Deductionism is the belief that all of physical reality can be mapped by formal constructs, such as mathematical models. In practice, these* are often the actual objects of scientific study*. Deductionism is the premise that nature is reducible ultimately to the terms of a deductive system. (Greek deductionism had held that one should be able to deduce natural details, like theorems of geometry, strictly from first principles.) Such a belief, often tacit, is an example of what Gerald Holton called *thematic content*: an implicit intuitive assumption. In its extreme, deductionism holds that models work because they are *identical* to the natural realities they model. Models are usually defined by equations, and the systems studied are chosen and re-defined in such a way that they can be described by (preferably simple) equations. Deductionism thus blurs the very distinction between mathematics and the physical world. However, one basic difference is that knowledge of physical structures is contingent, or “synthetic,” while mathematical structures are “analytic.” That is, physics depends on empirical evidence, while mathematical concepts depend only on reason and how they are defined. It is only because *physical* systems have first been re-defined as *mathematical* structures that there seems to be a built-in correspondence between model and reality. The correspondence between mathematics and physics is actually a correspondence of one deductive system to another. The correspondence with reality remains an article of faith. But it is often a self-confirming faith, since phenomena that can be treated with existing mathematics are the ones generally selected for study. One reason for this is that a deductive system is equivalent to a machine. A deductive approach serves technology in particular, since mathematical models can often be translated into literal machines or devices. But seeing the world through deductive eyes limits what can be perceived as significant for investigation. It may also limit the demand for new mathematics.