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My idea is to assign a truth value to this statement of Descartes. However, if I apply a negation I should get a false value to its negation and equally non-trivial. So the negation could be:

  • "I think therefore I am not"

  • "I do not think therefore I am"

  • "I do not think therefore I am not"

However, all these sentences are equally nonsensical. This made me realize "I think therefore I am" is a descriptor and not a predictor. Am I wrong in my concerns?

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    If you read it as "inference" , the negation will be: from the premise, the conclusion does not follow. Commented May 15 at 8:59
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    "I think therefore I am" is not a proposition; it is an argument, and therefore it has no negation. The two answer below explain the negation, not of Descartes's argument, but of a material implication having the same structure as the argument. Commented May 15 at 10:01
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    This statement is "a formulation that does not expressly appear in the Meditations", see SEP. Descartes comes closest in a reply to Mersenne, but "consistently blurs the distinction between inferences and propositions":"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." It is hard to negate something whose author cannot settle on what they are trying to say.
    – Conifold
    Commented May 15 at 10:43
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    This is much too amusing to be closed. Commented May 16 at 11:37
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    The comments here, particularly those of Mauro and David Gudeman are much better than the answers. Most of the answers are confusing the material conditional with the logical consequence relation. The cogito is really an expression of the intuition that I cannot coherently doubt that I am doubting, and hence my existence is an indubitable fact (indubitable to myself at least).
    – Bumble
    Commented May 16 at 13:41

11 Answers 11

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Entering into your existential game :-) I formalize Descartes’ statement “I think therefore I am” as

For all x: think(x) => exist(x)

Because “A => B” equals “not (A and non-B)” the negation of Descartes’s statement is

Exists x: think(x) and not exists(x), i.e.

"There is at least one thing which thinks but does not exist."

I consider this to be a false proposition, as expected.

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    This is the formalization that makes most sense to me, but I would say that the full statement is "(for all x: think(x) => exist(x)) AND think(I)", which would make the negation "(exists x: think(x) and not exists(x)) OR not think(I)", or equivalently, "think(I) => (exists x: think(x) and not exists(x))". In other words, "even if I think, we still can't conclude from that that I exist".
    – BackusNaur
    Commented May 15 at 18:52
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    I think this formalisation does not capture the meaning of "I think therefore I am". In Descartes' argument, the premise "I think" is undoubtable, because doubt is a kind of thought. That undoubtability is an essential feature of the argument, but is not represented in your formalism.
    – kaya3
    Commented May 16 at 19:34
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There is an implied necessarily here:

I think so I must necessarily be

In modal logic

T ⇒ □A

Negating it we must flip □ (necessarily) to ◊ (possibly)

So that gives

  ¬(T ⇒ □A)
= T ∧ ¬□A
= T ∧ ◊¬A

which can be literally vocalized as I think and I am possibly not

In normal English usage we would use a 'but' not an 'and'

ie. I think but I may not be


Side Note: It is a uniform fact of all spiritual teachings that this (the negation) is described as the default state of unregenerate human beings: The mind keeps on associating but one is not present. In simpler terms: Activities without awareness.

Its funny that Descartes is made so much of as though he is some prophet when the negation of his famous statement is everyone's experience!


Mikhail Katz 1 line PS, unfortunately deleted is worth saving:

P.S. I have always thought that a more reasonable principle would be "I am therefore I think"

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    I didn't understand the last two paragraphs, and certainly not the last sentence. I don't think I have any experience of thinking but not being.
    – yshavit
    Commented May 15 at 18:12
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    @yshavit Having an existential thought is very much thinking about what it means (or might not mean) to be. This isn't proof of non-existence, it's opening up to the idea that your ego/consciousness might not be what it thinks it is.
    – Flater
    Commented May 16 at 1:53
  • @yshavit It's a side comment — ignorable for the answer. Your question is pertinent of course but hard to answer (in comments!) Just like one fish protesting to another: Wet?! What is wet? I am not wet!! is hard to answer Analogous answer. For here just this much: To be is a verb. What action is carried out? By whom?
    – Rushi
    Commented May 16 at 2:04
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    @Rushi I'm afraid this would soon turn into a discussion not of deep truths, but of how we define words. For example, you seem to imply that verbs always describe an action; that is not a typical definition (outside of introductory courses), but I don't think a "yes it does" / "no it doesn't" discussion would be much more fruitful than the Monty Python "argument sketch". :-)
    – yshavit
    Commented May 16 at 6:08
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You could read that as material implication of the form A → B. Which you could also write as ¬A ∨ B. So the negation of that would be ¬(¬A ∨ B) so applying de Morgan's laws that can be written as (¬¬A) ∧ ¬B or A ∧ ¬B.

