The distinction between primary and secondary properties establishes the absolute priority, both ontological and epistemological, of quantity (objective and measurable) over quality (subjective and ineffable). In between the two properties, primary and secondary, are the dispositional properties, for example fragility, malleability, rigidity, and so on. But, from an ontological point of view, what are dispositional properties? This contribution takes into consideration two possible answers to this question: the one according to which the dispositional properties are invariant in variation and another according to which they are powers. The second answer is in turn subject to two different interpretations. We can consider dispositions, or powers, as integrally reducible to behavioral events (solubility, for example, is reduced to the fact that a certain substance melts when immersed in a certain liquid), or physical (the fragility of glass, for example, is reduced to the physical structure underlying it). However, we can consider powers as ontologically autonomous and not-grounded. This contribution aims to investigate the latter solution, with particular reference to the apparently oxymoronic notion of physical intentionality. This notion will provide a new, dynamic, and evolutionary version of the concept of disposition and at the same time offer a new look at the distinction between primary and secondary properties. This is a fortiori true since Galileo refers to triangles, circles, etc., that is to geometry.Philosophies 2018, 3, 43 2 of 12 wet; if we look at snow and then at the sun, what at first was white appears yellow; sugar seems to taste bitter when we are ill, and so on); mutually conflicting (a surface can seem smooth to the eye but rough to the touch); erroneous (as in any type of hallucination in which we see things that do not really exist); ambiguous (as in famous Gestalt figures such as the duck-rabbit).As is well known, Descartes signals an irreversible turn in relations between body and mind, and above all in the nature of the mental. The mind becomes something specifically immaterial, a substance separate from bodies (our own body included), totally extraneous to the material order of the world. Descartes' idea is this: the physical world is a great mechanism whose functioning is mathematically described by quantitative physics. The sole exception is thought, which does not allow itself to be reduced to such a mechanism and is substantially extraneous to the material and natural world. Quantitative-mathematical explanations can therefore be applied to everything, with the sole exception of the human mind. Thus, we come to create that explanatory void which is at the origin of the tension present in what Ryle calls the official theory of mind [1]: that is, mind-body dualism. In Descartes, this ontological antireductionism is the direct consequence of total adhesion to the scientific revolution initiated by Galileo. The presupposition is that if, in an illusion, even bodies are not as they actua...