1 it is said that Hilbert once illustrated his contention that the undefined ter
ID: 3010896 • Letter: 1
Question
1 it is said that Hilbert once illustrated his contention that the undefined terms in a geometry should not have any inherent meaning by claiming that it should be possible to replace point by beer mug and line by table in the statements of the axioms. Consider three friends sitting around one table. Each person has one beer mug. At the moment all the beer mugs are resting on the table. Suppose we interprete point to mean beer mug, li8ne to mean the table , and lie on to mean resting on. Is this a model for incidence geometry? Explain. is this interpretation isomorphic to any of the examples in the Text?
Explanation / Answer
Given that we have to consider a beer mug as a point and table as a line.
We know that we can get a line by joining two points. Therefore, we must be able to join to beer mugs to create a table.
In the given question, we have been given that three friends are sitting around a table. Their beer mugs are placed (resting on) a table. Now, we know that for three points to lie on the same line, they must be collinear. Therefore, as per incidence goemetry, three beer mugs must be collinear in order for them to rest on a table. But as per the instructions, we have not been told that the three mugs are collinear, they can form a triangle as well. Therefore, the given model is NOT for incidence goemetry.
The given interpretation is isomorpic to constructing a triangle using three points in incidence goemetry.
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