A Theory On Language And Mathematics

A Theory on Language and Mathematics Russell Lemburg 1.1

Let us define as a major premise the function of language as an aggregate of signifiers.

1.2

Let us then define as a minor premise the function of thought a priori to language, but priori to logic in a field indeterminate of symbolics.

1.21

The idea of logic is founded upon the idea of thought as a principle of choice and reason.

1.22

To reason is to choose; that is, to separate thought into the categorical, then proceed with a function of that category.

1.23

Take, as our first object, A as being reason about a logical pathway. We can proceed to adopt A in conjunction, or in unity, with B, under the constituency that we determine A in some set belonging to B. Likewise, we can reason A > B, or B > A for the purpose of principle.

1.231

This reason in principle is founded on objectivity.

1.232

We can reason that A is partially unified to B. This is reason in subjectivity founded on principle.

1.233

We can reason that A shares qualities involving subjective language to B. This is reason in subjectivity founded on language. This is founded entirely on subjectivity. Were it to contain complete objectivity, we would define A in terms of B, a utility which requires logic but no language.

2.0

To think is to found upon an idea of thought as principle of choice and reason, infinitely so.

2.1

To communicate is to found upon an idea of thought, with or without the utility of language, to encapsulate ideas or emotions and output them in aggregate form.

2.2

Principle is deductive.

2.21

Reason is deductive, practical, and speculative.

2.211

To reason is to complete and form upon abstractions which are utilized through indeterminate symbolics, all of which encompass the former principle of choice and reason. Because these are deductive, they are optionally inclusive.

2.3

Reason is distinctly human.

2.31

To be human is to be capable of reasoning (sic).

2.33

This reason extends beyond the gateways of abstraction and the indeterminate symbolics of language to moral devices such as good and bad, and the subjective gateways of pain and good will.

2.331

These categorical impulses to communicate the absorbed and experiential truths demonstrate the human attributes of the collective impulse.

A Theory on Language and Mathematics 2.4

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The collective impulse is a function of the attributes of the human mind; these are things which enable thought as a global range of human thinking, whose core is to discover the meaning of thought and morality.

2.41

Since the function of thought is inherently separated from the ideas of language, human reason is an independent function of will. Take the following example: Let us define an eccentricity of will as the basis of understanding morals. To define the principle

involved in making a moral decision, we will define function φ ( q ) as the function of a collective impulse as directed from a point of logic, q, and incorporate that output as an abstraction of its result upon society and the collection of external logic and thought. Let φ ( q ) = φ ( q, i ) as a function both an independent point of logic and a sum of points. If the points in set {q} are abbreviated to fit the maximum number of points in i, we have a moral theory with the greatest number of collective impulse. We would say then that the collective impulse is above standard deviation, or that it is highly one-to-one in respect to points i. This function is linear, and its probability range exists in a field of 1, true, and 0, false. We define the domain of the collective impulse function to be 0 ≤ φ ( q ) < φ ( q, i ) < 1, because the range of a normal collective impulse will theoretically never be completely true. Likewise, we can assume at face value that the ignorance of any collective impulse can give us 0, so the domain for the function is: { φ | [0,1] } for all [q, i]. 2.42

To derive the function involving all points of interest for a collective impulse, we take the function φ ( q ) and make that function absolute (that is, the positive sum of all negative and positive affinity in the set. The function then becomes | φ ( q ) | . We want to find the linearization at a, where the greatest possible number of points of logic in series with the number of all points. Now if this point q is adapted to fit the region under the curve in all

φ (q ) , we end up with the distance of all points q that fit the logical progression over a domain of all t. Taking the number of sample points about a range, we can use a Riemann sum (used for principle in 2.52.7): t

| lim ∑ f (qi* )∆t | , which indefinitely describes the sum of all points in domain [0,t] for all points of t →∞

i =0

logic in a period of time. To compare the gradual increase in the sum of points of logic in respect to an existing collective impulse of an idea (communicated or un-communicated), we can set the function of qi, all points of logic in the system, and interpret these points as the intersection of two sets.

First, let’s rewrite the Riemann sum as an indefinite integral in the proper domain, then intersect the remaining collective impulse function, both in terms of our original function | φ ( q ) | .

