Inferring P from P v Q': Is it Valid?

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In summary, the conversation discusses the use of an "inference rule" in a textbook which states that from P v Q, one can assume P. However, the question is raised if this rule also applies to P v Q', where Q' means not-Q. The speaker's intuition is that this rule does not hold in this case, but they are looking for a reasoned answer. It is clarified that the "v" in the rule stands for "OR" and it is noted that P can be inferred from P & Q or P & Q'.
  • #1
EvLer
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So, there is this "inference rule" in my textbook:
from P v Q, we can assume P

but does this hold for P v Q', i.e. given this, can I say we have P?

My intuition says "no", but I'd rather have a reasoned answer...
Thanks in advance.
 
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  • #2
From P v Q, you may not infer P. You can assume P anytime you like, so long as you discharge all assumptions by the end of your proof. By "v", you do mean "OR", right? From P & Q you certainly may infer P. And if, by Q' you mean not-Q, then you may infer P from P & Q' just as you may infer it from P & Q.
 

FAQ: Inferring P from P v Q': Is it Valid?

What is "Inferring P from P v Q" and why is it important in science?

"Inferring P from P v Q" is a logical principle that states that if one knows that P is true or that Q is true, and P v Q is true, then P must also be true. It is important in science because it allows scientists to make logical conclusions based on known information, which is crucial in the process of forming scientific theories and hypotheses.

How is "Inferring P from P v Q" used in scientific experiments?

In scientific experiments, "Inferring P from P v Q" is used to draw conclusions from the results obtained. For example, if an experiment shows that either A or B causes a certain effect, and it is known that A is not the cause, then it can be inferred that B must be the cause.

Can "Inferring P from P v Q" be applied to real-life situations outside of science?

Yes, "Inferring P from P v Q" is a logical principle that can be applied to any situation, not just in science. It is commonly used in everyday life to make logical deductions based on known information.

What are some potential limitations of using "Inferring P from P v Q" in scientific research?

One potential limitation is that the principle assumes that the information presented is accurate and complete, which may not always be the case in scientific research. Additionally, it may not account for all possible variables that could affect the conclusions drawn.

How does "Inferring P from P v Q" relate to the scientific method?

"Inferring P from P v Q" is an important tool in the scientific method as it allows scientists to make logical conclusions based on evidence and observations. It is often used in the process of formulating hypotheses and theories, which are then tested through experiments and observations.

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