In cryptography papers, the word "trust" is used the way a mathematician uses the letter "X". In those papers, "trust" is that thing you lose if the cryptography is broken.
It is popular, but of course improper, to read those papers and conclude that if you do the cryptography right in a commercial PKI, the subscribers to that PKI achieve trust, where "trust" is not defined and therefore means whatever the subscriber desires most. This is a salesman's trick and in need of active correction.
In a world in which each of us trusts everyone else, there is no need for security measures and we can turn our energies to other pursuits. However, that's clearly not the case.
However, it is possible for each of us to trust some other person, for a particular purpose. I knew a woman once who was a good friend and shared many of her secrets with me. I learned to trust her, through these conversations. I was talking with her husband once and happened to ask him whether it bothered him that she and I spent so much time together. He replied that it didn't because he trusted her. So, we both trusted her. Some of the secrets she told me were about all the affairs she was having with men in the office, so my trust in her obviously did not equal her husband's trust in her.
Even if trust were transitive, it would make no sense to propagate trust across a difference in purposes. In particular, it makes no sense to claim that if I trust A to do a good job with cryptography, carefully documenting its methods of verifying claims of identity, and A issues a certificate to B, then I should trust B to sign contracts or electronic checks.
Back to the electronic checking example, if
bank A issues an SPKI certificate to keyholder B with the
authorization to sign electronic checks on account X in that bank,
then I should accept electronic checks signed by B drawn on
account X, but of course not those signed by B drawn on some other
account. I do this not because I trust B in any way, but
rather because I will have a understanding (or even formal
contract) in place with A to the effect that if I present an
electronic check signed by a key certified by that bank, then that
bank will transfer the appropriate funds to me. It is the
transfer of funds that I care about, not whether keyholder B
can be trusted and especially not what keyholder B's name is.