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The Existential Triviality of Descartes' Cogito Sum

charles ferraro February 07, 2021 at 04:01 8400 views 57 comments
With respect to Descartes' epistemology, many interesting questions can be asked about it, such as, is "thought" produced by the "I," or is an impersonal "thought-in-general" the ontological precondition for the existence of the "I," or is my personal existence really indubitably certain, or is the "I" a special kind of substance, or is the Cogito Sum an inference or a performance?

But, perhaps, the most fundamental question of all is whether the occurrence of my "thinking" and of my "existing" is vulnerable, or invulnerable, to the possibility of complete cessation?

Descartes, himself, was aware of the legitimacy of this most basic question as evidenced by the following statements:

"I am, I exist. This is certain. How often? As often as I think."

And, more explicitly:

"For it might indeed be that if I entirely ceased to think, I should thereupon altogether cease to exist."

Clearly, Descartes considered his personal thinking, his Cogito, to be an inherently contingent occurrence because it was always open and vulnerable to the possibility of complete cessation.

No indubitably certain intuition was available to Descartes which would have guaranteed that the occurrence of his thinking was inherently closed, and invulnerable, to the possibility of complete cessation.

And because such an indubitably certain intuition was not available to him, this meant that the continued occurrence of his personal existence (his Sum), which was derived from, completely dependent upon, and guaranteed by the continued occurrence of his personal thinking (his Cogito), was as contingent and tenuous as the continued occurrence of his personal thinking (his Cogito), despite the indubitable certainty of the occurrence of his personal existence (his Sum).

So then, I submit that an inadequate or incomplete version of the truth was expressed by the famous phrase: "Cogito, ergo Sum." The: "When and while I am thinking (in the first person, present tense mode), I must be existing."

And that a more adequate and more complete version of the truth would be expressed by the phrase: "Cogito contingenter, ergo Sum contingenter." The: When and while I am thinking contingently (in the first person, present tense mode), I must be existing contingently."

Neither the Cogito, nor the Sum, is a necessary occurrence because neither exhibits an inherent exemption or freedom from the possibility of complete cessation. Yes, one (my Sum) will necessarily occur whenever and while the other (my Cogito) is occurring, but neither one must occur.

In conclusion, because of their contingent natures, the true significance of Descartes' Cogito and even of his indubitably certain Sum, is their inherent existential tenuousness and triviality.

Would appreciate any comments, pro or con, which are related specifically to the concepts involved in the above argument.

Comments (57)

counterpunch February 07, 2021 at 08:10 #497621
To my mind, the problem with Descartes epistemology is that it's sceptical doubt as opposed to reasonable doubt. He imagines an evil demon is deceiving him in order to cast doubt on everything that can be doubted. He doubts that the world he sees exists, or that he has arms and legs etc. That's unreasonable. Were it so, it would raise more questions than it answers.

Had Descartes stuck his hand in the fire - rather than a ball of wax, he would soon have discovered something prior to, and more urgently real than 'cogito' not subject to doubt - and that proved with painful certainty the existence of the physical self and an objective reality. Descartes doesn't recognise this problem.

But there is an epistemological triviality that follows from the text; in the fact that Descartes paints himself into a corner - having doubted everything that can be doubted, having established cogito ergo sum as certain, it is nonetheless, a solipsistic certainty - stranded in no space by the conditions of the thought experiment. No arms, no legs, no world - all is doubted away. His recourse is to God. From memory the passage reads something like:

"For light of reason tells us that God cannot be a deceiver" - and Descartes thereby rescues himself from the solipsistic corner of nowhere, where his certainty exists. That is the triviality of it. That it depends upon asserting the existence and nature of God - to rescue the conclusion from the limitations placed upon it by the sceptical conditions of its conception.
charles ferraro February 07, 2021 at 17:15 #497697
Reply to counterpunch

I respect your critical position regarding the problem of Descartes' solipsism, but I do not really see what it has to do with any of the specific concepts I set forth in my argument.
counterpunch February 07, 2021 at 17:43 #497708
Reply to charles ferraro To be honest Charles, I found your verbal gymnastics in the opening paragraph - somewhat incomprehensible. I'm not sure what it is you're trying to say - other than, "I'm struggling to make sense of Descartes." I'd scrap it. Now I look again, it's completely unnecessary to the question you ultimately settle upon - which is whether thinking might cease. If that is your primary concern, I'd make this your first line, and continue from there.

