Consequences of Four Incapacities

We begin in the middle of things (in medias res); we cannot begin with universal doubt. (Hence, we always begin with some positive belief, that is, some determinate belief.)

We should rely on a community of inquirers (not individual consciousness), and on a cable of reasonings (not a single thread of inference).

We have no cognition, no conception of the absolutely incognizable (so, we must reject Kant’s claim to have an idea of the noumenon, the thing-in-itself).

We have no power of Introspection (we have no access to an internal world that isn’t connected already with an external world).

We have no power of Intuition (so we must reject Descartes’ "clear and distinct ideas" or "rational intuitions" as simples or absolute starting points).

We have no power of thinking without signs (and since signs are complex—they are always signs of and to—there are no simples in thought).

[ In short, everything is connected ; -]
 

How to Make Our Ideas Clear

Precise definition is not the be-all and end-all of inquiry.
 
Doubt leads to Thought leads to Belief leads to Action, or Habits-of-Action.
 
Thought is a "mediate" element of consciousness, analogous to a melody, rather than "immediate" like a single note. (So, there will be no absolute simples in thought.)
 
Clarity of thought = clarity about the conceivable effects that might have practical bearing which accepting that thought would lead to = clarity about the habits of action implicated in accepting that thought.
 

Presuppositions of Science: Common Sense and Religion
 
- "Vitally important topics" = an individual’s practical, daily affairs (e.g. earning money, "getting ahead").

- These (vitally impotant topics) are best guided by common sense, tradition, "human instinct"—not by reasoning.

- But these are not the most important topics there are.
 
- "Cosmically vital topics" are the most important.

    -These include truth, God, beauty, and other ideals.

    - These are to be dealt with by reasoning, philosophy, science.

    - How does science presuppose religion?

    - Science presupposes implicitly a hope that truths may be found.

    - Peirce finds this hope equivalent to the hope that God is real.
 
- He insists on leaving the meaning of "God" conceptually vague. E.g. he doesn’t want to agree that God is properly conceptualized as the "Supreme Being." Any certainty one can have about the reality of God, Peirce thinks, must be a certainty of the heart, not intellectual certainty.
 
  - He reminds us that "exists" is not synonymous with "is real."

  - The supreme commandment of the "Buddhisto-chrisian" religion is: "to generalize, to complete the whole system even until continuity results and the distinct individuals weld together. Thus . . . the very supreme commandment of sentiment is that man should generalize. . . but, generalization should come about, not merely in man’s cognitions, which are but the superficial film of his being, but objectivly, in the deepest emotional springs of his life.

    - The generalization of sentiment takes place through poetry, but even more completely through religion.
 
   - The god of theology is a "strictly hypothetical" god, and is not at all the god of faith.
 
The Nature of Science

- The way to make a "natural classification" of science is to classify science as a certain kind of practice, carried on by a certain community of persons.

- There are 3 groups of men: those who enjoy (artists), those who do (practical men), and inquirers (scientific men).

- The scientific men divide into 3 groups, according as they engage in the practical sciences, the sciences of review, or the sciences of discovery.

- A science of discovery is one the purpose of which is discovery, which means making acquaintance with God, by developing the type of mind that can love and worship God better (48).

- It’s as though God’s purpose in creation was self-reproduction, or in other words, was to make an answering mind.
 

Mathematics, The First Science

- A mathematician dreams up a hypothetical situation (constructs a hypothesis), and then figures out what would be involved in that situation (asks what consequences the hypothesis leads to).

-As a mathematician, she is not concerned with whether or not there really is a situation such as her hypothesis portrays. I.e., she is not concerned whether her hypothesis is true of the real world or whether it is just an imaginary situation.

- But this definition of mathematics—constructing a hypothesis and tracing its necessary consequences— could just as well serve as a definition of "necessary reasoning," which is identical with what we normally call deduction (though logicians also refer to ‘statistical deduction,’ which is a form of non-necessary reasoning).

- So these terms are nearly synonymous: mathematical reasoning, necessary reasoning, and (strictly) deductive reasoning.

