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Peirce seeks to utilize his system of Existential Graphs (EG) to prove his pragmatism but changes course after trying and failing to incorporate modality by means of tinctures. My proposed system of Synechistic Graphs (SG) includes real possibility and conditional necessity by interpreting the scroll as a sign of subjunctive implication rather than consequence *de inesse*. This imposes restrictions on inserting entire propositions in shaded areas but is compatible with adding branches to a line of identity that already joins names in the outer and inner closes, thus attributing more concepts to the same object and reducing the range of states of things being signified. It also reflects the modern denial of existential import and resolves a problematic example from Peirce of different propositions that are equivalent in classical logic. Here is another one. 1. A married woman exists such that if her husband *fails* in business, then she *commits* suicide. 2. A married woman exists such that if every married man *fails* in business, then she *commits* suicide. Peirce only provides a simple EG intended to express #1 (CP 4.569, 1906), which he later mistakenly calls "a blunder" and replaces with an incorrect one (RL 477:32, 1913 Nov 7-8; https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00125/R_477_32.jpg). See attached (CP4_546eg.jpg) for what I believe are accurate renditions of both. Although it takes several steps, the graph for #2 can be derived from the graph for #1, but not vice-versa. In fact, #2 follows directly from "some married woman commits suicide" because any proposition whatsoever may be inserted in the shaded outer close after scrolling "suicide." Nevertheless, #1 is not *actually* falsified unless #2 is also falsified--either there is no married woman, or *every* married man fails in business and *no* married woman commits suicide--which "is the absurd result of admitting no reality but existence" (CP 4.546, 1906). By contrast, here are their counterparts in synechistic logic. 3. A married woman exists such that if her husband *were* to fail in business, then she *would* commit suicide. 4. A married woman exists such that if every married man *were* to fail in business, then she *would* commit suicide. Again, #4 can be derived from #3, but not vice-versa. #3 "means that every *possible* course of events would either be one in which the husband would not fail or one in which the wife would commit suicide," so "to make that false it will not be requisite for the husband actually to fail, but it will suffice that there are *possible* circumstances under which he would fail, while yet his wife would not commit suicide" (ibid). Hence it is conceivable that #4 could be true while #3 is false. On the other hand, one married man failing in business is much more likely than every married man doing so, as well as a plausible reason *why* that man's wife would kill herself--in that scenario, "her suicide is *connected* with his failure" (CP 4.569, 1906). Moreover, #4 does not follow directly from "some married woman commits suicide" because introducing the scroll in SG changes the modality from actuality to conditional necessity. With all that in mind, recognizing that details remain to be worked out, the following is a preliminary summary of how SG could potentially be used in a proof of Peirce's pragmatism. - Speculative grammar classifies concepts as symbols. Both EG and SG represent this by using names for concepts; e.g., "hardness." - All concepts are indeterminate, so their only mode of composition is mutual determination by means of propositions. Both EG and SG represent this as predicating multiple concepts of objects by attaching names to lines of identity; e.g., "something possesses the character of hardness and also possesses the character of brittleness." - The *logical* meaning of a concept is the continuum of all propositions that truthfully affirm or deny it of something. Both EG and SG represent this as the corresponding graphs being embedded in the blank sheet, where they are taken for granted as beliefs; e.g., "any diamond possesses the character of hardness" and "any strawberry does not possess the character of hardness." - Such beliefs correspond to *individual* habits of expectation. EG represents each of these as an *indicative* judgment (inner close) when an assertion (sheet) matches an assumption (outer close), all signifying the actual state of things (consequence *de inesse*); e.g., "*this* stone possesses the character of hardness, so if I rub it with a knife, then it *will* resist scratching." - Peirce's pragmatism defines the *ultimate* meaning of a concept as a *general* mental habit. SG represents this as a *subjunctive* judgment signifying a conditional necessity (inner close) whenever an assertion signifying an actuality (sheet) matches an assumption signifying a possibility (outer close); e.g., "any diamond possesses the character of hardness, so if I *were* to rub one with a knife, then it *would* resist scratching." - Beliefs are subject to revision with further experiences, especially surprising observations that prompt inquiry. SG represents the first step, abduction/retroduction, as scrolling the new graph-instance and inserting an explanatory hypothesis that matches a known subjunctive implication; e.g., "when I rub *this* stone with a knife, it resists scratching, and if it *were* a diamond, then that would be a matter of course." - A general mental habit manifests itself in self-controlled conduct. The subjunctive implication that describes it is the major premiss of a practical syllogism in which the minor premiss expresses a relevant intention and the conclusion prescribes a rational course of action; e.g., "if I were to rub any diamond with a knife, then it would resist scratching, and I *desire* a stone that possesses the character of hardness, so I *shall* obtain a diamond." I would greatly appreciate feedback on this first pass. If I am on the right track, then calling such logic "synechistic" is appropriate since Peirce maintains that proving his pragmatism "would essentially involve the establishment of the truth of synechism" (CP 5.415, EP 2:335, 1905). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >
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