# A Logical Remark on Swinburne’s Cartesian Argument for Substance Dualism

2021-06-08, updated 2021-06-08 next - previous

A logical proof that it is false that Swinburne improves Descartes’s Argument for Substance Dualism.

## 1. Swinburne’s Argument

Swinburne’s argument is an amended version of Descartes’s in Discourse on the Method [1, p. 127]:

Next I examined attentively what I was. I saw that while I could pretend that I had no body and that there was no world and no place for me to be in, I could not for all that pretend that I did not exist. I saw on the contrary that from the mere fact that I thought of doubting the truth of other things, it followed quite evidently and certainly that I existed; whereas if I had merely ceased thinking, even if everything else I had ever imagined had been true, I should have had no reason to believe that I existed. From this I knew I was a substance whose whole essence or nature is simply to think, and which does not require any place, or depend on any material thing, in order to exist. Accordingly this ’I’ - that is, the soul by which I am what I am - is entirely distinct from the body, and indeed is easier to know than the body, and would not fail to be whatever it is, even if the body did not exist.

According Swinburne, the structure of this argument is the following one:

• First premise: I am a substance which is thinking.
• Second premise: it is conceivable that ‘I am thinking and I have no body’.
• Third premise: it is not conceivable that ‘I am thinking and I do not exist’.
• Conclusion: I am a soul, a substance, the essence of which is to think.

To justify this conclusion, Swinburne assumes that Descartes meant by “soul” that belongs to a human being as a non-physical and indivisible part. He notes that the premises only entail a conclusion that ‘I am a substance for the existence of which having a soul is sufficient’ and he stresses on the point that Descartes’s argument does not show that having a soul is a necessary condition for Descartes’s existence, hence this new argument which is considered by Swinburne as an improvement of Descartes’s :

• First premise: I am a substance which is thinking.
• Second premise: it is conceivable that “While I am thinking, my body is suddenly destroyed”.
• Third premise: it is not conceivable that “I am thinking and I do not exist”
• Fourth premise: it is inconceivable that any substance can lose all its parts simultaneously and yet continue to exist.
• Conclusion: I am a substance, for the existence of which having a soul is both necessary and sufficient.

## 2. Objection

Based only on Descartes’s premises, it is provable that “I am thinking” is logically equivalent to “I have a soul and I exist”. Consequently, it is false that Swinburne’s argument is an improvement of Descartes’s.

To prove the above proposition, let us define this formal lexicon in the language of first-order logic with an existence predicate [2, pp. 106, 164]:

• $$c$$ = “I”,
• $$Tc$$ = “I am thinking”,
• $$Sc$$ = “I have (or I am) a soul”,
• $$Ec$$ = “I exist”.

Here is the argument:

• If I am thinking, then I am something, that is to say a thinking substance also called “a soul”:

$$\label{paralogism} Tc \to Sc$$
• If I am thinking, then I exist:

$$\label{eq:10} Tc \to Ec$$
• I am thinking:

$$\label{eq:11} Tc$$
• Therefore, I am thinking if and only if I am a soul and I exist; in other words, my existence as a soul is both necessary and sufficient for thinking:

$$\label{eq:12} \therefore ~~ Tc \leftrightarrow (Sc \land Ec)$$

The previous deduction corresponds to the following sequent:

$$\label{eq:8} Tc \to Sc, Tc \to Ec , Tc \vdash Tc \leftrightarrow (Sc \land Ec)$$

which is provable in minimal logic as follows:

\begin{prooftree} \AxiomC{$Tc \to Sc$} \AxiomC{$\scriptsize{1}$} \noLine \UnaryInfC{$Tc$} \RightLabel{$\scriptsize{\to E}$} \BinaryInfC{$Sc$} \AxiomC{$Tc \to Ec$} \AxiomC{$\scriptsize{1}$} \noLine \UnaryInfC{$Tc$} \RightLabel{$\scriptsize{\to E}$} \BinaryInfC{$Ec$} \RightLabel{$\scriptsize{\land I}$} \BinaryInfC{$Sc \land Ec$} \RightLabel{$\scriptsize{\to I, 1}$} \UnaryInfC{$Tc \to (Sc \land Ec)$} \AxiomC{$Tc$} \RightLabel{$\scriptsize{\to I}$} \UnaryInfC{$(Sc\land Ec) \to Tc$} \RightLabel{$\scriptsize{\land I}$} \BinaryInfC{$Tc \leftrightarrow (Sc \land Ec)$} \end{prooftree}

## 3. Conclusion

Two points:

1. The consequence of this formal proof is that it is false that Swinburne’s argument is an improvement of Descartes’s. Indeed, there is no need for new premises to deduce inside Descartes’s system the conclusion which claims that existing as a soul is both a necessary and a sufficient condition for thinking.
2. This formal proof strengthens Kant’s analysis [3, pp. 328–335]: Descartes’s argument is a “paralogism”, because it is illusory to believe that one can deduce “I have a soul” from the statement “I am thinking”. The logical validity of the previous argument is obviously not a proof in favor of its correctness: the premise formalized by \eqref{paralogism} remains doubtful and will remain so forever.

## Bibliography

[1]
J. Cottingham, Ed., The Philosophical Writings of Descartes. Cambridge Cambridgeshire ; New York: Cambridge University Press, 1985.
[2]
M. Fitting and R. L. Mendelsohn, First-Order Modal Logic, vol. 277. Kluwer Academic Publishers, 1998 [Online]. Available: http://dx.doi.org/10.1007/978-94-011-5292-1
[3]
I. Kant, Critique of Pure Reason, Rev Ed. London: Penguin Classics, 2007.

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