- This type of reasoning has several noteworthy features: it is reasoning about generals—general concepts, general truths. It is reasoning about would-be’s.

- It is diagrammatic. Diagrams represent general structures, general relations, after all; they show us what would be, in any case of the general type they diagram.

- The thinker interacts with the diagram, in necessary reasoning. The process has four steps [see below].
 
    - NB: the diagram represents a general relation. By making a general kind of modification, we can reveal a new general relation. We start with a general diagram, add a general modification, and end up with a new general diagram (revealing a new form of relation) as a consequence.

    - We are combining ideas, combining general concepts, and thereby getting new ideas.

    - We have an idea that is general—or in other words is indeterminate in many regards.We combine it with another general, largely indeterminate idea (our modification) and end up with a new general idea.

    - Peirce notes (51) that he is using the word "diagram" in a wider sense than usual. A diagram is a Sign (of whatever it is diagramming). Its Object is a  general relationship. E.g. a diagram of a triangle represents the
general relation among the angles of a triangle which is that they always add up to 180 degrees. This is true of triangles generally, not  just for some subset of triangles. Another way of saying that the diagram represents the relation in general is to say the diagram  represents "the Form of Relation merely" (51). And, a diagram  represents intelligible relations, specifically; that is, it represents  relations that human thought can conceptualize.
 
   - Peirce distinguishes many classes of signs. (Ten of these classes are especially important.) What kind of Sign is a diagram? A diagram is, on the whole, an Iconic sign. Later (in Stecheotic) he will define the Icon as a sign that resembles its object. Take a diagram of a triangle. The relation among its three angles (adding up to 180 degrees)
resembles the relation among the angles of any other triangle (since those will also add up to 180 degrees). It resembles the relation among the angles of a triangle generally.
 
 - A diagram, being a Sign, can be interpreted. Suppose I draw a diagram...I stare at it... Suppose it evokes an
 Interpretant in my mind. That Interpretant might be a vague idea. Or, staring at the diagram may lead me to add some lines to it, experiment with it. In this case the Interpetant is the action I take. Or, staring at the diagram may lead me to focus in on only certain features and filter the inessential features out of my mind, as I conceptualize the essential characteristics I am observing in the  diagram. In this case the Interpretant is the conceptual habit I  am forming—the habit of interpreting such diagrams with such concepts.

- The diagram is also acting on me, as I contemplate it. It acts on me by exciting my curiosity: "What would happen, I wonder, if I were to draw a new line here?"
 
- All deductive reasoning, all necessary reasoning, is diagrammatic. It always employs some sort of Sign (diagram) which represents a set of relations from which some other relation will be deduced. I have conveniently been discussing geometrical diagrams, e.g. the diagram of a triangle. But a set of algebraic equations to be solved simultaneously is also a diagram, in this "wider" sense of diagram.
 
- The important point here is this: all exact, deductive reasoning is diagrammatic,  and that means it proceeds by experimentation and observation. Thus, Peirce does not admit any huge gap between a priori reasoning and a posteriori reasoning—no huge gap between "pure reason" and empirical reason. Necessary reasoning differs importantly from non-necessary reasoning, to be sure. But both proceed by means of observation and experimentation.
 
   - Specifically, the process of necessary, deductive, diagrammatic reasoning consists of four steps: construct an icon, a diagram, that represents a set of relations scrutinize the diagram and try to think how you might modify it
in some way that would bring out some new feature of the relations it represents. Add those modifications.
 
- Observe the newly modified diagram, and notice any new features that the modification suggests.
 
- Repeat the experiment by varying your modification and observing the result again. (Does this modification bring out that same new feature, that same new relationship which the original diagram didn’t reveal clearly?) After repetitions, you will infer inductively that any diagram constructed as this one has been (including this type of
modification) will present the new features you have discovered, the new relations that have been brought out.
 
