All mathematical truths are knowable. All mathematical truths are eternal. So All that is knowable is eternal.
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:
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:
- There might be things that are both knowable and eternal, but that are not mathematical truths.
- There are things that are only eternal, and not knowable.
- There are things that are only knowable, not eternal.
- 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.
False, because not all truths are mathematical.