Or in words I think therefore I am, is the same as I don't think or I am. So the negation would be not (I don't think or I am) which would be I don't not think and I am not, therefore the negated statement would be:

I think and I am not.

Now that undoubtedly negates the material implication, because if that would be true you couldn't infer existence from thinking. It would raise some questions though as to how that is possible, but that wasn't the question I guess.

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Haxor is right that in classical logic, to negate the implication of "I think implies I am" would be "I think and I am not."

However in natural language, negating an implication means something different. If someone says "I think therefore I am" and another person says "That implication isn't true, I disagree with it", they're not saying "I think and I am not" but they are saying it's in principle possible for something to think and not exist.

The negation of an implication in normal language is often more like saying "those two things aren't related in that way".

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  • The second paragraph is especially interesting. If I read you correctly, you're saying that when someone says "I think therefore I am", that they are conveying the implicit premise "For all x, if x thinks, then x exists", and "I think", and that from these they infer "I exist.", and that when someone disagrees, they're (implicitly) disagreeing with the quantified premise (and so the soundness of the argument) rather than the validity of the argument, and do so by claiming the (equivalent of) the negation of that premise. (I don't disagree, I just want to unpack the reasoning.) Commented May 17 at 11:28
  • @JoshuaTaylor I suppose it comes down to the difference between reasoning about individual things and groups of things. In basic classic logic, the negation of "I think implies I exist" is "I think and I don't exist", but when someone disagrees with "I think implies I exist", they're not actually usually saying "I think and i don't exist", you know what I mean? They're usually saying something a bit more nuanced than that.
    – TKoL
    Commented May 17 at 11:35
  • You wrote that they might be claiming "it's in principle possible for something to think and not exist", which I'd read as a existential quantification: "there exists an x such that thinks(x) and hasExistence(x)" (I'm avoiding saying "there exists an x such that x does not exist", for obvious reasons.) If that's the core of their refutation, it seems like they're reading "I think, therefore I am" as the implicit argument "For any x, if x thinks, then x exists. Therefore, if I think, then I exist. I think, therefore I exist." and disagreeing with the premise. Commented May 20 at 20:24
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You ask:

Negation of "I think therefore I am"?

If you think it is true that "I think therefore I am", then to construct a sentence of the opposite polarity, simply use a relative clause:

"I think therefore I am" is true. OR It is true that "I think therefore I am".
"I think therefore I am" is not true. OR It is not true that "I think therefore I am".

This is the only way to accomplish the task. Why? Because, "I think therefore I am" is a complex sentence on account of having two potential independent clauses joined by the adverb 'therefore' which communicates that the first proposition is a premise and the second proposition is a conclusion. In fact, the sentence is an argument.

If you have an argument, and alter one of the premises, you no longer have the same argument. If you alter the conclusion, you no longer have the same argument. However, if you want to communicate that you accept the argument and then you reject the argument, that has to be meta to the argument itself. You yourself were aware of this when you constructed your question using the use-mention distinction.

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  • As an afterthought, it would also seem to lend itself to contraposition if one takes the sentence as a conditional.
    – J D
    Commented May 15 at 18:00
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Symbol Meaning
A "I think"
B "I am"
A → B "I think therefore I am"
¬(A → B) "It is not true that I think implies that I am"

Mathematically, using a truth table we can prove (as is done here and discussed at length here) that ¬(A → B) is also equivalent to A ∧ ¬B, which means that A is true and B is false at the same time. In our case, this would be equivalent to "I think and I am not". More equivalent statements can be obtained similarly, by using predicate logic.

