Edwina,
Yes. That is a major advantage of diagrams: ET> I agree that diagrams are more fundamental than words, since their attributes are less open to multiple interpretations. That includes both the written and spoken word, with the latter overlaid with meanings provided by tone and rhythm and the former open to many misinterpretations because of the lack of both. [As we find in email and text messages]. The phaneron, as initially experienced, is independent of any bias. But every step of interpreting the experience adds biases from the individual's conscious knowledge, unconscious habits, cultural traditions, and linguistic constraints of vocabulary, syntax, and semantics. Those biases may be good, bad, or neutral. As an example, the subjects for a psycholinguistic experiment were asked to sort photographs into similar groups, according to any grouping they considered relevant. Some of the subjects happened to be native speakers of Yoruba, which has a color classification that is very different from English and other European languages. After the subjects did their sorting, the experimenter said "Think in Yoruba." The subjects laughed and immediately resorted the photographs in a completely different grouping. When they switched from thinking in English to thinking in Yoruba, they completely reorganized their interpretations. And by the way, I also cc'd a note to Peirce-L, which I had sent to Ontolog Forum with the title "Modal Logic is an Immense Swamp". That note addresses issues about logic for which Peirce's writings are still at the forefront of research today. Before reading that note, I recommend the slides I cited in it: http://jfsowa.com/talks/eswc.pdf 1. For a brief overview of existential graphs, skip to slides 14 to 21 of escw.pdf. 2. For issues about mapping English (and other languages) to EGs, see slides 21 to 35. 3. For the differences between thinking in diagrams and thinking in words, see slides 36 to 52. To complete the loop, I'm also cc'ing this note to Ontolog Forum. John
>
>
> John, list
>
> I agree that diagrams are more fundamental than words, since their
> attributes are less open to multiple interpretations. That includes
> both the written and spoken word, with the latter overlaid with
> meanings provided by tone and rhythm and the former open to many
> misinterpretations because of the lack of both. [As we find in email
> and text messages].
>
> That is, since all communication is triadic, i.e., mediated within
> the knowledge base/habits of both the sender and receiver, then,
> there is no such thing as a dyadic direct transference of 'meaning'
> from one site to another. It's always an interpretation. That's why
> no-one can say: ' Peirce wrote this - and this is absolutely and
> finally what Peirce meant' - because of that triadic semiosic
> infrastructure of mediated interpreta tion.
>
> Diagrams, to me, have less possibility for
> variation-in-interpretation than words. That's why road signs use
> primarily diagrams rather than words; why statistical charts present
> their data in a diagram.
>
> Edwina
> Different people have different ways of thinking and talking. That
> is
> important, because the world is so complex, so diverse, and so
> dynamic
> that no single method could comprehend and describe it all.
> Peirce's
> method of diagrammatic thinking, which is the foundation for his
> logic
> and philosophy, is more fundamental than thinking in words.
> For Peirce, words are necessary, but imperfect methods of
> communication.
> For example, his 76 definitions of the word 'sign' do not imply 76
> different meanings. The multiplicity of definitions and
> "outlan dish"
> terminology in the Commens dictionary shows his lifelong struggle to
> map
> his diagrammatic insights to words.
> Phenomenology, phaneroscopy, or phenoscopy is the first stage of
> analyzing and interpreting the phaneron in diagrams. It depends on
> the three branches of mathematics (formal logic, discrete math, and
> continuous math) to derive and classify the elements and patterns of
> elements. The patterns are possibilities (hypotheses or guesses)
> whose
> probability is evaluated by the normative sciences.
> For background, see the three appendices below: (1) quotations by
> Peirce about diagrammatic reasoning; (2) quotations by other
> mathematicians; and (3) quotations by Peirce about formal,
> mathematical
> methods.
> For details, see Frederik Stjernfelt's "Diagrammatology: An
> Investigation on the Borderlines of Phenomenology, Ontology, and
> Semiotics". Stjernfelt goes into great detail about the
> mathematical
> foundations. He shows that Peirce and Husserl, despite completely
> different terminology, had developed closely related theories.
> http://frederikstjernfelt.dk/Peirce/Diagrammatology.%202007.pdf [1]
> Husserl, by the way, had a PhD in mathematics and a strong
> background in
> logic. Both Peirce and Husserl were influenced by Hegel, and both
> of
> them used mathematics to develop a better foundation for
> phenomenology.
> As Peirce wrote, "the arbitrariness of Hegel's procedure... is in
> great
> measure avoided by my taking care never to miss the solid support of
> mathematically exact formal logic beneath my feet." (R318, 1907)
> John
> ---------------------------------
> App endix 1: Quotations about diagrammatic reasoning
> These quotations by Peirce are discussed in "Natural logic is
> diagrammatic reasoning about mental models" and related to current
> research in cognitive science. See
> http://jfsowa.com/pubs/natlog.pdf [2]
> All necessary reasoning without exception is diagrammatic. That is,
> we
> construct an icon of our hypothetical state of things and proceed to
> observe it. This observation leads us to suspect that something is
> true, which we may or may not be able to formulate with precision,
> and
> we proceed to inquire whether it is true or not. For this purpose
> it is
> necessary to form a plan of investigation, and this is the most
> difficult part of the whole operation. We not only have to select
> the
> features of the diagram which it will be pertinent to pay attention
> to,
> but it is also of great importance to return again and again to
> certain
> features. (EP 2:212)
> The word diagram is here used in the peculiar sense of a concrete,
> but
> possibly changing, mental image of such a thing as it represents. A
> drawing or model may be employed to aid the imagination; but the
> essential thing to be performed is the act of imagining.
