Robert, List: RM: What you describe is right for the experimental sciences of nature, i.e. the knowledge of objects in the outer world. The objects of Phaneroscopy are in the inner world.
On the contrary, as Gary F. already pointed out, phaneroscopy does not concern itself with the distinction between the outer world and the inner world. It studies whatever is or could be present to the mind in any way. RM: I understand that it [the Triadic Reduction Theorem] embarrasses you because it ruins all your arguments, as well as those of Gary F. and Gary R. who follows you. Nonsense, which arguments of mine does it supposedly "ruin"? In this particular thread, I provided nine quotations yesterday demonstrating that Peirce consistently defines mathematics as the science which draws necessary conclusions about hypothetical states of things, i.e., its method is strictly deductive and its subject matter is strictly hypothetical. Anyone is free to disagree with him about this, but no one can legitimately attribute a different view to him without providing a direct quotation where he explicitly repudiates it later. RM: But to make sure you read Peirce's thinking on it, I extract the following blunt quote because it is the core of my entire approach since 1977. CSP: And analysis will show that every relation which is *tetradic*, *pentadic*, or of any greater number of correlates is nothing but a compound of triadic relations. It is therefore not surprising to find that beyond the three elements of Firstness, Secondness, and Thirdness, there is nothing else to be found in the phenomenon. (CP 1.347, 1903) No one is disputing what Peirce states here. In fact, it is a good example of the two major principles underlying his *mature *classification of the sciences as summarized by André in the three slides that Gary F. posted this morning. Phaneroscopy depends on mathematics in the sense that it makes use of its general principles, both by manifesting instantiations of them and by providing critical and validating feedback. This reflects a considerably more developed understanding of the relationships among different sciences than his earlier description of "empirics" as "the study of phenomena with the purpose of identifying their forms with those mathematics has studied," especially since the latter encompasses not only phaneroscopy but also logic, metaphysics, and all the special sciences. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Jul 14, 2021 at 4:46 AM robert marty <robert.mart...@gmail.com> wrote: > Gary F., John Alan, Gary R., List, > > > What you describe is right for the experimental sciences of nature, i.e. > the knowledge of objects in the outer world. The objects of Phaneroscopy > are in the inner world. It so happens that in this world, the relations > between A preliminary mathematical result govern mathematics and > Phaneroscopy that you never mention -and for a good reason- which is the > Triadic Reduction Theorem. I understand that it embarrasses you because it > ruins all your arguments, as well as those of Gary F. and Gary R. who > follows you. I do not fail to mention it in part 6.2 of my article on the > Podium of Universal Categories (concise) which I reproduce below. But to > make sure you read Peirce's thinking on it, I extract the following blunt > quote because it is the core of my entire approach since 1977. > > > > *And analysis will show that every relation which is tetradic, pentadic, > or of any greater number of correlates is nothing but a compound of triadic > relations. It is therefore not surprising to find that beyond the three > elements of Firstness, Secondness, and Thirdness, there is nothing else to > be found in the phenomenon. *(CP 1.347) [ emphasize mine ] > > > > In this case the dependency is native. It is based on the reduction of > adicity justified by the fact that phanerons and the elements of phanerons > are entities connected by their mode of being. So, as far as the > observation of phanerons is concerned, Peirce and all those aware of this > theorem can observe them with the categories already in their mind. The > others tinker. > > > > *[ BEGINNING ]* > > > > *6.2 Why three categories and only three?* > > > > The answer is well known, but it is appropriate to recall it: is the > "Reduction Thesis," a proof of which is given by Robert Burch in his > Peircean Algebraic Logic (PAL). He states that all relations can be > constructed from ternary relations in PAL but not from unary and binary > relations. We also have two proofs established by and Joachim H. Correia > and Reinhard Pöschel (2006) with less strong restrictions. Peirce often > evokes this thesis, either as evidence drawn from the abstract observation > of signs. He sometimes accompanies it with justifications limited to simple > examples. It is at the heart of his "Logic of relatives" and his > "Existentials Graphs." There is abundant literature on this subject. It is > a separate issue that I do not deal with here. > > > > Peirce considers that everyone can get this result from the observation of > phanerons. Even if he did not provide mathematical proof himself, he > nevertheless reinforced the credibility of the reduction by a sketch of > inductive reasoning, which starts with the easy reduction