- There are three kinds of warrant for a belief: (1) some beliefs I accept simply on the warrant of common sense, tradition, "instinct." (2) other beliefs are warranted by necessary inference, deductive reasoning. (3) still other beliefs are warranted by the fact that we have arrived at them using a method that is reliable—we are confident that even if our present inference turns out in the long run to be incorrect, still our method would, in the long run, reveal that to us and permit us to correct our inference. This is the warrant of inductive reasoning. By accepting the conclusion of an inductive argument, we are saying that we trust the method that was followed.
 

Cenoscopy

- Philosophy begins with beliefs that one cannot doubt—not, that is, at the moment. That is, philosophy begins with the principles it receives from common sense or "human instinct." They are vague, but they are not nonsense.
 

Phaneroscopy (Phenomenology

 -  The "phaneron" is the collective total of everything that appears before consciousness—all phenomena. Phenomenology, the first branch of philosophy, describes the phaneron. It looks for any simply patterns there may be among phenomena, and it describes them, without asking whether that which appears is "reality" or "mere appearance." Peirce finds three elementary patterns in the field of phenomena—or, as he also calls them, three Categories.
 
    - He notes that he is categorizing phenomena on the basis of their "form" or structure, rather than on the basis of their material being. This is consistent with what natural scientists do. In chemistry, e.g., elements are classified according to their valency. Peirce has developed a system of diagrams, called Existential Graphs, which represent the elementary structures, or elementary structural relations that are present in phenomena.
 
- Existential graphs represent relations, including the relation between a set of premises and a conclusion. In fact, they can be useful for revealing what conclusion is warranted on the basis of a given set of premises. But facilitating inference in this way is not, Peirce says, their primary purpose. Rather, he invented the system of Existential Graphs in an effort to solve certain deep problems in logic.
 
- One such problem is this: how can concepts be combined? (p. 59, end of col. 1). When two concepts combine, "the two explicit indefinites mutually define each other."
 
    - "It appears then, that ... all combination of concepts takes place by the mutual definition of indefinites."
 
    - These two domains coincide: the domain of ideas and the domain of signs; thus, to study combination of ideas, we should study combination of signs. The essential structure of a Sign is that it has an Object (actually, two Objects, but we’ll ignore that for now) and it has an Interpretant (actually, three Interpretants).
 
    - Going back to the phaneron, what Peirce wanted to do was this: Consider only its indecomposable elements[i.e. those with no internal structure they could break down along] To make a "natural" classification, as natural scientists do—and that means a classification based on structure or form, rather than on materials.
   - His solution = make a classification based on form, but on external form or structure, ... as chemical elements are classified based on "valence" or [combinabilities].
    - From this he distinguishes the following possible structures-of-relatedness: (p. 61:) medad, monad, dyad, triad. [I won’t define those all here; check p. 61.]
    - He can prove, using his Existential Graph method, that no indecomposable element can have a higher valency than three. Phenomenology makes out three kinds of elements that are invariably all present to the mind: Firstness, Secondness, and Thirdness. See pp. 62-63 for description of these.
 

Normative Science

We could say there are two normative sciences: one, ethics, concerning the control of the existent, and the other, logic, concerning the control of thought. But then we would also have to break down the first into two parts: esthetics and critical ethics. Esthetics (or axiagastics) concerns the summum bonum [highest good]— that is, the admirable or valuable or good, generally (not just the beautiful, e.g) —that which excites a feeling akin to worship. This is the science that concerns the ideal, the ultimate aim. Critical ethics concerns ways of actualizing the ideal, ways of making the existent conform to the ideal. It is a science of the general conditions of control —and chiefly a doctrine of self-control. Logic is an application of ethics to thought. Thought controls itself when it determines belief not by a mere association of ideas, but rather by reasoning —and reasoning is a piece of deliberate, self-controlled conduct. But logic is best approached as a science of signs. Thinking takes place only in signs. Thinking, the function of mind, consists in making a sign interpret itself in another sign, which could be an emotion or an action but in any case must produce yet another sign that "agrees with" [continues, interprets] those earlier signs. [ The picture here is one of Signs/ideas generating or "reproducing themselves as" other equivalent signs, which in turn reproduce other signs, . . . etc. The process is one of on-going interpretation.] "Thought is nothing but a tissue of signs" (66) . . . "The life we lead is a life of signs. Sign under sign endlessly" (66). Here Peirce uses the example of a triangle being dipped into water, making a water line. The point is, there’s no absolutely first and shortest line in the dipping process; for any line, there could be a shorter line. Either there’s no line at all (no dipping), or there’s a continuous tissue of lines. Peirce criticizes James et al. for wanting to protest that thoughts/signs must eventually terminate in actions—as though that were what Peirce’s Pragmatic Maxim had meant. Peirce here points out that according to his Maxim, thoughts/signs must eventuate, not in actions but in "resolutions to act," that is, in habits of action. But habits are generals, not existents. (As generals, they"govern" existents.) And James et al. tend to treat generals as though they were existents; that’s why they seem to regard "actions" as equivalent to "habits of action," unlike Peirce.