Quoting charles ferraro
"For it might indeed be that if I entirely ceased to think, I should thereupon altogether cease to exist."


Because of the inclusion of that first paragraph, it didn't seem to me you knew, quite what's up with Descartes - and the question you settled upon isn't the biggest problem. The problems I described are the biggest problems. A method of sceptical doubt, leading to Solipsism - escaped with reference to God. If that doesn't interest you, that's fine and dandy. No harm no foul. But conversely, I have no interest in an idea that assumes cogito ergo sum is established by sound reason, by discussing the implications thereof.
charles ferraro February 07, 2021 at 17:51 #497709
Reply to counterpunch

Of course, everyone is entitled to their opinion. Too bad you're incapable of understanding what I wrote.
Perhaps your "verbal gymnastics" are better than mine.
counterpunch February 07, 2021 at 18:00 #497712
Reply to charles ferraro Too bad you're a crappy writer - who opens by bombarding the reader with questions that are not the subject of the post - using unnecessary jargon in an attempt to impress. I'd be more impressed if you said what you meant directly, using simple terms where possible - and jargon where unavoidable.

Quoting charles ferraro
is an impersonal "thought-in-general" the ontological precondition for the existence of the "I,"


Do you mean, is his soul the thinking thing? Dues Ex Machina? Descartes thought so, yes! He located the soul in the pineal gland!

charles ferraro February 07, 2021 at 18:51 #497726
Reply to counterpunch Reply to counterpunch

Too bad you're a pompous idiot. Why don't you grow up and learn how to engage others with civility? Is this direct enough for you?
counterpunch February 08, 2021 at 00:20 #497852
Reply to charles ferraro Why not engage with others contentiously? Civility is so sterile. Why not bang the table, and scream "you can't handle the truth." Besides, with the pineal gland thing, I thought we were coming around to your question.

Quoting charles ferraro
But, perhaps, the most fundamental question of all is whether the occurrence of my "thinking" and of my "existing" is vulnerable, or invulnerable, to the possibility of complete cessation?


...afterall, it is pretty much the same question as:

Quoting charles ferraro
"is an impersonal "thought-in-general" the ontological precondition for the existence of the "I,"
— charles ferraro


Both can be summed up as:

Quoting counterpunch
Do you mean, is his soul the thinking thing? Dues Ex Machina? Descartes thought so, yes! He located the soul in the pineal gland!


So there's a direct answer to both your question.
hypericin February 08, 2021 at 02:08 #497861
everyone's life is bracketed by the permanent, omnipresent possibility of death. Does that make it trivial?
charles ferraro February 08, 2021 at 04:38 #497881
Reply to hypericin

Unfortunately, yes! Unless, of course, someone who fully understands and respects the argument can demonstrate that there is a serious error, or omission, in the argument that invalidates it?
Antony Nickles February 08, 2021 at 07:56 #497912
Reply to charles ferraro
Quoting charles ferraro
But, perhaps, the most fundamental question of all is whether the occurrence of my "thinking" and of my "existing" is vulnerable, or invulnerable, to the possibility of complete cessation?


Descartes:For it might indeed be that if I entirely ceased to think, I should thereupon altogether cease to exist.


Quoting charles ferraro
...a more adequate and more complete version of the truth would be expressed by the phrase: "Cogito contingenter, ergo Sum contingenter." The: When and while I am thinking contingently (in the first person, present tense mode), I must be existing contingently."


I'm not well versed in Descartes, but Cavell read a phrase of Emerson's that I always thought interesting. Emerson quotes his reader saying what they are too timid to: " 'I think' 'I am' ", and the take is along the lines of the distinction that Wittgenstein sees between words and their expression (that they are said, by me, right now, in this place, etc.). With Emerson it is in the sense, as you say, of a performance. But J.L. Austin will identify a class of words that perform something in being said (expressed), as in: I do, I promise, ect. The saying of it is to marry--Saying I promise is to make the promise. In this sense, saying "I think!" "I am!" is to perform the creation of your own existence. To assert yourself; claim who you are; what you are made of (averse to conformity, Emerson will say).

Now this is a little different than our imagining of "ceasing to exist", but is it really? Put the way you say as "existing contingently", when we simply conform to everyone else, part of us, in a sense that really matters to us, ceases to be; to be distinct.

