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.