List: Genuine triads are of three kinds. For while a triad if genuine cannot be in the world of quality nor in that of fact, yet it may be a mere law, or regularity, of quality or of fact. But a thoroughly genuine triad is separated entirely from those worlds and exists in the universe of representations. Indeed, representation necessarily involves a genuine triad. For it involves a sign, or representamen, of some kind, outward or inward, mediating between an object and an interpreting thought. Now this is neither a matter of fact, since thought is general, nor is it a matter of law, since thought is living. CP 1.480
The purpose of this note is to offer a chemical perspective of a few of the challenges that CSP was facing because he was knowledgable in the mathematics and logics of the chemical table of elements that strongly influenced his notion of representation. Underlying this message is the question of the magnitude of the distinctions between CSP semiotics and certain modern trends in non-linear mathematics (catastrophe theories of Rene Thom, and Chaos theory (in relation to so-called “complex adaptive systems”). One perspective way of looking at this post is ask the question: Does CSP logic of representations start the historical process of the separation of applied physical mathematics from applied biological mathematics? The difference that makes a difference (Bateson) is the clear and distinct difference (Descarte) is the notion of atoms as merely metaphysical abstractions vs atomic numbers as informed numbers representing real objects. A central challenge to understanding the nature of chemistry is the assemble of parts into wholes. The constraints of chemical thought are severe. By way of contrast the mathematical system of symbols is basically without any natural constraints in the sense that no natural units of existence are associated with mathematical symbols. The physical symbol system is intimately intertwined with mathematical symbols, defined in terms of a few basic symbolic units (mass, distance, time, electricity, light, temperature, and in some countries, “mole”, a pure number that can be used to count numbers of particles of specific forms, that is, atoms or molecules.) In the mathematics-physics symbol system, CSP’s conundrums wrt to the foundations of logic are secondary to the notions of the laws of arithmetic and the equivalence relations ( upon which Rene Thom based his semantics of form.) So, what are the specific challenges emerging from the constraints on chemical logic, that is, the bedrock issues that underlie CSP’s philosophy? The following are examples from high school chemistry and were known in the 19 th Century. Let’s start with an example from the Bedrocks, not artifacts of Aristotelian syllogisms. Consider the legi-signs for three metallic elements: Li, Na, K. Each of these legisigns is a physically independent object with a physically measurable predicates and can exist in gas, liquid or solid phases. Are these representatems monads? Or, as predicates, the gas, liquid and solid phases measurable physical properties, each of these metals has unique identity for temperature and pressures for phase transitions. So, as predicates, each metal has a triadic form. But, as atoms that potentially can form compounds, each is a univalent so that all three are in the first row of the table of elements. These three legisigns have the chemical indexical value of being univalent, that is, the same predicate. Now consider a second set of legisigns. F, Cl, Br. Each of these legisigns is a physically independent object with physically measurable predicates and can exist in gas, liquid and solid states. As gases, these three elements exist as pairs of atoms, F2, Cl2 and Br2. They are compounds of atoms. Are these representatems monads or dyads? The chemical indexical values of these three elements can be constrained to the valence of one and this is used to place all three symbols in the same categorical row of the table of elements. But this categorization is NOT logically unique. Chlorine and Bromine valences are context dependent may be as high a 7 in the perchlorate and perbromate salts. In other words, same subject symbol, different predicate indices! Now, consider the pairs of legisigns. Are these logical terms monads? or dyads? LiF, LiCl, LiBr. NaF, NaCl, NaBr. KF, KCl, KBr. Are LiF and KBr relatives? Why? Are the symbols for LiF and KBr relational symbols? Why? What are the relationships between the LiF and KBr symbols? Why? What is a genuine triad? Do the three pairs of symbols, LiF, NaCl, and KBr, that are without any common constituents, without any common symbolic logical or mathematical factors, form a genuine triad? "But a thoroughly genuine triad is separated entirely from those worlds and exists in the universe of representations. “ What is the nature of chemical logic such that these three pairs of symbols, LiF, NaCl, and KBr, are said to be of identical relations? or identical relationships? What does CP 1.480 inform us wrt CSP’s conceptualization of the role of representatem in philosophy of logic? The severe constraints on chemical logic are consequences of the concept of assembling parts (atoms) into wholes (molecules and higher order composites such as cells and natural sorts and kinds.) Do the severe bedrock constraints of chemical logic set boundaries on the meaning of the terms “relatives, relations and relationships” in comparison with the meaning of these terms in modern mathematics? Finally, these examples originate in the simplicity of classical inorganic chemistry of metal salts, while CSP asserted that the real bedrock of logic was organic chemistry, the chemistry of life. Cheers Jerry
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