In some sense, yes, although for conventional computers you might settle on very slow verification. Unless you mean that, your mind has only finite memory/lifespan and therefore you cannot verify an arbitrary conventional computer within any given credence, which is also true. Under favorable conditions, you can quickly verify something in PSPACE (using interactive proof protocols), and given extra assumptions you might be able to do better (if you have two provers that cannot communicate you can do NEXP, or if you have a computer whose memory you can reliably delete you can do an EXP-complete language), however it is not clear whether you can be justifiably highly certain of such extra assumptions.
In some sense, yes, although for conventional computers you might settle on very slow verification. Unless you mean that, your mind has only finite memory/lifespan and therefore you cannot verify an arbitrary conventional computer within any given credence, which is also true. Under favorable conditions, you can quickly verify something in PSPACE (using interactive proof protocols), and given extra assumptions you might be able to do better (if you have two provers that cannot communicate you can do NEXP, or if you have a computer whose memory you can reliably delete you can do an EXP-complete language), however it is not clear whether you can be justifiably highly certain of such extra assumptions.
See also my reply to lbThingrb.