I don't claim any higher knowledge of Pierce than what came up in passing as a humanities grad, but having some knowledge of the others mentioned, some points:
> When people discuss the connections between language and cognition such as the possible existence of language in nonhuman species, communication in nature, language acquisition, thinking and human language more generally, cognitive scientists and evolutionary anthropologists usually appeal to concepts such as symbol and sign. A couple of decades after Peirce’s semiotics, Saussure invented his own theory of signs that he also called semiotics though unfortunately with little understanding of Peirce’s work. (Both Peirce and Saussure borrowed the name and interest in semiotics from the 17th-century philosopher John Locke; the term derives from the Greek word σημεῖον, or semeion, for ‘sign’, *‘miracle’*, etc.)
I don't think it a coincidence that the rise of linguistics coincides with a decline in cognition that we can all observe today as reaching a sort of critical mass, in which the mention of a thing is gauged to be a judgment of a thing, particularly in social media contexts. The 20th century (and later) insistence upon "scientifying" everything under the sun is downright insidious.
I often think we'd be better off if there were never such an idea in the heads of any of the people who study it.
> A further foundational contribution from Peirce was his doctrine of synechism, the idea that everything in the Universe is connected, that nothing can be understood in isolation, not even people. This is expressed well in statements such as the following from his paper ‘Immortality in the Light of Synechism’ (1893): "Nor must any synechist say: ‘I am altogether myself, and not at all you.’ If you embrace synechism, you must abjure this metaphysics of wickedness. In the first place, your neighbours are, in a measure, yourself, and in far greater measure than, without deep studies in psychology, you would believe. Really, the selfhood you like to attribute to yourself is, for the most part, the vulgarest delusion of vanity."
This is poorly understood by the author of the linked article, it seems, and a perfect example of my previous point. The author of the linked article presumes that by offering a term to describe a thing, Pierce was making a judgment (positive) about it. That is not the case. Synechism was offered by Pierce as a logical framework of sorts, to limit inquiry to certain possible outcomes. Pierce said that he only thought Time, Space, and Scientific Laws were constants in the universe, and that other less pervasive states were able to exist in isolation from each other.
Describing a thing does not denote a judgment of it. Write it on the chalkboard 1,000 times, 21st century....