Esthetics
    A moralist (ethicist) would be able to tell us that we are capable of self-control and that the aim toward which we reach with our self-control should be the broadest,highest, most general aim possible. But the moralist cannot tell us what that aim is. That’s the job of esthetics.
   If we are to have a general aim, why not say it is pleasure? That would work well, as the most satisfying aim, if we were to allow that a result, a particular state, could bethe ultimate ideal, the most admirable ideal.
   But in an era when we are aware of evolution, how could wefind any result, any static, arrived-at state, as the most admirable ideal of all? The only thing of that sort that could stay satisfied with itself would be a state
in which reason is feeling satisfied because it is looking forward to an endless future of endlessly improving its "results." Reason, as something embodied but never completely so; reason in a state of incipiency and growth—that is the ultimate ideal.
   Hence the ideal of conduct which esthetic science clarifies is this: the growth of reason, and reason’s embodiment.
The ideal is to render the world more reasonable whenever it is "up to us."
 

Ethics
    In this selection, Stuhr, our editor, gives us some of Peirce’s thoughts on"the ethics of terminology." Peirce has said (cf. end of ‘Esthetics’) that logic contributes to reasonableness by showing us methods that will develop knowledge
most quickly, build up the sciences most quickly. But since science is done by a community, clear communication of meanings is needed, for science to grow. And that requires that we choose our words, our terminology, carefully.
(p. 70): Good language is the very essence of good thought.
 

Stecheotic (Basic Definitions from Semiotics, i.e. from Logic in the larger sense)

    NB: I am not reproducing the basic semiotic terms here. If I have time, I will do so later. Meanwhile, Jen Lane and her group got a pretty good start at sorting it out; and I have made another handout available [the one which ends with the 10 Classes of Signs]. Here, however, is a brief set of notes on different kinds of Arguments. The notes, above, on mathematics and diagrams are also relevant. The notes that follow here cover, roughly, the material from pp. 75-80, or rather, some of it. **THESE NOTES ARE EXTREMELY PARTIAL—THERE IS A LOT MORE MATERIAL IN THE "STECHEOTIC" AND "CRITIC" SELECTIONS THAN WHAT IS COVERED HERE.
(Why? ‘cause i’m running out of time!)
 
    Arguments are of three basic kinds: abduction (hypothetical reasoning), induction, and deduction. In abduction, the premise signifies the conclusion iconically. The premise is an icon of the conclusion. In induction, the premise signifies the conclusion indexically. The premise indicates the conclusion. In deduction, the premise signifies the conclusion symbolically. The premise is a symbol of the conclusion.
 
   But there are two kinds of arguments called "deductions": In the strictest meaning of "deduction," deduction is necessaryinference about a hypothetical state.  Logicians also speak of "probable deduction," which is
necessary inference, all right, but is necessary inference about a probability in regard to the course of experience. It is this type of deduction that Peirce proceeds to examine next: Here, we begin with a hypothesis that is the conclusion of an Abduction. Next, we use Induction to make predictions and test the abductive hypothesis.
 