Quoting charles ferraro
In conclusion, because of their contingent natures, the true significance of Descartes' Cogito and even of his indubitably certain Sum, is their inherent existential tenuousness and triviality


So it is not the proof that is tenuous, but us--are we to be trivial?
charles ferraro February 09, 2021 at 01:48 #498097
Reply to Antony Nickles

Words that perform something in being said, or expressed.

Words that create something in being said, or expressed.

OK GOT IT!

So, then, man is like the biblical Creator God who SAID, "Let there be light, and there was light," when he SAYS "I think contingently, I am contingently," and, lo and behold, he thinks contingently, and he is contingently.

In other words, man can perform the creation of his own contingent existence whenever and while he thinks contingently.

OK

But, unlike the Creator God, his creative act is open, at every moment, to the possibility of complete cessation.

I don't know about you, but this perpetual openness to and oppressive, arbitrary, unrelenting subjection to the possibility of complete cessation clearly indicates, to me, that the contingent Cartesian thinking and the indubitably certain contingent Cartesian existing don't really matter that much, even if they are man's own creation.

Wayfarer February 09, 2021 at 01:53 #498099
Quoting charles ferraro
Clearly, Descartes considered his personal thinking, his Cogito, to be an inherently contingent occurrence because it was always open and vulnerable to the possibility of complete cessation.


However, with the 'complete cessation' - presumably either death, or perhaps through entering a trance, or perhaps anaesthesia - then indeed there is no thinking, nor self-awareness. But Descartes' point, is that it is indubitable that when he is thinking, then he must exist. The fact that he might cease to exist doesn't refute this claim. And in the context of the argument, his existence is not a contingent fact: it is a basic fact, upon which other facts, such as the possibility of forming ideas, are based.
Wayfarer February 09, 2021 at 02:00 #498101
Incidentally, St Augustine articulated a clear pre-cursor to Descartes, centuries previously:

[quote=St Augustine, City of God]Without any delusive representation of images or phantasms, I am most certain that I am and that I know and delight in this. In respect of these truths, I am not at all afraid of the arguments of the Academicians, who say, “What if you are deceived?” For if I am deceived, I am. For he who is not, cannot be deceived; and if I am deceived, by this same token I am. And since I am if I am deceived, how am I deceived in believing that I am? For it is certain that I am if I am deceived. Since, therefore, I, the person deceived, should be, even if I were deceived, certainly I am not deceived in this knowledge that I am. And, consequently, neither am I deceived in knowing that I know. For, as I know that I am, so I know this also, that I know. And when I love these two things, I add to them a certain third thing, namely, my love, which is of equal moment. For neither am I deceived in this, that I love, since in those things which I love I am not deceived; though even if these were false, it would still be true that I loved false things.[/quote]
charles ferraro February 09, 2021 at 03:03 #498109
Reply to Wayfarer

Nowhere in what I have written and posted here, and elsewhere, on this Forum have I ever claimed that the truth of Descartes' Cogito Sum was not an indubitably certain intuition.

If you think I did, then you are sorely mistaken.

What I have argued for, WHILE ALWAYS SIMULTANEOUSLY SUBSCRIBING TO THE INDUBITABLY CERTAIN INTUITIVE TRUTH OF THE COGITO SUM, is the contingent nature of the Cogito and of the Sum. They are not mutually exclusive. The truth of the latter does not cancel out the truth of the former, and is not intended to do so.

I simply highlighted and placed emphasis on the contingent aspect of both the Cogito and the Sum, their inherent openness and susceptibility to the possibility of complete cessation, as mentioned by Descartes himself.

To me, this provided the correct, broader context within which to place the indubitable certainty of the Cogito Sum.

Bartricks February 09, 2021 at 03:27 #498115
Reply to charles ferraro What you say sounds correct to me. As I read him, his point is that the thought "I exist" is necessarily true whenever or wherever it occurs. But its existence is not necessary. That is, though it will invariably be true 'if' it occurs, whether it occurs or not is a contingent matter. As such though I can know for certain that I exist, my existence is nevertheless contingent. So the most certain of matters is contingent, not necessary.
charles ferraro February 09, 2021 at 03:32 #498116
Reply to Bartricks

Thanks Bartricks! You understood my point.
counterpunch February 09, 2021 at 04:16 #498123
Quoting Bartricks
What you say sounds correct to me.


People are so susceptible to flattery.

Quoting charles ferraro
Thanks Bartricks! You understood my point.


Agree with me and I'll ask you why!

