Cartesian circle

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The Cartesian circle is a potential mistake in reasoning attributed to René Descartes.

René Descartes 17th-century French philosopher, mathematician, and scientist

René Descartes was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–1649) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. He is generally considered one of the most notable intellectual figures of the Dutch Golden Age.

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Descartes argues – for example, in the third of his Meditations on First Philosophy – that whatever one clearly and distinctly perceives is true: "I now seem to be able to lay it down as a general rule that whatever I perceive very clearly and distinctly is true." (AT VII 35) [1] He goes on in the same Meditation to argue for the existence of a benevolent God, in order to defeat his skeptical argument in the first Meditation that God might be a deceiver. He then says that without his knowledge of God's existence, none of his knowledge could be certain.

<i>Meditations on First Philosophy</i> philosophy book by Descartes

Meditations on First Philosophy in which the existence of God and the immortality of the soul are demonstrated is a philosophical treatise by René Descartes first published in Latin in 1641. The French translation was published in 1647 as Méditations Métaphysiques. The title may contain a misreading by the printer, mistaking animae immortalitas for animae immaterialitas, as suspected by A. Baillet.

The Cartesian circle is a criticism of the above that takes this form:

  1. Descartes' proof of the reliability of clear and distinct perceptions takes as a premise God's existence as a non-deceiver.
  2. Descartes' proofs of God's existence presuppose the reliability of clear and distinct perceptions.

Thus, Descartes' argument is circular.

Descartes' contemporaries

Many commentators, both at the time that Descartes wrote and since, have argued that this involves a circular argument, as he relies upon the principle of clarity and distinctness to argue for the existence of God, and then claims that God is the guarantor of his clear and distinct ideas. The first person to raise this criticism was Marin Mersenne, in the "Second Set of Objections" to the Meditations:

The existence of God is a subject of debate in the philosophy of religion and popular culture.

Marin Mersenne French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"

Marin Mersenne, Marin Mersennus or le PèreMersenne was a French polymath, whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those which can be written in the form Mn = 2n − 1 for some integer n. He also developed Mersenne's laws, which describe the harmonics of a vibrating string, and his seminal work on music theory, Harmonie universelle, for which he is referred to as the "father of acoustics". Mersenne, an ordained priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He was also a member of the Minim religious order and wrote and lectured on theology and philosophy.

"you are not yet certain of the existence of God, and you say that you are not certain of anything. It follows from this that you do not yet clearly and distinctly know that you are a thinking thing, since, on your own admission, that knowledge depends on the clear knowledge of an existing God; and this you have not proved in the passage where you draw the conclusion that you clearly know what you are." (AT VII 124–125)

Logical consequence is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.

Descartes' own response to this criticism, in his "Author's Replies to the Fourth Set of Objections", is first to give what has become known as the Memory response; [2] he points out that in the fifth Meditation (at AT VII 69–70) he did not say that he needed God to guarantee the truth of his clear and distinct ideas, only to guarantee his memory:

"when I said that we can know nothing for certain until we are aware that God exists, I expressly declared that I was speaking only of knowledge of those conclusions which can be recalled when we are no longer attending to the arguments by means of which we deduced them." (AT VII 140)

Secondly, he explicitly denies that the cogito is an inference: "When someone says 'I am thinking, therefore I am, or I exist' he does not deduce existence from thought by means of a syllogism, but recognizes it as something self-evident by a simple intuition of the mind." (AT VII 140) Finally, he points out that the certainty of clear and distinct ideas does not depend upon God's guarantee (AT VII 145–146). The cogito in particular is self-verifying, indubitable, immune to the strongest doubt.

A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

Modern commentators

Bernard Williams presents the memory defense as follows: "When one is actually intuiting a given proposition, no doubt can be entertained. So any doubt there can be must be entertained when one is not intuiting the proposition." (p. 206) He goes on to argue: "The trouble with Descartes's system is not that it is circular; nor that there is an illegitimate relation between the proofs of God and the clear and distinct perceptions [...] The trouble is that the proofs of God are invalid and do not convince even when they are supposedly being intuited". (p. 210)

As Andrea Christofidou explains:

"The distinction appropriate here is that between cognitio and scientia; both are true and cannot be contradicted, but the latter is objectively true and certain (with the guarantee of God), while the former is subjectively true and certain, that is, time-bound, and objectively possible (and does not need the guarantee of God)." (pp 219–220)

A more interesting defense of Descartes against the charge of circularity is developed by Harry Frankfurt in his book Demons, Dreamers, and Madmen: the Defense of Reason in Descartes' Meditations (Bobbs–Merrill, 1970; reprinted by Princeton University Press, 2007). Frankfurt suggests that Descartes' arguments for the existence of God, and for the reliability of reason, are not intended to prove that their conclusions are absolutely true, but to show that reason can be compelled to accept them, even in the face of radical skeptical arguments. In fact, according to Frankfurt, the validation of reason is accomplished by the rejection of the main sceptical hypothesis, which is the first real (albeit negative) conclusion of the argument, whilst the proposition about God's existence is a merely preparatory step. It must be conceded that once reached the real conclusion of the argument, the Cartesian method would forbid the sceptic to reply that perhaps the cartesian proof was suggested to the meditator by the evil genius itself, in the first place (thereby accusing Descartes of vicious circularity). This accusation fails, since it requires the evil genius' existence to be still deemed (at least) a possibility – an idea which precisely, after the expanded "God's proof" the meditator has acquired a specific reason to reject.

However, according to Frankfurt the proof presupposes the validity of the principle of non-contradiction, since otherwise an argument leading to the (provisional) conclusion that a benevolent God exists, wouldn't force Descartes to reject the possible existence of the demon. Thus the proof might, after all, beg the question against a kind of skepticism radical enough to put in doubt the rule of non-contradiction.

Moreover, according to Frankfurt's Descartes, the meditator feels forced to accept his conclusion merely because of the evidence of the supporting argument, while Frankfurt himself started by explaining that the radical doubt is meant to be a criticism of evidence as a criterion of truth (even subjective truth, if you want). As Frankfurt pointed out, it seems hard to deny that the general proposition "evident statements can be false or misleading" can be thought without hindrance, and that Descartes seems to have countenanced this kind of doubt, when close to the end of the First Meditation he wrote that

"...as I sometimes think that others are in error respecting matters of which they believe themselves to possess a perfect knowledge, how do I know that I am not also deceived each time I add together two and three, or number the sides of a square, or form some judgment still more simple, if more simple indeed can be imagined?"

The outcome seems to be that a doubt aimed at evident ideas is supposed by Frankfurt to be overcome by means of a further evident idea, thereby begging the question.

See also

Notes

  1. "AT" refers to Oeuvres de Descartes, ed. by Charles Adam and Paul Tannery.
  2. "The Cartesian Circle". www.owl232.net. Retrieved 2017-10-09.

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