Perceptions of Analytical Applications

Perceptions of analytic applications (Part) from Rosanna Festa

Mathematical logic places points in space based on the corresponding logic function. In history there are processes of transformation of languages: in Formulation of fundamental spaces we spoke of infinitesimals (the infinitesimal calculus of Leibniz), now they are thousandths; Newton's laws found their most natural expression in the analytic language of differential equations at the end of the process of understanding his time (thanks above all to Leibniz's differential calculus, that is the infinitesimal calculus). The figures were progressively replaced by equations. The work of conversion to analytic language was completed by the continent's mathematicians, as was the gradual conversion of Newton's geometric mechanics into analytical mechanics, including Euler, D'Alembert and Joseph-Louis Lagrange. Deep theories that arise as scientific notations are Boolean logic, logical implementation, the discussion of Hilbert's problems, problems dealt with in my book Scientific and procedural notations, which uses simplified notations to understand the process from mathematical analysis to the phenomenon physical passing through the systems of points and rigid solids. Matter is transformed, this becoming takes shape in the complex geometry, represented by Hume by relations of ideas, thus also the ideas are transformed, which is a solid principle of analytic philosophy and therefore in philosophy we make full use of complex geometry, which man rationalizes into laws. Knowing contemporary physics is a privileged point for contemporary philosophy, and for this reason they must be associated. It is sufficient to carry out a consistency analysis of a text on the philosophy of science, we will have antithesis, thesis, limits, theoretical solution properties. We will be able to have the discussion of the closest question within the "limits", then the scientific subdivision, linguistics, operationism. The operation has a meaning according to the first declension (derivation), the second declension (derivation), and so on, which introduces the philosophy for the notion and for the logic, and then an inference. "As will become apparent later, not only in Kyburg's reason for eschewing the translation <consistent> not a compelling one, but de Finetti himself often appeals to criteria of coherence / consistency which, though not extending beyond the intuitive and informal, seem to have much in common with those of logical consistency and are certainly in strong tension into almost open conflict in de Finetti's discussion of the countable additivity issue where it is decisively resolved in favor of the informal criteria, obliging him to place severe limitations on the latter, to the point of denying explicitly that the existence of a Dutch Book necessarily signals incoherence. This trumping of the operationalistic by informal, quasi-logical criteria should not be altogether surprising to anyone who has paid attention to de Finetti's more philosophical observations, since there is a good deal of evidence, particularly in his earlier work, that he saw the laws of probability very much as laws of log ic "(1).

(1) De Finetti, Countable Additivity, Consistency and Coherence by Colin Howson, in The British Journal for the Philosophy of Science, volume 59, number 1, March 2008.

While Einstein's theories must be variants, Newton's laws are calculated results, this is important in the history of philosophy, because the concept of time changes. Variants for philosophy turn out to be problematic as far as Einstein is concerned in physics; in astrophysics the laws of general relativity and quantum mechanics are applied and the Universe is discussed on a mathematical scale. Speaking of the close parallelism between mathematics and modern philosophy, mainly expressed by Spinoza in the order of ideas and things (idea 1, event 1), this relationship splits only with Immanuel Kant. First all knowledge and all the general concepts of things are linked by humanistic aspects, in which geometry and mechanics are among the first, or mathematics and geometry in the age of Science and the Absolute State (2), mathematics is hence a "provisional" result.

(2) Philosophers and ideas, Philosophical experiences and history of thought, Mondadori, 2005, The modern age, Hobbes, p. 323

The mathesis universalis, Galileo Galilei, Descartes, pascaline, Leibniz associate mathematics with physics, following Newton's mathematical physics. It is this intrinsic difference between philosophy and physics that turns on a light bulb in modern philosophy, essential to investigate more deeply starting from the Renaissance thought of immense space, of the infinite Universe. Kant denies the character the "transcendent" character of metaphysics because space and time are dimensions n too large, and given the impossibility of metaphysics as a science, given by Kant, faced then as today with the mathematical scale imposed in physics, transcendent is a privileged position in space, on Mars for example, in order to diversify the experimental method and other components, a position farther away in this immense ocean. The symbiosis between contemporary physics and contemporary philosophy due to the methods of eccentricity of both, in Albert Einstein's theory and in pre-relativistic philosophy, in which the infinite presupposes a position in space, therefore in mathematics, physics and mechanics, it presents itself as such also on an experimental basis as such, starting from the concept of infinity and the minimum values of the context. Testing speed is like taking a trip across the Channel, you would enter with the ideas of Galileo Galilei and you would come out with the ideas of Enrico Fermi, Stephen Hawcking and so on. The most intelligent solution is realized as an excellent Pareto, also because there is moral philosophy, which is the world of the unreal. Real and unreal are part of man's intelligence, as well as physics. Physics also needs other mathematical scales, since metaphysics is inaccessible.