Quoting charles ferraro
What I have argued for, WHILE ALWAYS SIMULTANEOUSLY SUBSCRIBING TO THE INDUBITABLY CERTAIN INTUITIVE TRUTH OF THE COGITO SUM...


But it's not a fundamental certainty, because it's arrived at by a method of sceptical doubt. Had Descartes plunged his hand into the fire, he would have found he could not doubt the existence of his physical self, or the objective reality of the fire. In a manner that is fundamentally prior to cogito - the pain pleasure response inherent to the biological organism would force him to accept the truth of objective reality. And thus, that the thinking thing is really the biological thing, and not the soul thing.
Wayfarer February 09, 2021 at 04:34 #498125
Reply to charles ferraro Yes, you’re correct, I completely fail to see the point of the OP.
charles ferraro February 09, 2021 at 04:39 #498126
Reply to Wayfarer

Thanks Wayfarer.
jgill February 09, 2021 at 04:49 #498128
Quoting charles ferraro
. . . the true significance of Descartes' Cogito and even of his indubitably certain Sum, is their inherent existential tenuousness and triviality.


I've always thought his comment on existence and thought trivial. On the other hand his brilliance is apparent with the discovery of analytic geometry.



charles ferraro February 09, 2021 at 04:59 #498130
Reply to jgill

But, hopefully, now you have reasons for what you thought. He was a genius!
Wayfarer February 09, 2021 at 07:47 #498161
Quoting charles ferraro
Thanks Wayfarer


Perhaps you might say a few more words about ‘contingency’. You say that Descartes should have said, ‘I must be thinking contingently.’ Contingent upon what, exactly? That’s the thing I’m having trouble grasping.
Bartricks February 09, 2021 at 14:24 #498190
Reply to jgill Presumably you think Newton's most important contribution was the sterling job he did as head of the Royal Mint, and that Jesus' excellent joinery is unjustly overlooked.
baker February 09, 2021 at 14:53 #498200
Quoting charles ferraro
In conclusion, because of their contingent natures, the true significance of Descartes' Cogito and even of his indubitably certain Sum, is their inherent existential tenuousness and triviality.

Of course. Whatever philosophy Descartes devised, it's always is reference to RCC doctrine. The moment one divorces Descartes' thoughts from the doctrine of the Roman Catholic Church, is the moment when they're rendered trivial.
Per RCC doctrine, the individual person/soul is contingent upon God and has no existence on his own.


charles ferraro February 09, 2021 at 18:26 #498243
Reply to Wayfarer

If some entity or activity is closed to, not vulnerable to, not subject to, or not susceptible to the possibility of complete cessation, then I consider that entity or activity to be “NECESSARY.”

Certainly, I CAN have an “idea” or “conception” of such a necessary being in the first, person, present tense mode, but I CANNOT have a direct “experience” of such a necessary being in the first, person present tense mode.

It would be called NECESSARY THINKING ACTIVITY, or a NECESSARY “COGITO.”

If some entity or activity is open to, vulnerable to, subject to, or susceptible to the possibility of complete cessation, then I consider that entity or activity to be “CONTINGENT.”

Certainly, I CAN have an “idea” or “conception” of such a contingent being in the first person, present tense mode, AND I CAN also have a direct “experience” of such a contingent being in the first person, present tense mode.

It would be called CONTINGENT THINKING ACTIVITY, or a CONTINGENT “COGITO.”

This differs significantly from the meaning of necessary and contingent being as used traditionally in philosophy.

Traditionally, a necessary being had its originating cause situated within itself, but a contingent being had its originating cause situated outside itself in another, higher being.

This might be the case, but, for my purposes, it is too overreaching and leaps to conclusions I cannot verify empirically or through my personal experience in the first person, present tense mode.




Wayfarer February 09, 2021 at 20:54 #498268
Quoting charles ferraro
Traditionally, a necessary being had its originating cause situated within itself, but a contingent being had its originating cause situated outside itself in another, higher being.


