— C.S. Peirce (1861), “My Life, written for the Class-Book”, (CE 1, 3)
The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know.
— C.S. Peirce (1877), “The Fixation of Belief”, (CP 5.365)
If the object of an investigation is to find out something we do not know then the clues we discover along the way are the signs which determine that object.
People will continue to be confused about determination so long as they can think of no other forms but analytic-behaviorist-causal-dyadic-temporal, object-as-stimulus, sign-as-response varieties. It’s true ordinary language biases us toward billiard‑ball styles of dyadic determination but there are triadic forms of constraint, determination, and interaction not captured by S‑R chains of that order.
Pragmatic objects of signs and concepts are anything we talk or think about and semiosis does not conduct its transactions within the bounds of object as cue, sign as cue ball, and interpretants as solids, stripes, and pockets.
References
- Peirce, C.S. (1859–1861), “My Life, written for the Class-Book”, pp. 1–3 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
- Peirce, C.S. (1877), “The Fixation Of Belief”, Popular Science Monthly 12 (Nov 1877), pp. 1–15. Reprinted in Collected Papers, CP 5.358–387. Online.
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are shown in the next two Figures.
![[\mathcal{X}] \to [\mathcal{Y}]](https://s0.wp.com/latex.php?latex=%5B%5Cmathcal%7BX%7D%5D+%5Cto+%5B%5Cmathcal%7BY%7D%5D&bg=ffffff&fg=000000&s=0&c=20201002)
is implied any time we make use of one basis 
which happens to be included in another basis 
When discussing differential relations we usually have in mind the extended alphabet 
has a special construction or a specific lexical relation with respect to the initial alphabet 
one which is marked by characteristic types of accents, indices, or inflected forms.
‑gear curves, the indexing scheme results in the data of the next two Tables, showing one period for each orbit.
where 
may be read as a temporal parameter indicating the present time of the state and where 
is the decimal equivalent of the binary numeral 
with a subscript 
equal to the numerator of its rational index, taking for granted the constant denominator of 
In that way the temporal succession of states can be reckoned by a parallel round‑up rule. Namely, if 
is any pair of adjacent digits in the state index 
then the value of 
in the next state is 
with the dyadic rationals (or the binary fractions) in the half-open interval 
Formally and canonically, a state 
is indexed by a fraction 
whose denominator is the power of two 
and whose numerator is a binary numeral formed from the coefficients of state in a manner to be described next.
are just the values 
for 
where 
is defined as being identical to 
To form the binary index 
of the state 
Expressed by way of algebraic formulas, the rational index 
Those are the trajectories generated subject to the dynamic law 
where it’s understood all higher order differences are equal to 
and all higher differences 
are fixed, the state vectors vary only with respect to their projections as points of 
Thus there is just enough space in a planar venn diagram to plot all the orbits and to show how they partition the points of 
It turns out there are exactly two possible orbits, of eight points each, as shown in the following Figure.
Inquiry Into Inquiry 