According to Wikipedia:
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.
Also according to Wikipedia, tacit knowledge does not involve propositions.
Tacit knowledge (as opposed to formal, codified or explicit knowledge) is the kind of knowledge that is difficult to transfer to another person by means of writing it down or verbalizing it.
Since tacit knowledge is not codified into propositions it is not able to be contradictory.
When Daoists claim they aim at "the whole thing" but include only tacit knowledge they may simply be wrong in their claim. However, they may be right if such explicit knowledge is derivative of the whole thing and no longer, according to them, part of the whole thing, but rather part of something else, say, a text.
To see that the latter might be the case consider this description of wu wei:
Following the development of wu wei in a political sense by Shen Buhai, and then Mencius, the Zhuangzhi and Laozi turn towards an unadorned "no effort". Laozi, as opposed to carved Confucian jade, advocates a return to the primordial Mother and to become like uncarved wood. He condemns doing and grasping, urging the reader to cognitively grasp oneness (still the mind), reduce desires and the size of the state, leaving human nature untouched. In practice, Wu wei is aimed at through behaviour modification; cryptically referenced meditation and more purely physical breathing techniques as in the Guanzi (text), which includes just taking the right posture.
This suggests that a Daoist might not consider explicit knowledge as relevant. Note the emphasis on behavior modification, not propositions. Note how this might simply include "right posture". If one takes out the propositional statements (or beliefs) one is left with habits that can be modified.
These habits can be viewed as "practices" without involving specific "beliefs". Examples of similar practices need not even look like Daoism or Wu wei. Here are three from diverse sources:
- Rupert Sheldrake's Science and Spiritual Practices "illustrates how science helps validate seven particular practices which underpin all major world religions." Sheldrake is looking at practices (habits) that even atheists perform.
- Will Johnson's The Posture of Meditation shows how Rolfing, a practice of posture, can help meditators of any belief (or no belief) system improve their practice.
- Steven Gundry's The Plant Paradox advices that the best change in diet would be to stop eating certain food.
None of the three sources reference (to my knowledge) Daoism or Wu wei, but they could be said to promote practices at least similar to Wu wei. So propositional knowledge about Wu wei or Daoism may not be necessary to practice Wu wei. Even the explicit knowledge codified in these books is not necessary to practice what is recommended in these books if people already perform Sheldrake's spiritual practices, Johnson's posture habits or Gundry's diet without having read the books.
This makes me suspect that not only is Daoism and Wu wei not in contradiction with each other but they may actually know the whole thing without believing any propositional knowledge about what they tacitly know.
Gundry, S. R., & Solimene, C. (2017). The plant paradox. Tantor Media, Incorporated.
Johnson, W. (1996). The posture of meditation: A practical manual for meditators of all traditions. Shambhala Publications.
Sheldrake, R. Science and Spiritual Practices: Transformative experiences and their effects on our bodies, brains and health. Counterpoint. 2017.
Wikipedia contributors. (2019, February 17). Contradiction. In Wikipedia, The Free Encyclopedia. Retrieved 12:26, March 8, 2019, from https://en.wikipedia.org/w/index.php?title=Contradiction&oldid=883799251
Wikipedia contributors. (2019, February 18). Tacit knowledge. In Wikipedia, The Free Encyclopedia. Retrieved 12:24, March 8, 2019, from https://en.wikipedia.org/w/index.php?title=Tacit_knowledge&oldid=884010284
Wikipedia contributors. (2019, March 7). Wu wei. In Wikipedia, The Free Encyclopedia. Retrieved 12:40, March 8, 2019, from https://en.wikipedia.org/w/index.php?title=Wu_wei&oldid=886618125