People may strive to make few to no assumptions involving things that they care about. They may be far less careful with other areas, however. Outside of a certain range of issues and beliefs that either directly affect them or that they are strongly concerned with, they may not strive for deliberate reasoning at all. If they are not consistently sound, then they might simply assume a great number of things. What is an assumption? An assumption is made when someone believes something to be true despite having no proof; people assume when they blindly assert or hold to something that is not necessarily true.
No assumption is reliable--all assumptions are unverified leaps and all of them carry innate logical fallacies. The very nature of an assumption is directly contrary to the nature of knowledge. To know something is to be aware that it is true. To assume something is to believe without proof. Thus, a person cannot both assume something and know it at the same time. Each is mutually exclusive, and the presence of one forces the other away. Just as light and darkness cannot be present in the same place at the same time, so too assumptions and knowledge cannot be simultaneously present in the same place. If an assumption turns out to be true, then anyone who believes it does turn out to be correct, but only by accident.
With what an assumption is established, what then is it not? Hypothesizing about a proposition to see what follows if it is true is not the same as actually making an assumption about reality. A person can reason from a premise without actually accepting that premise as true, for this only entails seeing what follows from the premise and does not involve assuming it to be correct in the process. The two are quite different. Of course, the presence of a single assumption erodes the verifiability of any conclusion that rests on it. But in all cases, assumptions can be identified and removed, and thus, even if the conclusion must be altered accordingly, the conclusion can be made certain. An assumption is an enemy to knowledge.
The person who makes no assumptions recognizes just why knowledge of certain kinds eludes us; human limitations abound, and they do actively prevent us from obtaining knowledge beyond a certain point (that point varies depending on the issue at hand). Knowledge, of course, is possible--after all, to deny knowledge is to claim it (it is impossible for a conscious, rational being to not know anything at all [1])--but it cannot involve assumptions, or else it is not actually certain and thus is not actually knowledge. Rationalism weeds out these assumptions and purifies the epistemic framework [2], delivering it from the uncertainty that assumptions carry.
Assumptions are a catastrophic acid to the credibility or knowability of any theology, ethical system, epistemological framework, or general worldview that relies on them. The goal of a sound thinker is to recognize assumptions wherever or whenever they appear and to not make them. Contrary to what some may claim, this is not an impossible task. It is the only methodology that grounds actual knowledge.
[1]. See here:
A. https://thechristianrationalist.blogspot.com/2017/11/the-impossibility-of-total-skepticism.html
B. https://thechristianrationalist.blogspot.com/2017/01/the-error-of-presuppositions.html
[2]. https://thechristianrationalist.blogspot.com/2017/07/the-necessity-of-cartesian-skepticism.html
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