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What do you mean by a "negation?" If you want to take an inverse, then that isn't guaranteed to be either false or true. Your answer of "I do not think therefore I am not" is the inverse. Again though, an inverse is not guaranteed to be true or false when the original statement is.

Did you want something that actually is always false, given the original statement is true? Then negate only the consequent. Which you also came up with in "I think therefore I am not"

If you are looking for something that "makes sense" then it seems fairly simple to take the contrapositive and come up with "I am not, therefore I think not".

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There are some good ideas on the modal logic, however, but the reading is vague in this light. We must consider first whether my existence is necessary if I think. Could it possibly be that if I think I did not exist? We cannot think of a modal world (or a possible world) in which a version of I thought of something and did not exist. So we start with the following conditional statement:

Universal(x) (Tx-->□Ex)(the modal operator can be outside the conditional as well)

OR

□Universal(x) (Tx-->Ex) (Universal simply because the I descartes refers to is arbitrary: anyone who thinks exists).

Now, are we to consider the existence to be a necessary property of the thinker (A de re reading) or are we to consider it that necessarily everything that thinks exists (de dicto). Here would be the two potential negated translations:

  1. Existential(x) (Tx ^ ◊ -Ex) There is something that thinks and potentially has the property of not existing
  2. ◊ Existential(x) (Tx ^ -Ex): There possibly is something that thinks and does not exist

Both are equally as false, so you can conclude ad absurdum: I think therefore I am... in both de dicto and de re readings.

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In reverse, looking at this from a physical and not meta-physical perspective, there are states of mind that would be a negation of this statement and yet still prove it and negations that would disprove it.

  1. Part of the brain fails, one is not able to form thoughts (words) but can still think in pictures, yet one still exists.

  2. After a hard hit in the head, blood withdraws temporarily from the brain, inability to form thoughts (words, pictures) follows, temporarily one doesn't exist.

  3. What's left of someone is just an automaton, the person is able to act, yet can't think. Is there anything of the person left inside or not?

This list can be extended. From there you could look at the statement again and draw your own conclusions.

I tried but I can't think of any good examples for actual sentences. I suspect, this because the statement is poetic in nature and for that you really need a good grasp of English in emotional sense.

I misread Joshua's post above at first. Because at a first glance I thought --> is an operator that means creates not follows. But there is an interesting hint in there:

Existence creates thoughts.

So the less poetic but more concise statement would be I'm thinking hence I came into existence

This is still consistent with the original meaning as at poetical level some awakaning most cetrainly is implied.

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Negation of "I think therefore I am "?

The statement is negated when the conclusion is flipped and made negative. Your first choice is the winner:

"I think therefore I am not"

"I do not think therefore I am"

"I do not think therefore I am not"

The second possible choice illustrates a logical fallacy: denying the antecedent. Denying the "if" portion of an "if-then" statement does nothing. The conclusion is untouched.

This absence of proof is shown by the third choice, where, from the premise "I do not think", "I am" might follow just as easily as "I am not".

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There are, apparently, multiple propositions wrapped up in "I think therefore I am", and it looks to me like most of the answers posted so far are failing to take into account some of those.

One reasonable way of unpacking all the things it says, explicitly and implicitly, might be that it is a conjunction of:

  • (A) I think, and
  • (B) I am, and furthermore
  • (C) for all x, if x thinks then x exists.

If we buy that, then "I think therefore I am" says "A and B and C".

However, we can observe that the B part is logically redundant, since it's a logical consequence of (A and C). So, "I think therefore I am" is logically equivalent to simply "A and C".

So its negation is "not A or not C", i.e. "either I don't think, or there exists x who thinks but doesn't exist".

It is perhaps interesting to note that this negation has nothing to say about my existence (that is, it doesn't imply that I exist, and it doesn't imply that I don't exist).

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  • It might mean I think ∴ I = exist Commented May 17 at 22:29
  • I mean, when I see "I think" and "I am" they are more the same thing than two separate activities. Like thinking is a type of being. Commented May 19 at 19:30

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