If the castration complex is to normalize the child, Lacan argues, what the child must be made to perceive is that what satisfies or orders the desire of the mother is not any visible (imaginary) feature of the father (his obviously better physical endowments, and so on). The child must come to see that the whims of the mother are themselves ordered by a Law that exceeds and tames them. This law is what Lacan famously dubs the name ( nom ) of the father, trading on a felicitous homonymy in French between nom (name) and non (the "no!" to incestuous union). When the father intervenes, (at least when he is what Lacan calls the symbolic father) Lacan's argument is that he does so less as a living enjoying individual than as the delegate and spokesperson of a body of social Law and convention that is also recognised by the mother, as a socialised being, to be decisive. This body of nomoi is what Lacan calls the big Other of the child's given sociolinguistic community. Insofar as the force of its Law is what the child at castration perceives to be what moves the mother and gives the father's words their "performative force" (Austin), Lacan also calls it the "phallic order."
Formal logic has held sway for more than two millennia and was the basis of experiment and the great advances of modern science. The development of mathematics was based on this logic. You cannot teach a child to add up without it. One plus one equals two, not three. Formal logic may seem like common sense and is responsible for the execution of a million and one everyday things, but - and this is the big but - it has its limits. When dealing with drawn out processes or complicated events, formal logic becomes a totally inadequate way of thinking. This is particularly the case in dealing with movement, change and contradiction. Formal logic regards things as fixed and motionless. Of course, this is not to deny the everyday usefulness of formal logic, on the contrary, but we need to recognise it limits.