5 To the description of physical equations
Physics formulates the universal laws of the real world by means of the language of physical equations. Both mathematical language in physical equations and verbal language are global, i.e., capable of cognition of the whole world. In this section, we are going to show that besides language the other global sign system involves operational structures too. We will show that the units that make up the equations enter into relationships that, like the word meanings in a sentence, are supported by operational structures. Physics describes not reality itself, whatever it is, but its quantitative aspect; that’s why the description language of physical equations is mathematics. So physical equations describe quantitative reality. The physical equations include a limited number of quantitative parameters and describe the relations between them. Thereby, the physical description with equations reduces a large number of objects to a lesser number of description units and so physics describes not just quantities of the parameters but the quantitative aspect of reality in its entirety. We will take here just a few simple equations with variables connected by arithmetic operations.
Not only non-coupled operations but also non-coupled single states are used with information units. Denoting nothing, single states nevertheless influence the semantics of the unit: They determine the starting point in its denotatum. The quantitative single state determines the ordinal scale of a quality denoted by the used unit and / or the initial amount of this quality on it.
A single quantitative state is incorporated into the meanings of parametric, or gradable, adjectives and nouns. Parametric adjectives are, for instance, ripe, tasty, expansive, good, strong, massive, energetic and parametric nouns are force, mass, energy , etc.
Let us call nouns and adjectives that contain a single quantitative state dimensional. Dimensional nouns nqquantity, degree, height, width, thickness, volume, weight, temperature, speed, kindness , etc., are part of parametric nouns. Dimensional nouns differ from the other parametric nouns: The parameter they recognize is recognized not only by the corresponding dimensional adjective Δnq but also by its negation Δnq . Let us compare the dimensional noun height and the parametric but not dimensional noun kindness . Height : not only high but alsonot high means ʻhaving some heightʼ. Kindness : not kind doesn’t mean ʻhaving kindnessʼ.
The dimensional adjectives large, high, frequent, strong, deep , etc. differ from the other parametric adjectives which recognize object parameters by recognizing not an arbitrary value of the quantitative parameter but a value that is implemented on only one of the opposite parts of the parameter values’ range. So, high means not merely ʻhaving heightʼ but ʻhaving a great heightʼ; smart , not just ʻhaving mindʼ but ʻhaving a great degree of mindʼ; low , ʻhaving a small heightʼ. One can explain this characteristic of dimensional adjectives by the assertion that a dimensional adjective meaning comprises a single quantitative state |Q | which forms quantitative information in the basis of its semantic information. If dimensional nouns are used with dimensional adjectives as words containing |Q |, they must have or be vested with |q 0|, which should be included in |Q |.
Single quantitative states in conjunction with single elective states participate also in forming numeral meanings, which become numeral information when used with a noun in speech. Numeral meanings are formed in interconnected semantic relations of single states where one implies the other. The single states are interconnected as following: The elective state |E | recognizes the ordinal number k -th expressed by an ordinal numeral ΔK (related to a preceding ordinal numeral as “after”) forming theni ’s increment if the quantitative state |Q | recognizes the number k expressed by a cardinal numeral K (related to the corresponding lesser cardinal numeral as “more than”) forming theni ’s alternative increment. Operational structures are involved here not in speech but to form numeral meanings. However, the meaning of an ordinal number is formed, as we have shown, in interconnection with the meaning of the corresponding cardinal number. This means that the need for operational structures arises not only in case of the interconnection of word meanings in speech, but also in the formation of interconnected meanings of a numeral of one category and the corresponding numeral of the other.
Units of measurement are used in equalities and equations. A noun used as a unit of measurement, like foot , includes a dimensional noun as its hypernymic base (ʻdistanceʼ in case of foot ), which we will call dimensional base, and presumes the single state |Q | of the cardinal meaning K . So, units of measurement are used mostly with a numeral and recognize the numerical value of the dimension recognized in turn by a dimensional base, for example, seven miles (in distance ), 5 feet (in height ).
Units of measurement can have the same dimensional base, for example: (ʻdistanceʼ) + (ʻdistanceʼ) = (ʻdistanceʼ); (ʻdistanceʼ) × 2 (a dimension base is absent: dimensionless coefficient) = (ʻdistanceʼ); 1,000 × (ʻweightʼ) = (ʻweightʼ). Or they can have different dimensional bases, like in the equality: (dimensional base ʻlengthʼ) × (ʻwidthʼ) = (ʻareaʼ) and the equations – geometric formulas and algebraic equations: V l (dependent variable) = a dm ×b dm × c dm , or (without units of measurement) V  = abc , where the variables a ,b , c are edges (ʻlengthʼ, ʻwidthʼ, ʻheightʼ), the variableV is the ʻvolumeʼ of a rectangular parallelepiped.
Units of measurement have different dimensional bases in physical equations too: s  = vt , where s is the ʻwayʼ of a body moving with uniform velocity (e.g., s nautical miles),v , ʻvelocityʼ (e.g., v knots ), t , ʻtimeʼ (e.g., t hours); pV  = const, where p is ʻpressureʼ,V , ʻvolumeʼ of an ideal gas.
Here, we will not analyze units that include a single elective state |e |. We only note that it can be part ofvi and of nioperational structures pointing to the starting point in the time sequence.