
A photo of implicit atheism and explicit atheism as compared to implicit theism and explicit theism in the Beg-Thims dialogue (2015).

A photo of implicit atheism and explicit atheism as compared to implicit theism and explicit theism in the Beg-Thims dialogue (2015).

In atheism terminology, explicit atheism, as compared to implicit atheism (e.g. Alfred Lotka), indirect atheism, i.e. “those who hold ideas that, in some way or another, imply atheism” (Ѻ), which can be of a practical or theoretical variety (Ѻ), or crypto-atheism (e.g. Thomas Hobbes) is a type of open and frank statement of one’s disbelief in the existence of god, and or denial of the existence of god, e.g. by proof via religio-mythology and or other proofs god does not exist, concordant with direct and open discussion, of traditionally carpet swept taboo topics, e.g. whether god is involved when hydrogen reacts with oxygen or man reacts with woman, in publications, presentations, and daily interactions.

Overview
In science, to go through one example, so to direct distinguish "implicit" as compared to "explicit" atheism, in the context of chemistry, when in 1885 Johannes Wislicenus took down the Wisdom of Solomon (11:21) quote: “god as arranged all things by measure and number and weight”, from the University of Leipzig chemistry classroom wall, then above the periodic table, when he succeeded Hermann Kolbe, via the subtle comment to his tour guide “that must go”, chemistry thereafter became “atheism implicit”.

Atheism | Implicit

“Just as man and woman attract one another, so oxygen attracts hydrogen, and, in loving union with it, forms water, that mighty omnipresent element, without which no life nor thought would be possible.”
— Ludwig Buchner (c.1855); cited by Henry Finck (1887) as an example of "gross materialism"

Atheism | Explicit

“Just as there is no god involved when oxygen reacts with hydrogen, so to is there no god involved when man reacts with woman.”
— Libb Thims (2014), mental synopsis personal note of the Goethe 1809 point on the atheism timeline; an atheism explicit variant of the c.1855 Ludwig Buchner quote: "Just as man and woman attract one another, so oxygen attracts hydrogen", Sep 10; cited (Ѻ) by Inderjit Singh (2015) as favorite philosophical quote

In other words, in the Buchner quote, standalone, someone reading it in the following century, e.g. Henry Bray (1910) or Mirza Beg (1987), might intuit, imbibe, read, think, or interpret that Buchner was giving a theism-implicit statement, i.e. that "god" could be read into the reaction of oxygen with hydrogen or man with women, regardless of the fact that Ludwig Buchner is one of German's most-famous atheists. In the Thims' statement, however, it is EXPLICITLY stated that god is NOT involved when man reacts with woman. The statement is atheism "explicit".

If, however, when the students came into the class, and Wislicenus opened his introduction to the periodic table by stating that the “The laws of nature have arranged all elements by column (property) and row (external shell configuration)” AND “there is no god involved in any of this process”, this would have been an example of “explicit atheism”. The world's chemistry classrooms, however, have been implicit ever since.

In 1979, George Smith, supposedly, defined “implicit atheism” as the absence of theistic belief without a conscious rejection of it and “explicit atheism” as the absence of theistic belief due to a conscious rejection of it.” (Ѻ)

In 2013, Stephen Bullivant, via citation to a “contentious but intriguing” claim by Jesse Bering (2010), commented that, supposedly, changes in explicit atheism do not translate to higher levels of implicit atheism. [1] This Bering assertion, however, seems doubtful in respect to conscious implicit atheism as compared to conscious explicit atheism, the latter of which resulting in a rewiring of the mind in respect to the public discourse the switch in atheism type brings about.

Quotes
The following are related quotes:

“The first atheist of whom we know is one Diagoras, who lived in the late fifth century BCE. It is typical that nothing of this works aside from random fragments survives and that he was forced to flee Athens because he declared that there were no gods. Even in the ages preceding Christianity, the enunciation of explicit atheistic, or even agnostic, views carried with it the threat of both legal punishment and social obloquy.”
— Sunand Joshi (2014), The Original Atheists [2]

“I was an ‘implicit atheist’ prior to 2014 (see: Beg-Thims dialogue) and an ‘explicit atheist’ thereafter.”
— Libb Thims (2017), mental note, Aug 26

References
1. Bullivant, Stephen. (2013). The Oxford Handbook of Atheism (editors: Stephen Bullivant and Michael Ruse) (explicit atheism, pgs 429, 639). OUP Press.
2. Joshi, SunandT. (2014). The Original Atheists: First Thoughts on Nonbelief (pg. 7). Prometheus Books.