Is there a consensus on the philosophical assumptions of science?

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The discussion centers on the foundational assumptions of science, questioning their consensus and validity. Key assumptions include the rationality, accessibility, contingency, objectivity, and unity of the universe. While these principles have significantly contributed to scientific advancement, their absoluteness is debated. A notable contradiction arises between the assumptions of objectivity and unity. The conversation references Isaac Newton's rules for scientific inquiry, emphasizing simplicity, consistency, and testability of explanations. However, it notes that modern science, particularly in the last century, has diverged from these principles, with some theories, like string theory, straying into realms that challenge traditional scientific methodology. This shift has blurred the lines between science and philosophy, raising concerns about the testability of certain scientific claims.
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There are numerous lists online of the basic assumptions of science--too many for me to feel comfortable that there is actually a standardized consensus on this. Here is my question. What are the most generally accepted 'a prioris' of science? And how well do they stand up under careful scrutiny?

There is one particular list I found amenable to my to my own sense of the matter. And yet for each assumption I found myself wanting to add the qualification "to a degree".

The universe is rational - can be determined by systems of logic.
The universe is accessible - we have the means to interact with the universe.
The universe is contingent - relationships of cause and effect operate within parameters.
The universe is objective - exists independent and indifferent to sense perception.
The universe is unified - nothing can be "separated" from the universe.

From a methodological standpoint I think the above assumptions have been absolutely crucial to the great success and advancement of modern science, and yet I am not 100% convinced of their absoluteness. Recently it was keenly pointed out to me that the last 2 in the above 5 are contradictory. Can anyone tell me why?
 
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For many years, the differences between science and philosophy were well defined by the "father" of modern science Isaac Newton. His rules were as follows:

source: http://www.bun.kyoto-u.ac.jp/~suchii/intro.PS/Newton%27s-rules.html

Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Renge Interprets: No extraneous explanations for phenomena that may or may not be true. Try to explain phenomena with the minimum amount of causes that can lead to a phenomena taking place, and keep the explanations as simple as possible.

Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

Renge Interprets: Once you have an explanation for one phenomena try to see if it can at least to some extent explain another phenomena.

Rule 3: The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

Renge Interprets: Try to find factors that remain the same or constant in the underlying experiments even as other things vary.

Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

Renge Interprets: The conclusions *must* be testable by experiment. Other ideas that cannot be tested must remain a hypothesis until they can be tested and only at that time are conclusions supposed to be modified. It is this which chiefly separates science from philosophy (philosophers are not limited by the concept that their speculation must be testable).

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It should be mentioned that in the last 100 years some scientists have strayed somewhat from these principles. For example, string theory violates practically all of the above rules and many other theories fall into realms that are beyond our ability to test them ("historical" science in astronomy and biology falls into this category in places). Yet for much of the 17th-19th centuries most of the useful ideas in science were created following these principles. The change in the 20th century has made certain areas of science in some ways more like philosophy and the difference between the two is much harder to see. (for example, the above list you gave for assumptions of science sounds more philosophical than scientific because none of those conclusions about the universe are testable).
 
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