The acoustic oscillations experienced by protogalactic clouds, proto-clusters and proto-superclusters do not disappear with the advent of recombination and today they would be recognizable in the distribution of galaxies. The undulations can be seen both in the angular distribution from here, and from the Milky Way, as well as in depth, in z. Since z is isotropic, we also have that t moves proportionally to q, and proportionally to mass. Abstract, linear algebra, group theory, ring theory, not field theory (for statics reasons) can be applied to complexes of theories that equate physical systems such as Relativity, the Higgs boson, neutrinos. , however, computational algebra can be applied. This variable z is given to us by Hume, and corresponds to the critique of metaphysics: therefore, for Hume, only what is perceived is real. hic et nunc, from our impressions. True is what is achieved in the moment of impression, while any generalization and anticipation of the future establish only hypothetical and probable links. Humean empiricism constitutes a radical critique of the claim to see universal and necessary laws operating in the world and an invitation to a greater awareness of the limits of human reason. But let's take stock.

Going forward we report the quotes of Karl Popper, Emanuele Severino and the undersigned Rosanna Festa.

"The point of view that I call" psychologism "is still at the basis, so it seems to me, of a modern theory of the empirical basis, even if its supporters do not speak of experiences or perceptions but, rather, of" statements ": statements which represent experiences. Neurath and Carnap call them protocol statements. A similar theory was held, in even earlier times, by Reininger. His starting point was the question: where is the correspondence, or concordance, between a statement and the state of things it describes? He came to the conclusion that statements can only be compared with statements. (3) Spinoza and Leibniz hold firm to the Cartesian principle that reality external to human thought is not the immediate content of the latter. (that is, that "formal reality" is not "objective reality"); but both consider the relationship between thought and external reality as a particular case of a universal law of reality. * Carnap's thesis is that all philosophical investigations speak of "forms of discourse". The logic of science must investigate "the forms of scientific language". It does not speak of physical "objects", but of words; not of facts, but of statements. To this correct mode of speech, the "formal mode of speech", Carnap contrasts the mode of ordinary speech, or, as he calls it, the "material mode of speech". If it is allowed (as, in Neurath's view, everyone is allowed) to simply "delete" a protocol statement that is not convenient, any system becomes defensible. I propose to look at science in a way that is slightly different from that advocated by the various psychological schools: I wish to make a clear distinction between objective science on the one hand and "our knowledge" on the other. (4) Some terms of Peirce's statements on continuous series are reductive, because the quantities of infinitesimals possess distinct properties but above all of real quantities. Since Kant theorizes that to speak in terms of numbers one must not neglect mathematics which is assumed to be a true science, and therefore Fermat's

theorem is valid, if associated with countable (finite) sets, algebraic relations are obtained, if denumerable (infinite nhumerable) we obtain more precise quantities, and these occur more often in continuous series and in the calculation of powers (and in the continuum). (1) The part of Peirce's mathematical philosophy according to which the infinitesimal quantities, which constitute the structure of continuity, are not exactly expressible and discriminable and therefore the placement in a linear series consists in a critical statement, in fact, in the theory of complexity one must refer to the origin of the function if it is extended to several points, in fact this location can be antithetical. Mathematics is the study of the indefinites (infinitives) while logic is the development of indicators (indicators) or of states (signs) in which the logical definition is assumed to be true or probable. In mathematics there are also undefined entities because the mathematical entity is considered akin to mathematical calculus of a static nature. What is meant by references to mathematical infinity and its formal relations, in addition to conditional reasoning, which together form relations with a certain validity or even the algebraic structure? Understood as biunivocal relations, starting from what is deduced from the concept of infinity, we have obtained results from the hypothesis of demonstrable data more generally starting from the fundamental equation, that is, from the formula established by the conditional connective. (2) Set theory is an important topic for applied mathematics, because in applied mathematics we can apply different types of number generalization. (3) The foundations in Peirce's resolution regarding associated properties are found in mathematical analysis, particularly identity relations, and are part of the meaning of the term mathematical, even in epistemology. Thus in the philosophy of mathematics mathematical indices are used as indices of the term obtained from a strictly mathematical point of view. Peirce does not feel the crisis of the foundations of mathematics because it is based exclusively on a "mathematical-synthetic" criterion, and not a "logical-analytical" one. The problem is to describe the system of relations of mathematics within a process, or within an analytic philosophy, making clear the distinction between logical-analytic and analytic in the strict sense "(5).

