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In common use, the word "supposition" and the word "assumption" may be used, for the most part, interchangeably, with the word "assumption" being the more commonly used and understood word. However, there are some words of caution that must accompany the use of the word "assumption" - far more so than "supposition."

Supposition comes from latin "suppositio" which means "to place beneath.
"Assumption is from "assumptio" which means "taking up."

This indicates that the word "assumption" is a more powerful, emotional, word. If I "assume" something, this means that I have "taken it up" and am in complete agreement with the postulate. Furthermore, I have done so without necessarily having explored, completely, all the facts that may or may not make the assumption true. An assumption is, therefore, another word for "unfounded belief." The very word "Assume" conveys this meaning and it has been adopted as such in the common vernacular.

Alternatively, the word "supposition" bears no such negative connotation, and by stating that your belief is a supposition, you are acknowledging that it may be partially formed, and that you are open to further suggestions regarding its value.

Source

Would you possibly tell me if the explanations of a site about my topic true?

Or, I am wondering the difference between supposition and assumptions and hypothesis.

In addition, I cannot understand well what the following means?

Alternatively, the word "supposition" bears no such negative connotation, and by stating that your belief is a supposition, you are acknowledging that it may be partially formed, and that you are open to further suggestions regarding its value.

  • In a mathematical/physical context, I would use "assumption" as the facts you start with. "Supossition" would be more like a guess. But I think the three would be considered equivalent in that context. – jinawee Aug 19 '14 at 12:34
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    The author is correct; the answer (commentary) discounts the subtle but accurate difference, favoring a more simplistic style. While it is true that they are synonymous to a high degree, their subtle nuances of meaning are not 100% identical. – user42738 Oct 5 '16 at 12:19
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I think you may safely ignore what this author says. There is no substantive difference between an assumption and a supposition.

  • It is true that assumption is far more common than supposition; but this Google NGram suggests that that is merely historical fashion:

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    Scholars today are more likely to use assumption than presupposition; a hundred and fifty years ago the opposite was true.

  • It is also true that you are likely to hear people scorn a proposition as "merely an assumption". But it is equally true that you may to this day hear such propositions scorned as "the merest supposition". Either may be an "unfounded belief"; equally, either may be taken as the starting point of an argument intended to prove that it is false.

  • And the etymology is wholly irrelevant—to argue otherwise is the etymological fallacy. Etymology tells you where a meaning started, not what it has come to mean today.

These two words are essentially synonymous. They are both significantly different from hypothesis in one critical respect. An assumption or supposition is usually (but not always) taken as a true proposition on which one will base an argument, even if that argument leads in the end to proving the proposition false. But a hypothesis is always advanced as a proposition whose truth is, from the outset, in question. The purpose of the following discourse is to establish whether it is or is not true.

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If a prosecutor assumed a defendant could travel (drive) 4.5 miles at 30 mph in 9 mins it would eventually be found not to be true. The physical probability would have to be considered traffic lights,curves, time of day etc. From a mathematical calculation 9 mins would be correct. The physical time to travel would be significantly different.

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