The logical fallacy of weak inference occurs when a conclusion is not shown to be true given the evidence or reasoning presented. This is closely related to hysteron proteron.
Bill Nye, debating against the scientific Creation Model:What keeps the United States ahead, what makes the United States a world leader, is our technology, our new ideas, our innovations. If we continue to eschew science, eschew the process, and try to divide science into observational science and historic science, we are not going to move forward, we’ll not embrace natural laws, we’ll not make discoveries, we’ll not invent and innovate and stay ahead.
Bill claims that if students were taught to understand the difference between observational and historical science, then this would cause us to not move forward, to reject natural laws, to stop making discoveries, to stop inventing, and to stop innovating. This is non sequitur. It doesn't follow from the premise. It is a weak inference. It should be noted that Bill has implied that knowing the difference between observational and historic science is the same thing as eschewing science and the scientific process. This, of course, is an outright lie.