There is a continuum, from theories that probably are not true but easily could be, to theories that could only be true at the cost of overthrowing large edifices of successful orthodox science. Now, where does Lamarckism stand in this continuum? It is usually presented as well over on the 'not true but easily could be' end of the continuum. I want to make a case that, while not in the same class as levitation by the power of prayer, Lamarckism, or more specifically the inheritance of acquired characteristics, is closer to the 'levitation' end of the continuum than to the 'Loch Ness monster' end. The inheritance of acquired characteristics is not one of those things that easily could be true but probably isn't. I shall argue that it could only be true if one of our most cherished and successful principles of embryology is overthrown. Lamarckism therefore needs to be subjected to more than the usual 'Loch Ness monster' level of scepticism. What, then, is this widely accepted and successful embryological principle that would have to be overthrown before Lamarckism could be accepted? That is going to take a little explaining. The explanation will seem like a digression, but its relevance will become clear eventually. And remember that this is all before we start the argument that Lamarckism, even if it were true, would still be incapable of explaining the evolution of adaptive complexity.