(3) Karl R. Popper, Logic of scientific discovery, The self-correcting character of science (4) Emanuele Severino, Philosophy from the Greeks to our time, modern philosophy (5) Rosanna Festa, Function and calculator. Areas, fields, applications.

In analytical philosophy it is possible to reduce the term to a series of elements in data that are assumed to be macros, or fields, or categorical terms, which make the proposition true in the terms we indicate and can be better explained if we configure a configuration of sense. The methodology of calculating phenomenological data in chemistry means that there are "validating" elements, as we know not all data in computer science is treated in distinct units, and therefore there are different configurations of the elements in feasibility analysis.

In the first order analysis of language an information system is also a system for describing a processing for synthesis from the point of view of programming. A computer microprocessor can perform rapid sequencing by isolating a part of it and treating the remaining part in intermediate ways. (6) The first definition that comes to mind is that of a series of cardinal numbers, in the same way as those treated by Cantor for the finite series.

Starting from logics that occur before the proof, there are relations similar to the reduction of n integers in the logic of the first order which are the fraction of an integer. This is a problem similar to that addressed by Popper in the method for building models of random sequences *. It is also a question of separating in logic through the connectives those numbers that we must indicate and are in a certain sense "deconstructed" and reduced to possible separations, such as the "sections" of the rational numbers so called by Dedekind, to enumerate and then separate the units . In the same way, if we take a computer, it first records the input data and then makes a separation based on fractions, or on continuous series, or again on the basis of tracers.

In the same unit the number of integers is not the same as that of rational numbers, but it is still a smaller number like N: 2. (7)

in this way, among other things, the reduction of information into sequences that vary according to minimum paths is obtained. “The reduction of information (from 12 to 10 bits) when the 0s and 1s are used in the same proportion is not sensitive, and becomes minimal for even longer sequences. On the other hand, the loss is much more sensitive if one of the symbols occurs more often than the altro. Can we apply these concepts to establish the information speed of a message in normal language? Not exactly, but some evaluations elaborated by experts have defined it as very low, that is 1 bit per letter, while an unrestricted choice of letters would increase the amount of information by 5 times. In fact, all the elements of the language contribute to reducing the content of the information, because the spelling rules - for example the obligation of the "u" after the "q" -, the need for pronounceable combinations, the grammatical rules and even the effect of the context on several sentences limits the choice. In information theory, these choice limitations produce the so-called redundancy, because if the text gives less information than it could, it means that, in theory, a part of it is not necessary. An example of redundancy in the body of a single word is given by con, the only Italian word to have the consonants c, n in this order. In practice, a certain redundancy is essential for faithful transmission because, if it is true that in theory we could invent a code that abolishes all redundancy by restricting the normal language to one fifth of its size, one wonders what would happen if we used this code to send a telegram. If only one mistake were made in the transmission, the machine that translates from the code at the receiving end would give an incorrect message and perhaps perfectly current as to the meaning. [...] Extending the information theory to continuous signals, the problem arises that there is no satisfactory subdivision of time into successive "steps", which can however be inserted by sampling the signal, i.e. measuring the intensity of the signal only at intervals fixed (these techniques find practical application in some communication tools, such as modern telephone systems, but now these applications do not concern us directly, because sampling for us is a completely theoretical exercise that allows us to simply measure the information contained in a continuous signal). Each measurement is like a single signal in a binary notation system.

(6) “One of the basic facts concerning information theory is that the rate at which messages can be transmitted over a radio cable is limited by the available bandwidth (ie it depends on the information capacity). For a message of the simplest type, of the on-off type like the Morse alphabet, a very narrow band is enough, while a television program, in which millions of "samples" are transmitted per second for the reproduction of the image, requires a very wide frequency band. As we can see, a very small change in wavelength, in the ultra-short wave sector of the spectrum, produces a very strong change in frequency: in this part of the spectrum, therefore, there is room for a large number of high-power transmitters, each with its frequency assignment. Information theory also deals with interference that disrupts communications. […] In telegraphic and telescopic networks, both by wire and by radio, the disturbance can come from various causes, such as for example from the amplifiers or "repeaters" of a telephone cable.

Other causes of interference are storms and the bombardment of the atmosphere by particles from the Sun. Even the flow of electrons in a wire can cause disturbance, so much so that many researches aim at the construction of electronic devices that can maintain the relationship signal-to-noise at a satisfactory level.

One of these tools is the maser, a crystal capable of being "charged" with electronic energy; when it is thus loaded it is able to receive very weak signals and to retransmit them enormously amplified. The maser is very quiet compared to the amplification it produces, and can be made even quieter if kept at a very low temperature (-268 ° C), in liquid helium. " (7) K. Popper, Logic of scientific discovery, p. 323.