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∫

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t

Thus, the comparison: { | φ (q )dt |} ∩ {φ | φ ( q, i )} , letting the first component be u and the second v, gives us the sum of all remaining collective impulses of logic where all the points in q lie in some set respective to i, justifying the sum of all points as an intersection of the set to u and v. Therefore, t

{∫ | φ (u )dt |} ∩ {φ (v)} in all [u,v]. We can calculate the collective impulse quite directly in this way. We state that the intersection is as follows: 1. u and v is the set that contains all elements of u that also belong to v, or all elements of v that also belong to u. With a point of logic, we have u as the boundaries of the definite integral defined by [0,t], which are constant to (1)(u – 0), or u, meaning that one point u as a constant and certain point of logic refer to an independent variable u, and the collective points i > 2 + n, where n is any integer. This means that in order for thought to be collective, it must be accompanied by more than one individual mode of thought. 2. φ (u , v) gives us our construct of collective impulse in terms of all u and all v in our respective domain, without implied intersection. That is, the sum of all individual points of thought and logic in reference to a single sum of similar thought or points of logic. This function is sequential, meaning that the sums of its points have both beginning and end indices. We can compute the singular thought-base index by subtracting the collective impulse function from our singular point of logic function:

φ (q) − φ (i ) , noting that since φ (q) < φ (i ) , we will have a positive reference to the magnitude of one point of logic in respect to the collective impulse. Since a collection of points of logic can be larger than 1, based upon the time-rate reference to these points (not encapsulating number of individuals), we can also have a positive number. However, we note that a positive answer to this inequality is extraneous. 2.5

To think a priori in language is to think outside of the constructed elements of that language. Kant claims: “That all our knowledge begins with experience there can be no doubt... But... it by no means follows that all arises out of experience.”

2.51.1 According to Kant, a priori knowledge is transcendental, or based on the form of all possible experience, while a posteriori knowledge is empirical, based on the content of experience. Kant states, “...it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion).” 2.51.2 To relate these ideas to the foundations of language, is to magnify language as a collective impulse of ideas in respect to their points of logic, each in a respective domain [0, φ ], as a

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representation of the sum of a certain similar point of logic over a domain from 0 to its function of logic. Here, 0 provides the measure of falsity in a system, which can be interpreted either as an ignorance of a logical premise (simply not knowing of its existence or lack of experience with it), or a strict denial of its meaning. 2.51.3 We use the Fundamental Law of Calculus to describe, as the summa of a position of an object over time would give us distance, the summa of a set of logical points would give us the concentration of the logic. We could also term this concentration the interest. Likewise, we can describe nature in terms of symbols as Boolean or Statistic, either of which give us a resulting collection of ideas as a function of the attributes of the human mind, which enable thought as a global range of human thinking, whose core is to discover the meaning of thought and morality. 2.51.4 These fields of logic present us with the collective impulse, but also relate the growth of understanding and progression, logically speaking.

Definition 1: Let us define as a major premise the function of language as an aggregate of signifiers. Corollary 1: An aggregate of signifiers need not be language, but constitutes its primary method of function. 2.52.1 Take, for sake of example, the way in which a human being would conceive of a lamp. Ideally, the lamp for one might take into consideration ethereal properties such as light and dark, but also of the physical properties of the lamp, such as shade, texture, and contour. With these principles, we can describe the symbolic representation of the lamp by use of language which mediates our impulsive thought process to internally visualize the meaning of the lamp. 2.52.2 Platonically, the exact meaning of the lamp would be represented in a world of forms, completely unaltered by any human interpretation. To say simply, the lamp is. 2.52.3 To be is to exist. 2.52.4 To say an object is is to say that the object exists in nature. 2.52.5 Again, platonically, the realistic meaning of the lamp is represented in a world of reals, altered by human interpretation and the limits of symbolism. 2.52.6 Consider, at length, that the lamp is described by A. Letting A be our primary subjective descriptor, our input medium (a communicable human being), interprets A as 1 −

φ ( A) − φ (q) . φ (i )

We can see that the real definition of the lamp in the world of reals is true, or given a value of 1. The function of thought for the observer is a function of A, in terms of logical appropriation to the sum of all meanings that A have produced. Let us consider that the collective impulse of these thoughts is measured by the collective consciousness of the meaning of a lamp. For this to be true, the observer is limited by the statistic reality of all thoughts within i at a complete domain of

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[A, i), not inclusive. Given this, our average is the function of the observer’s thought in respect to the complete thought of observing all the real properties of the chair minus the observational thought from the communicator. That is, the real property of this representation is quantified by the sum of all logical points minus the average value of all symbolic harmony with the observer, averaged with respect to all possible outcomes, subtracted from the point of logic from the communicator. The complete domain is less than one as long as there is a point of observational logic, q, from which the communicator has observed and produced in the symbolics of language. Our domain for all subjective communication is then, roughly: 0 ≤ φ ( A) < φ ( q ) < φ (i ) < 1. 2.52.7 Truth is any function which matches the closest quantity {φ ( q )} ∩ {φ (i )} . Strictly speaking, this says that truth is a matter of an independent mode of thought intersected with the greatest number of similar objective thought. For the function to be true, however, φ (i ) would need to define itself as true. Let µ = {φ ( q )} ∩ {φ (i )} . Then, let φ (i ) → 1 as µ → φ (i ) . Since the intersection of this function is all objects remaining in the set, it cannot contain itself, and therefore neither

