All mathematical truths are knowable. All mathematical truths are eternal. So All that is knowable is eternal.

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    We do not answer HW questions for people. We can help, but please explain why you are having difficulty with this example. – Conifold Aug 25 at 0:31
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    Here is a Wikipedia page that might help: en.wikipedia.org/wiki/Syllogism This looks like "figure 3". All of the sentences are universal affirmative. Try replacing the terms with something else to see if the form works for them as well or not. – Frank Hubeny Aug 25 at 0:53

Wrong. Following the sylogism: All mathematical truths are knowable, and all mathematical truths are eternal; so all mathematical truths are both knowable and eternal — those are two qualities of 'all mathematical truths', and so far that's all they are. There is nothing that implies that 'all that is knowable is eternal' or that 'all that is eternal is knowable'.

See the following Venn diagram:

enter image description here

We, therefore, conclude that there is a group called the eternals and a group called the knowables. There are things that are only knowables, and things that are only eternals, but then there are things that are both. Among those things that are both, you have 'all mathematical truths'. So we have to keep in mind that:

  1. There might be things that are both knowable and eternal, but that are not mathematical truths.
  2. There are things that are only eternal, and not knowable.
  3. There are things that are only knowable, not eternal.
  4. Mathematical truths are both knowable and eternal, but that doesn't imply a link between all things that are eternal and all things that are knowable.
  • You wrote an Euler diagram NOT a Venn DIAGRAM. There are differences between the two types of diagrams. – Logikal Aug 26 at 16:59
  • @Logikal Thanks for the input, I did a quick search and I interpreted that Venn’s are Euler’s that show all possible relations. To me, the diagram I drew shows all possible relations. So wouldn’t it be a Venn nevertheless? – William Aug 27 at 10:47
  • No you are wrong. EULER and VENN diagrams are distinct. One is not a type of the other. One is used by math and the other by philosophy. Venn diagrams are distinct by always showing three interloping circles. One for the subject, one for the predicate & the other for the middle term for an argument. There are never circles within circles. Circles within circles exclusively means Euler diagrams nothing else. Math diagrams do not show all possible outcomes. It was meant to show set membership. Logic is not the same as math. People try to pretend it's all the same . There are distinctions – Logikal Aug 27 at 11:06
  • @Logikal Everywhere I go, your claim is contradicted. Can you add credible sources to that? Or maybe even do your own self-answered question in this SE? – William Aug 28 at 23:49
  • Try any logic book written by a philosopher not a mathematician. Where did you look? Show me the links and I think you misread them. EULER was a mathematician. VENN DIAGRAMS are named after JOHN VENN. THEY ARE THREE circles. No Venn diagrams have circles within circles. Euler diagrams are for set theory. VENN diagrams are for argument validly. Two different purposes by two distinct fields. Where are you looking? Do you know what contradiction mean? Something is off. – Logikal Aug 28 at 23:54

False, because not all truths are mathematical.

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