"Consider the following three Cartesian theses:
Substance dualism: Any substance with mental properties lacks material properties and any substance with material properties lacks mental properties.
Property dualism: Mental properties and material properties are different properties.
Real distinction between mind and body: The mind and the body are numerically distinct substances.
How are these theses logically related? Substance dualism is the strongest of the three, and entails the other two. It entails the real distinction between mind and body. For the mind is a substance with mental properties, and the body is a substance with material properties. Now if the mind lacks material properties, and the body lacks mental properties, then the mind and the body cannot be the same substance. But the real distinction between mind and body does not entail substance dualism. For that mind and body are two numerically distinct substances is compatible with both of them having both mental and material properties.
Substance dualism also entails property dualism. For if a substance with mental properties lacks material properties, then mental and material properties are different properties–otherwise, a substance with mental properties would be a substance with material properties. But property dualism does not entail substance dualism. It could be that mental properties and material properties are different properties and yet a substance with mental properties is also a substance with material properties.
But the real distinction between mind and body and property dualism do not entail each other. It could be that mind and body are numerically distinct substances but mental and material properties are the same. For instance, it could be that mind and body are distinct because they have different properties: the mind has a property M that the body lacks, and the body has a property B that the mind lacks. This does not preclude that both M and B are both mental and material properties. So the real distinction between mind and body does not entail property dualism. Nor does property dualism entail the real distinction between mind and body. For even if mental and material properties are different properties, it can still be the case that the mind, which has mental properties, and the body, which has material properties, are the same substance."
(Gonzalo Rodriguez–Pereyra, pp.70–71)
Rodriguez–Pereyra, G. (2008). "Descartes's Substance Dualism and His Independence Conception of Substance". Journal of the History of Philosophy 46(1): 69–90.
Fig.1 Lucy Jones "Philosophy of the Mind Episode Two: Criticisms of Substance Dualism", YouTube.
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"What is the function of abductive inference? For [Charles Sanders] Peirce it is 'the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary consequences of a pure hypothesis. Deduction proves that something must be; induction shows that something actually is operative; abduction merely suggests that something may be' (CP 5.171, cf 1991a, p.333). Abduction may thus be conceived of as a principle that allows us to reconstruct how conceptual order is achieved through the imposition of a hypothesis (in the form of a minimal theory, an idea, a rule or a law–like hypothesis) – which inaugurates constructivist thinking. Here I can only hint at the great variability of this schema; it enables us to bridge the traditional gap between the arts and the sciences because it can be used as a model both of explanation and of understanding."
(Hans Rudi Fischer, pp. 368, 2001)
Peirce, Charles Sanders (CP). (1931–35, 1958) "Collected Papers of Charles Sanders Peirce". Bd. I–VI (1931–34) ed by Ch. Hartshorne and P. Weiss. Vol. VII–VIII (1958) ed. By A.W. Burks. Cambridge, Massachusetts/London.
Peirce, Charles Sanders (1991a), Naturordnung und Zeichenprozeß. Schriften über Semiotik und Naturphilosophie. Hrsg. und eingeleitet von Helmut Pape. Frankfurt/Main, Suhrkamp.
Foundations of Science, special issue on "The Impact of Radical Constructivism on Science", edited by A. Riegler, 2001, vol. 6, no.4: 361–383. "Abductive Reasoning as a Way of Worldmaking", Hans Rudi Fischer, Heidelberger Institut für systemische Forschung und Therapie, Kussmaulstr. 10, D–69120 Heidelberg, Germany.
"In consequence of this revolutionary assertion Kant states that: 'Space is not an empirical concept which has been derived from outer experiences.' (B/38) On the contrary: '…it is the subjective condition of sensibility, under which alone outer intuition is possible for us.' (A/26; B/42)
In other words, Kant asserts that space (and time) are not objective, self–subsisting realities, but subjective requirements of our human sensory–cognitive faculties to which all things must conform. Space and time serve as indispensable tools that arrange and systemize the images of the objects imported by our sensory organs. The raw data supplied by our eyes and ears would be useless if our minds didn't have space and time to make sense of it all. ...
Kant's view of space (and time) is the groundwork of his Critique [of Pure Reason], However the inseparable bond he claimed between geometry and the nature of space serves to undermine his case rather than support it. ...
When Kant refers to geometry, he must mean Euclidean geometry, since Non–Euclidean geometry, the brainchild of the 19th Century, was unknown to him. Hence space, in Kant's philosophical system must conform to Euclidean geometry. Norman Kemp Smith, in his Commentary on the Critique, remarked that for Kant '…space in order to be space at all, must be Euclidean.'
Space, in Euclidean Geometry, is a concept which is independent of the attributes of our human minds and senses. The word Geometry is derived from Greek – geo 'earth', and metron 'to measure', namely 'earth measurement'. With such semantic–conceptual roots its hardly conceivable that Euclid regarded Geometry as divorced from an objective independent space."
(Pinhas Ben–Zvi, 2005, Philosophy Now)
Ben–Zvi, P. (2005). "Kant on Space." Philosophy Now, January/February 2005(49).