I am unable to come up with an answer to the question - "what is an assumption?"

Given a statement X, how do i know how many assumptions are there in it. It often happens that one statement is said to contain more assumptions than the other. Also, one is often asked to compare between two assumptions to say which one is a stronger assumptions, so how are two assumptions compared.

Is there any literature on the subject, what are the current lines of thought on the subject?

  • I think there's two parts to this: implication and inference. A statement can assume (imply) something. But a person reading/hearing the statement can infer something that was not implied. It may be helpful to separate the two.
    – user18800
    Jan 4 '16 at 20:11
  • If anyone is aware of good literature on what an assumption is, please include it as an answer.
    – Joe
    Aug 5 '20 at 2:59

An assumption - at least in a philosophical context - is typically a presupposition, often unstated. One person makes a statement and another objects that for this to be plausible something else is being presupposed. Philosophers are often good at identifying assumptions made by other people - it comes with the territory :)

Generally speaking, it is better to have fewer or weaker assumptions, because there is less for an opponent to object to. An assumption might be weaker because it carries a smaller ontological commitment, or it avoids entailing a disputed proposition or relationship, or because it is just simpler.

A major part of philosophy is concerned with the issue of identifying and scrutinising the assumptions behind statements - at least with philosophy in the analytic tradition. If there were an answer to your question, "how do I know how many assumptions are there..." it would imply the existence of a mechanical process for doing philosophical analysis.

In practice, the process of analysis is far from mechanical. Often we only realise that there is a problem with a statement when we discover later that it leads to a falsehood, or a conflict or a confusion. Sometimes this discovery comes from new data, sometimes from thought experiments, sometimes from trying to resolve paradoxes, sometimes from trying to reconcile insights and theories from different branches of knowledge. Often, even terms and ideas that we thought were simple and unproblematic turn out to require significant analysis in order to bring clarity to a problem.

But we can't tell in advance how much analysis we'll need or what assumptions we will find in future. These are simply part and parcel of the process of expanding our knowledge and understanding of the world.

  • I have a question about this. I’m trying to understand if there is a well defined concept of an assumption. If I hold out a glass and say, “If I let this go, it’ll drop to the floor,” can someone else rightly say, “You’re assuming that the force of gravity will cause the glass to accelerate toward the Earth.”? Meaning, is that an assumption? Or is it a fact? Can a fact be an assumption? I’m not trying to argue over semantics. I’m truly trying to understand if there is a clearly defined notion of an assumption.
    – Joe
    Aug 5 '20 at 2:57
  • 1
    I would say that the effect of gravity is an assumption, but an entirely reasonable one. Why would you assume gravity will not operate in this case? That would be far less plausible. As long as nobody is going to dispute the effect of gravity there is no practical point in identifying it as an assumption. It is more useful to identify assumptions if they are disputed, or if they might turn out to be false.
    – Bumble
    Aug 5 '20 at 13:00
  • If I understand you correctly, I believe you are saying then that assumptions are the hypotheses of an argument, which is based on context, i.e. nothing is inherently an “assumption”, but rather any fact, claim, belief, etc., can be “an assumption” if it is being used as the starting point for an argument. The same exact fact, claim, belief etc., may be the conclusion of another argument. So what makes something “an assumption” is not how likely it is to be true, or how much logic or evidence supports it, but only its use in a given context. This is exactly the same as “presupposition”, right?
    – Joe
    Aug 5 '20 at 13:54

Formally an assumption is the premiss "A" of an implication "A => B". Here "A" and "B" themselves may be formulas of arbitrary complexity. On knows, that the implication is true if and only if either A is false or A and B both are true.

In the applications, the formula "B" is given and one looks for a formula "A", which is true and such that the implication "A => B is true". Then one knows that "B" is true.

The first task is to find such formula A, i.e. to find the hidden premiss.

  • nevermind my previous comment. How is it that the implication is true if A is false? Also the second part of your answer, B is already given to be true , we are only fitting an A such that A=>B is true.
    – user12196
    Dec 2 '15 at 0:30
  • 2
    The fact that the implication A => B is true, when A is false, is named "ex falso quodlibet", i.e. from a false premiss one can conclude everything. It sounds a bit strange. It follows from the definition A => B := not(A and not B); i.e. (not A) or B. The latter is true when A is false, independently from B. - Concerning the original problem I think one asks, why is B true? Hence one looks for an implication A => B with true A.
    – Jo Wehler
    Dec 2 '15 at 5:20

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