of a 4-unary > relation and goes on to assert that it would be the same for 5-unary, > 6-unary, etc. relations (CP 1.347, 1.294-299). > > > > *And analysis will show that every relation which is tetradic, pentadic, > or of any greater number of correlates is nothing but a compound of triadic > relations. It is therefore not surprising to find that beyond the three > elements of Firstness, Secondness, and Thirdness, there is nothing else to > be found in the phenomenon. *(CP 1.347) > > > > In Peirce's eyes, it is a justification that one can adopt the reduction > as a postulate. He then presents the study of phanerons or phaneroscopy, as > one would an experimental science-based, in this case, on a postulate drew > by abstractive observation of the functioning of signs in social life. > Consequently, he affirms (CP 1.284) that the direct observation allows > isolating pure forms (1.287) characterized by features that lead to a > division in three big categories (CP 1.286) whose explanatory value entrust > to readers who are as many potential reviewers (CP 1.287). > > > > *[ END OF QUOTE ]* > > Moreover, Peirce informs his reader (including you, I hope) of this > structural dependence; here are some significant excerpts from MS 908, "The > basis of Pragmaticism in Phaneroscopy," 1905, EP2: 360) chosen so as to > highlight the 13-point plan of Peirce's argument. Point 9 in particular, > considerably increases the scope of the assertions of CP 1.347 above (It > may concern you personally): > > *1- **"I invite the reader to join me in a little survey of the > Phaneron (which will be sufficiently identical for him and for me) in order > to discover what different forms of indecomposable elements it contains. > [...] This ... will be a work of observation. But in order that a work of > observation should bring in any considerable harvest, there must always be > a preparation of thought, a consideration as definite as may be, of what it > is possible that observation should disclose. That is a principe familiar > to every observer. Even if one is destined to be quite surprised, the > preparation will be of mighty aid."* > > *2- **"We are to consider what forms are possible rather than kinds > are possible, because it is universally admitted, in all sorts of > inquiries, that the most important divisions are divisions according to > form, and not according to the qualities of matter, in case division > according to form is possible at all. "* > > *3- **"They are further considerations, however, which warrant our > expecting more confidently to finds in elements of the Phaneron certain > forms than to find in elements of the Phaneron certains forms than to find > certain others."* > > *4- **"Therefore, if there is a phaneron, the idea of combination is > an indecomposable element of it. This idea is a triad; for il involves the > ideas of a whole and of two parts (a point to be further considered below). > Accordingly, there will necessarily be a triad in the Phaneron".* > > *5- **"But out of triads exclusively it is possible to build all > external forms, Medads, monads, dyads, triads, tetrads, pentads, hexads, > and the rest".* > > *6- **"I **mean the principle that whatever is logically involved in > an ingredient of the Phaneron is itself an ingredient of the Phaneron; for > it is in the mind even though it be only implicitly so." * > > *7- **Thus, the entire function of the tetrad is performed by a > series of Triads; and consequently, there can be no unanalyzable tetrad, > nothing to be called an quartan element of the Phaneron. Plainly, the same > process will exclude quintanity, sextanity, septanity and all higher forms > of indecomposable elements from the Phaneron.* > > *8- **To many a reader this reasoning will appear obscure and > inconclusive.* > > *9- **This is by no means the only difficulty of mathematics, which > incessantly employs them, but it is perhaps the chief reason why we find > among particularly able professional men, and even among thinkers, so many > who are completely shut off from mathematics. But those whom this > demonstration fails to reach may find themselves convinced by the facts of > observation when we come to consider them.* > > *10- **Much might be profitably added to this preliminary a priori > study; but even with the greatest compression I shall cover too many of the > valuable pages of the Monist. We must hasten, then, to try how well or ill > our a priori conclusions are supported by the actual examination of the > contents of the Phaneron. Let us begin at once.* > > *11- **Can we find a Phaneron any element logically indecomposable, > which is such as it is, altogether otherwise than relatively, but > positively, and regardless of aught else?** I answer, there are many such > elements.* > > *12 -What room, then, is there for Secundans and Tertians? Was there some > mistakes in our demonstration that they must also have their places in the > Phaneron? No, there was no mistake* > > *13 - But the phaneron does contain genuine Secundans.* > > Regards > > Robert Marty > Honorary Professor; PhD Mathematics; PhD Philosophy > fr.wikipedia.org/wiki/Robert_Marty > *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* >
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