Charles Saunders Peirce ("purse") is our greatest philosopher, our greatest 19th century mathematician and logician, the planner of The Bureau of Standards, and the creator of Semiotics: Theory of Signs. (Texts and reference books often write more about the independent semiotics ideas of French scholar, Ferdinand Saussure (x-y). I build upon Peirce's work since they provide a generative basis whereas Saussure's is quasi-axiomatic.)

My MADMATH semiotic references derive from my acronym, "ISIS", for what I consider the four primary signs which Peirce taught us.

I(ndicator)S(ignal)I(con)S(ymbol).

INDICATOR Extending Peirce, I redefine
INDICATOR: ORDERED PAIR OF SIGNS: THE 1st IS HIGHLY VISIBLE, LOW IN INFORMATION CONTENT; THE 2nd LOW IN VISIBILITY, HIGH IN INFORMATION CONTENT.
(Examples: LIGHTNING INDICATING THUNDERSTORM; LITMUS PAPER TURNING RED, INDICATING LIQUID ACID IN TEST TUBE.

SIGNAL Extending Peirce, I redefine
SIGNAL: INDICATOR UNDER PHYSICAL AND LINGUISTIC CONTROL.
(Peirce mentioned only PHYSICAL CONTROL.) Example: TELEGRAPHIC SIGNAL -- under PHYSICAL CONTROL OF ELECTRIC CIRCUIT AND BREAKER KEY; under LINGUISTIC CONTROL OF MORSE CODE.)

INDICATOR-SIGNAL STRATEGY: THE GOAL OF SCIENCE IS TO SEARCH FOR SIGNALS AND TRY TO TRANSFORM INTO SIGNALS!

This can be seen in a Table of Indicators and SIGNALS.

ICON An ICON IS A SIGN THAT SUGGESTS OR INVOKES ITS MEANING OR REFERENCE.
Examples: "No Smoking!" ICONED as CIGARETTE WITH SLASH THROUGH IT; ONOMATOPOEIC WORDS; etc.

SYMBOL A SYMBOL IS A SIGN WITH ARBITRARILIY ASSIGNED MEANING OR REFERENCE.

(An ICON is HIGHLY VISIBLE, but with LIMITED MEANING OR REFERENCE. A SYMBOL has LOW 'VISIBILITY", BUT UNLIMITED INFORMATION CONTENT.)

ICON-SYMBOL STRATEGY: THE GOAL OF LITERACY IS TO MAKE THE ICON A BRIDGE TO THE SYMBOL.