Can a Negative Claim Ever Be Proven?

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SUMMARY

The discussion centers on the philosophical debate regarding the provability of negative claims, particularly in the context of existence. Participants argue that while negative claims can be proven in specific instances, such as asserting the absence of oranges in a bowl, proving the non-existence of abstract concepts like God is inherently more complex. The conversation highlights the distinction between mathematical proof and empirical evidence, emphasizing that proof in mathematics is definitive, while scientific claims rely on inductive reasoning and observable evidence. The necessity of a clear definition of terms like "oranges" and "God" is also underscored, as it affects the validity of claims made.

PREREQUISITES
  • Understanding of deductive and inductive logic
  • Familiarity with the concept of proof in mathematics
  • Basic knowledge of epistemology and its role in defining proof
  • Awareness of philosophical arguments regarding existence and non-existence
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  • Research the principle of contradiction in mathematics
  • Explore epistemological models that define proof
  • Study the philosophy of science, particularly empirical verification
  • Examine case studies of negative claims in philosophical discourse
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Philosophers, students of logic, and anyone interested in the nuances of argumentation and the nature of proof in both scientific and mathematical contexts.

  • #31
TheStatutoryApe said:
I do not understand what is unreasonable about it. I am fairly certain that scientists have not access to the universe as a whole and only make observations of small parts of it in order to draw conclusions about the nature of the whole.
They don't draw conclusions, but they do make working assumptions and extrapolate.

But you cannot extrapolate to show something does or doesn't exist.
 
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  • #32
TheStatutoryApe said:
make observations of small parts of it in order to draw conclusions about the nature of the whole.

Making predictions about unobserved phenomena, based on observed phenomena is inductive reasoning. It is not the same as direct observation, whether it uses direct observation as basis or not.

Science involves prediction based on evidence; inductive reasoning.
It is not pure observation.

You cannot 'prove' something with induction, like you can with deduction.
http://en.wikipedia.org/wiki/Problem_of_induction

Even observations can be faulty and lead to error.

You cannot 'prove' that something doesn't exist, simply by saying you've never seen it.
You cannot 'prove' that something unseen exists based on what you can see.

You can make all kinds of assumptions, predictions, and inferences, but that is not proof.
 

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