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The phrase "philosophical assumption" is correct and can be used in written English.
It refers to a belief or idea that serves as the basis for a philosophical argument or discussion. Example: The philosopher's argument was built upon the philosophical assumption that happiness is the ultimate goal of human existence.
Exact(8)
Hawking is making a philosophical assumption on what it is to know reality.
What's really behind the complaint is the philosophical assumption that profit is "exploitation".
According to this philosophical assumption, there is no unique "real world" that preexists independently of human mental activity and symbolic language.
This view is allegedly not in conflict with science, but only with the philosophical assumption that the events predicted by science must happen, and this assumption Russell sees no reason to accept.
Contrary to the common philosophical assumption that processes of moral judgment are chiefly processes of reasoning, Tessman surveys Jonathan Haidt and Joshua Greene's work on dual process models of moral judgment, which consider how moral judgments of non-negotiable requirements might more standardly occur through automatic, unconscious, intuitive processes.
This line of reasoning is not based on any evidence or research; it is a philosophical assumption - an ipse-dixitism (a dogmatic assertion).
Similar(52)
The second peculiarity is that within film studies itself an institutionalized area of academic study there is a sub-field of film theory that has significant overlap with the philosophy of film even though the majority of its practitioners operate on significantly different philosophical assumptions than Anglo-American philosophers of film.
The two models are based on competing philosophical assumptions.
In this book Keith Graham examines the philosophical assumptions behind the ideas of group membership and loyalty.
How do our philosophical assumptions influence science and the ethics we bring to biotechnology?
By doing so, we can come to see our own philosophical assumptions and prejudices in a new light.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com