φ (i ) nor µ will reach 1. However, we know that theoretically ∆φ (i ) → 1 > ∆µ → φ (i ) . Therefore, we know that at the point at which both intersect, we have arrived at the conditional magnitude of truth, justified only by the greatest number of logical points under the condition of the collective impulse. To find this, we add the number of points over time as a summa of independent points of logic and test this magnitude in relation to φ (i ) . Considerably, φ (i ) >

φ (q) at tmax, but at a point in [0,1], we will find that the deltas are variable upon some time rate of change. This property (the reason we sum the points over infinite time), enables us to differentiate points of φ ( q ) to find when

d φ (q) = 0 at tmax. However, if both functions increase dq

at constant rate, we could or could not arrive at a point of truth, indeterminately so. 2.52.8 We state, then, that there is calculus involved in logic, and this calculus enables us to find the rates of change from rate, as well as from number. This determination avoids the statistics of the matters of logic, and gives us an adaptable and more reasonable solution to the growth of a point of logic in respect to a certain collective consciousness, which we have hereby defined as i. 2.52.9 The calculus of these independent points of logic as a function, φ ( q ) , in respect to the collective impulse function φ (i ) tend to 1. In the domain of complete falsity and complete truth, we assume at some point in this range q = i have at one point a similar time rate of change, thus,

dφ (q ) dφ (i ) = . At a maximum, we assume also that at some point, relative to time, that dq di [

d (q ) dφ (i ) = ] = 0 . We know that when the function is linear and continuous, it has no dt dt

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A Theory on Language and Mathematics maximum value, so we state that [ continuous and therefore

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d (q ) dφ (i ) = ] = c . If this is the case, our rates of change are dt dt

dφ (q ) dφ (i ) < . dq di

2.52.10 When these rates of change are equal, the singular thought function never reaches the collective impulse, so it evolves into a non-communal point of logic; that is, there is no immediate relationship to the theory of language as widespread phenomena. 2.52.11 When

dφ (q ) dφ (i ) dφ (q ) dφ (i ) > , φ ( q ) = φ (i ) . Since ∉ for all q, we never reach a function dq di dq di

whose rate of change at a single point exceeds the rate of change for a group consciousness. Therefore, this statement is false. 2.52.12 The measure of falsity in this system is at a local maximum to [q,i] within all [0,1] (all levels of tested absolute truth or absolute falsity).

Definition 2: The idea of logic is founded upon the idea of thought as a principle of choice and reason. Corollary 2: The principle of choice and reason requires logic. 2.6.1

We note that in choice and reason there exists a field of metaphysics concerned with subjective and objective morality.

2.6.2

By an objective standpoint, the methods of the calculus of logic are apparent.

2.6.3

A singular thought, verified as true by the laws of nature, has a value which tends to 1 at a rate higher than the relative maximum of the collective consciousness within its respective domain. This causes an intersection of ideas, thus enabling the communication of the abstract to the logical field of subjective morality through an objective compass.

We state then, that the rate of change over time of a singular point tending to 1 can be greater than the rate of change over time for a collective set of logical points.

(

dφ (q ) dφ (i ) → 1) > ( → 1) , but remember that at the evaluation, this statement is false: dt dt

dφ (q ) dφ (i ) > , if we let our independent variable of differentiation be different from time, we dq di assume that the rate of quantity of a singular point is greater than the rate of quantity of a collective set of logical points. Let’s test this theory graphically. Consider we have a point of logic which is consistent upon one logical idea, perceivably uninvolved in language or symbolics, but rather, becoming collectively similar to the collective logic. Furthermore, we have a collective number of logical points (dissimilar to our singular

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point of logic in that it shares only particular agreements in logic). This point of logic is increasing at a rate of, say, 2i12 − 3i1 . Note that this rate deals with quantity, i, whereas our rate in singular logic deals with one point of logic over a certain time domain. Consider the domain [0,1] as the maximum range of all objectively true critical points. We can infer that the differential output of our singular rate at a sample point will intersect if there exists one point in which the rates of change are similar. We call this point the absolute harmonic function of logic, when the collective consciousness agrees with our critical point. At this time reference, the point of logic becomes a member of collective consciousness, for their relativistic magnitudes of truth are exactly the same. Further, our axes are noted by φ as the dependent axis and q,i as the independent axis. The value of truth, then has a value of {φ | 0 ≤ φ < 1} .

2.6.4

We end up with a function similar to this: At the minimum, we arrive at different slopes, but the same critical point, slightly above absolute falsity and can then state that the rate of our singular logic function is not high enough to reach subjective reality. This theory will be greatly explored in further detail.

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