    Peirce considers, in effect, how any ideas are connected. How, for example, do we connect premise and conclusion, in an argument? . . . Remember that ideas and signs are coextensive domains. So we should try asking, how do we connect one sign with another—e.g. the verbal signs of language. Logicians in the past have usually tried to describe all word-combining, all concept-combining, as a matter of using just one connective word ("is") and using it as an external link between two terms ("S is P"). Peirce rejects this approach. His new system of Existential Graphs suggests an alternative. Roughly, he’s offering something like this: In the old say, words/ideas went together in linear strings:

term + copula + term (for example: "S is P")

As if we had: block + link + block

In Peirce’s logical space, instead of solid blocks and solid little links, we have ideas/signs moving around that are more like comets, with their respective tails. When they sweep into an area together, two of them (or more) may link up, merge, or flare up into something quite new.

Each "comet" (idea/sign/concept/word) is fairly indeterminate—it has no sharp boundaries like a block has, and it has a tail that stretches out vaguely. However, when two of these comets enter in the same region of space, something definite happens to each of them. Each is modified by the presence of the other; and through their combination, something new happens— perhaps a settling down, consolidating; perhaps an explosion.

Recall: "ideas combine by the mutual definition of indeterminates"

 Here is another process that can be described as a process of ideas combining by mutual definition of indeterminates: Consider the process of learning a proper name: (a) The first time it is used, the name is used as an index, connected with its object (the person named) as part of this very existential situation in which you speak it, probably while looking and pointing at that person for me. (b) The next time I hear that name, the sound I hear is an icon of the sound you pronounced in the first case, case "a." It resembles that other sound. (c) When I have acquired a habitual acquaintance with the name, as being the name of that person, then that name is a symbol; I interpret it, by convention and habit, as naming that person. It means that person, in the sense that its meaning is a "precept," a rule telling me who I should go turn my attention to when I that name is spoken. Note what has happened here: several signs (the original index, then a number of icons of that index) have combined to produce a determinatesign—the name of the person as a symbol of that person.
 

Critic [ caution: these notes too are quite scanty ]

  Peirce agrees with Descartes that the famous "Je pense, donc je suis" could not have been meant as a syllogism. It is not even reasoning at all, Peirce says. It is simply Descartes stumbling up against a particular inability to conceive his own nonexistence. And that is not what we mean (Peirce means) by reasoning (which is something more particular thanany old association of ideas, any old coming to a conclusion).
 
    Reasoning is of two kinds:Necessary reasoning: this is a diagrammatic showing, a making evident.  Non-necessary reasoning: this is an application of a rule of thumb,i.e. it is a case of trusting in a method.
    A diagram (always used in necessary reasoning) is an Icon. Its Object (remember: any Sign has an Object and an Interpretant) is a set of rational relations among a group correlates. And what the diagram does is make evident,
perceivable, some general relation among correlates.
    Only Icons can provide evidence—i.e. can make their Object evident.Indices thrust their Object on consciousness by force [the force of existential connection].Symbols apply [i.e. invoke] a habit, a rule of thumb.
Only icons supply evidence. Yet, ordinary Icons do not provide evidence; rather, the suggest.
    But diagrams do provide evidence.A Diagram shows the-following -of-the consequent-from-the-antecedent —and shows the generality of that following, i.e. shows it as a general, a would-be. Notice, then: In diagrams, we see generals, would-be’s, right here and now! But we cannot say we see the general in the static diagram. Rather we see the generality in the process of intention + construction of the diagram as an Interpretant of some symbol/idea which someone intended to demonstrate. [In that process, we observe Generals—or, perhaps we should say: we observe generation and generalization.] So, we have:
a Diagram-icon & its initial symbolic Interpretant which together constitute a Kantian schema,
which is observable . . . . . . . . . . . . . . but also general (its Object is); this generality being so because the Diagram’s middle, dynamic Interpretant (p. 79) was active experimentation, in which the mind used learned rules of thumb to make acceptable tranformations, . . . until it generateda transformate (transformed) diagram which is, now,the eventual, rational Interpretant (p. 80) of the transformand (original) diagram.