Final answer:
Theorems and postulates are foundational to supporting conclusions in mathematics and science, wherein the former is a proven statement while the latter is an assumed truth. Evidence must be critically evaluated to ensure it does not fall prey to logical fallacies and must be sufficient to bolster the hypothesis within the frame of probability rather than absolute certainty.
Step-by-step explanation:
Understanding Theorems and Postulates in Argumentation
When using theorems or postulates to support a conclusion, the theorem is a proven statement in mathematics based on previously established statements, such as other theorems, and axioms, whereas a postulate is assumed to be true without proof. To support a conclusion, one can draw on these well-established facts or agreed-upon principles for their reasoning. For example, when discussing the theory of special relativity, we reference its postulates as starting points for further reasoning in physics.
Critical Evaluation of Arguments
In philosophy, a conclusion acts not as an endpoint but rather as an invitation for further scrutiny and discussion. This involves presenting clear evidence, which might include experimental data or logical reasoning, explaining how this evidence supports the thesis. Essential to this scrutiny is ensuring that arguments are not based on circular reasoning, that the premises are not inadequate, false, or irrelevant, and that no alternative arguments with equal or greater support are overlooked.
Scientific Hypothesis Testing
In science, new evidence can always potentially refute a hypothesis, so rather than proving a hypothesis true, scientists collect evidence to increase its likelihood of being true. When we talk about hypothesis testing, we never declare a hypothesis unequivocally proven, as we operate under the umbrella of probability laws and non-absolute certainties.