Per Intellectum, Vis
What would you fix? Trying to come up with a theme / catchphrase for a family event. I want to signify respect for education, the scientific method and observation.
Intellectus means "understanding." I think it's a fine enough phrase, but personally I'd go with something a bit more idiomatic. You could do:
Mens is often used as metonymy for the "intellect." Cf. Juvenal's mens sana in corpore sano.
You could also do something like in scientia or in eruditione, though they don't sound as snappy.
More problematic is vis, which is most often physical strength or even violence. For a more general strength, you could do something like:
Here fortior means "stronger", and the phrase would correlate the use of mens with becoming fortis, "strong."
Finally, if you're thinking about political strength (which, I suspect, you're not, since it's for a family event), you could substitute potestas for vis.
Ultimately, though, I'd rest with:
Fortior per mentem
Even then context matters, as it could, literally, mean "stronger throughout the mind," though I myself kind of like the double meaning there.