how we assume things...

And a very good and interesting way of looking at language, which I have forgotten.

As to my means?

The means are simple:

Deduct deduction.

Deduction, if deducted as an assumed assertion, eventually leads to a multiplying of assertions which in the end leads to deeper obscurity and vague...even as to what deduction is and how it is presented through a multitude of words.

The movement from a subject to a predicate necessitates the predicate eventually becoming a subject.

It is a process of how we assume reality by continual seperation of one assumption to another. This necessitated that how we assume reality occurs given a state of underlying form, ie linear reasoning. This is further evidenced, through your correct claim, that inherent within the word "deduction" is "duce" or "dux" which is Latin for "lead".

This nature of projection, as linear, necessitates that deduction evidences a rational foundation in man of apriori "space". This apriori state which is not only assumed but how we assume reality necessitates further that we intuitively and intellectually are aware though spatial axioms....in this case "the line" where one assumption is projected to another assumption or set of assumptions through a linear form. Space is thus axiomatic and apriori do to its form that in grounded the nature of assumption itself.

Basic platonic form sets the foundation for our rational nature, and they are most likely not even platonic but stem from some prior philosophy considering the involvement of Egyptian philosophy seeding itself with the greeks.

Will look through rest of the post later, but yeah not only was it helpful but very valuable and well thought out.

Real good post Scott, and I very rarely do I throw out compliments...so take it for whatever it is worth.

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