> Mathematical
> diagrams are of two kinds; 1st, the geometrical, which are composed
> of
> lines (for even the image of a body having a curved surface without
> edges, what is mainly seen by the mindâs eye as it is turned
> about, is
> its generating lines, such as its varying outline); and 2nd, the
> algebraical, which are arrays of letters and other characters whose
> interrelations are represented partly by their arrangement and
> partl y by
> repetitions. If these change, it is by instantaneous metamorphosis.
> (NEM 4:219)
> We form in the imagination some sort of diagrammatic, that is,
> iconic,
> representation of the facts, as skeletonized as possible. The
> impression of the present writer is that with ordinary persons this
> is
> always a visual image, or mixed visual and muscular... This
> diagram,
> which has been constructed to represent intuitively or
> semi-intuitively
> the same relations which are abstractly expressed in the premisses,
> is
> then observed, and a hypothesis suggests itself that there is a
> certain
> relation between some of its parts -- or perhaps this hypothesis had
> already been suggested. In order to test this, various experiments
> are
> made upon the diagram, which is changed in various ways. (CP 2.778)> Diagrammatic reasoning is the only really fertile reasoning. If
> logicians would only embrace this method, we should no longer see
> attempts to base their science on the fragile foundations of
> metaphysics
> or a psychology not based on logical theory. (CP 4.571)
> ---------------------------------
> Appendix 2: Related quotations by other mathematicians
> The following quotations are discussed in "Peirce, Polya, and
> Euclid:
> Integrating Logic, Heuristics, and Geometry" and compared to closely
> related comments by Peirce. http://jfsowa.com/talks/ppe.pdf [3]
> Archimedes: "Eureka!" Shouted as he jumped out of his bathtub.
> Leonhard Euler: "The properties of the numbers known today have
> been
> mostly discovered by observations... long before their truth has
> been
> confirmed by rigid demo nstrations."
> Paul Halmos: "Mathematics -- this may surprise or shock some -- is
> never deductive in its creation. The mathematician at work makes
> vague
> guesses, visualizes broad generalizations, and jumps to unwarranted
> conclusions. He arranges and rearranges his ideas, and becomes
> convinced of their truth long before he can write down a logical
> proof... the deductive stage, writing the results down, and writing
> its
> rigorous proof are relatively trivial once the real insight arrives;
> it
> is more the draftsmanâs work not the architectâs."
> Albert Einstein: "The words or the language, as they are written or
> spoken, do not seem to play any role in my mechanism of thought.
> The
> psychical entities which seem to serve as elements in thought are
> certain signs and more or less clear images which can be voluntarily
> reproduced and combined... The abovementioned elements are, in my
> case,
> of visual and some of muscular type. Conventional words or other
> signs
> have to be sought for laboriously only in a secondary stage, when
> the
> mentioned associative play is sufficiently established and can be
> reproduced at will."
> ---------------------------------
> Appendix 3: Quotations by Peirce about formal, mathematical methods
> 1898; We pretend that the [existential] graph is a general
> description
> of a certain recognized state of things. We only pretend that it is
> so;
> for our purpose is merely to study formal logic, and the graph is a
> mere
> specimen of an assertion for whose matter we care nothing. In the
> contents of consciousness we recognize three sorts of elements,
> Fir stness, Secondness, Thirdness. (R339, 11 June 1898)
> 1902: Accordingly by regarding logic as a science of signs or
> formal
> semeiotic, and in the main as a science of symbols, or formal
> symbolic,
> we accurately cover its subject matter, and at the same time insure
> ourselves against all risk of being led astray into psychology. (R
> 425:117-118, 1902)
> 1903: For every symbol is a living thing, in a very strict sense
> that
> is no mere figure of speech. The body of the symbol changes slowly,
> but
> the meaning inevitably grows, incorporates new elements and throws
> off
> old ones. (CP 2.222).
> 1903: Phenomenology ascertains and studies the kinds of elements
> universally present in the phenomenon. (CP 1.186, 1903)
> 1905: The other doctrine of mine which Royce attacks, as remarkably
> shows how unscie ntific his training has been. He attacks my
> one-two-three doctrine in the very field where it is most obviously
> defensible, that of formal logic. (Letter to William James, August
> 1905)
> c 1906: Phaneroscopy... is the science of the different elementary
> constituents of all ideas. Its material is, of course, universal
> experience, -- experience I mean of the fanciful and the abstract,
> as
> well as of the concrete and real. Yet to suppose that in such
> experience the elements were to be found already separate would be
> to
> suppose the unimaginable and self-contradictory. They must be
> separated
> by a process of thought that cannot be summoned up Hegel-wise on
> demand.
> They must be picked out of the fragments that necessary reasonings
> scatter; and therefore it is that phaneroscopic research requires a
> p revious study of mathematics. (R602, after 1903 but before 1908)
> 1907: My trichotomy is plainly of the family stock of Hegelâs
> three
> stages of thought, -- an idea that goes back to Kant, and I know not
> how
> much further. But the arbitrariness of Hegel's procedure, utterly
> unavoidable at the time he lived, -- and presumably, in less degree,
> unavoidable now, or at any future date, -- is in great measure
> avoided
> by my taking care never to miss the solid support of mathematically
> exact formal logic beneath my feet.... (R318, 1907, p. 37)
> CSP: The little that I have contributed to pragmatism (or, for that
> matter, to any other department of philosophy), has been entirely
> the
> fruit of this outgrowth from formal logic, and is worth much more
> than
> the small sum total of the rest of my work, as time will show.< br />> (CP 5.469, R318, 1907)
> In a footnote to CP 4.240, Peirce added "'Formal logic' is also
> used, by
> Germans chiefly, to mean that sect of Logic, which makes Formal
> Logic
> pretty much the whole of Logic." Since Whitehead and Russell also
> adhered to that "sect", the term 'formal logic' means any version of
> logic that uses some precisely defined notation, linear or graphic.
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