Are ‘Consequences’ sufficient to prove infant baptism?

From Benjamin Keach: Gold Refin’d, or Baptism in its Primitive Purity (London: 1689), 69-70, 146 (orthography and punctuation modernized).

What commission our brethren have got, who sprinkle children, I know not. Let them fetch a thousand consequences, and unwarrantable suppositions for their practice, it signifies nothing, if Christ has given them no authority or rule to do what they do in his name. Natural consequences from Scripture we allow,but such which flow not naturally from any Scripture we deny; can any think Christ would leave one of the great sacraments of the New Testament, not to be proved without consequences?

We affirm, that in all positive or instituted worship (such as baptism is) which wholly depends upon the mere will and pleasure of the law-giver, it is absolutely necessary there should be an express command, or plain and clear examples, though in other respects we allow of natural deductions and consequences from Scripture for the confirming and enforcing of duties, and for the comfort and instruction of God’s people. But as there is neither express command nor example for infant-baptism; so it can’t be proved by any consequence or inference, that naturally and genuously rises from any Scripture, as we have proved, nor does draw any such consequences to prove it.