I see. Of course that is true, but I'm still failing to see its relevance to what Descartes sought to demonstrate. He wasn't attempting to argue for the immortality of the soul, but to find a first principle upon which certain knowledge can be founded.
charles ferraro February 09, 2021 at 20:55 #498269
Reply to funky

It seems to me that the major opponent to the so-called "perennial" truth of the Aristotelian/Thomistic notion of static, eternal, divinely created, substantial forms, or substantial species, was not Renee Descartes. It was, instead, the theory proposed by Charles Darwin which claimed, and provided empirical evidence to verify, that natural species, or forms, evolved over long periods of time through the combined processes of natural selection and spontaneous genetic mutation.









charles ferraro February 09, 2021 at 21:11 #498271
Reply to Wayfarer

The first principle Descartes discovered was the Cogito Sum. But, unfortunately, it was an indubitably certain principle that was inherently contingent. So any knowledge based upon it would be indubitably certain, but also be equally as contingent. The indubitably certain knowledge, like the indubitably certain principle upon which it was based, would be subject to the possibility of complete cessation. In no way, would it represent any kind of eternal truth.
Wayfarer February 09, 2021 at 21:20 #498273
Quoting charles ferraro
So any knowledge based upon it would be indubitably certain, but also be equally as contingent.


I don't know about that. Descartes was well aware of the concept of necessary truths, or a priori truths. Typical amongst these are the truths of reason and mathematics, which are very much what I think Descartes had in mind when speaking of 'clear and distinct ideas'. The scholastic idea of 'the rational soul' was precisely that the faculty which grasped such truths was the immortal element in man. Even though Descartes broke from scholasticism in fundamental ways, I think this element of their dualism was preserved albeit in a radical new form. It was common knowledge in Descartes' time that the soul was created by God, and so, whilst contingent in the sense of being dependent on God, was of a higher order than material particulars, on account of being less removed from its source.

In contrast to contemporary philosophers, most 17th century philosophers held that reality comes in degrees—that some things that exist are more or less real than other things that exist. At least part of what dictates a being’s reality, according to these philosophers, is the extent to which its existence is dependent on other things: the less dependent a thing is on other things for its existence, the more real it is.


17th Century Theories of Substance, IEP.

So it's true that in this picture, the individual soul is contingent upon God, but that doesn't mean that it is incapable of grasping necessary truths.
Valentinus February 09, 2021 at 22:20 #498282
Reply to charles ferraro
One element that stands out vividly after reading across the works of Descartes is the confidence that his Method is more important than any particular result it can yield by him using it. His opposition to the vision of Aquinas was directed at the desire to settle questions rather than to make them the work of future thinkers.
In that context, I read the close embrace of thinking and being as a challenge rather than an explanation. To the degree it explains something, other things stand outside, waiting to be explained.
charles ferraro February 09, 2021 at 22:38 #498283
Reply to Wayfarer

I did not claim that there are no necessary truths or that the contingent Cogito can't grasp them. What I am claiming is that there is nothing "divine," or eternal about necessary truths. Necessary truths are simply tautologies, some simple, others more complex, like 5 = 4+1 or 5 = 20+10 - 25, etc. This is NOT the meaning of necessary, as I tried to explain it to you previously.

Truths would be necessary, or eternal, as per your definition of the term, only if they were thought by a necessary Cogito that I could experience in the first person, present tense mode, which I can't.
Wayfarer February 09, 2021 at 22:46 #498286
Quoting charles ferraro
What I am claiming is that there is nothing "divine," or eternal about necessary truths.


A distinction can still be made between necesssary and contingent, without referring to the "divine". Arithmetical proofs, for example, are true in all possible worlds and the contingency of an individual life doesn't undermine that. In any possible world, whatever mind exists will grasp certain fundamental truths, such as basic arithmetical principles.

charles ferraro February 09, 2021 at 23:19 #498293
Reply to Wayfarer

I don't mean to be facetious, but has anyone actually verified that arithmetical proofs are true in all possible worlds? Have they visited any of these worlds and done so? Where are these worlds? Have we questioned these other minds about this?
Wayfarer February 09, 2021 at 23:42 #498297
Quoting charles ferraro
I don't mean to be facetious, but has anyone actually verified that arithmetical proofs are true in all possible worlds? Have they visited any of these worlds and done so? Where are these worlds? Have we questioned these other minds about this?


Not at all facetious, but the point is, it's true in principle. How could a world hold together where less was greater than more?

Empiricism has its limits. When you ask for 'empirical proof' regarding analytical propositions, then you're crossing those limits. It's like you're asking 'but why does two plus two equal four? You can't prove it.' To which the response is: it need not be proven, it is true according to the axioms of arithmetic. We depend on the structure of rational thought to make sense of the world, to create any kind of theory whatever (pace Immanuel Kant). So if you demand what is the proof for those structures, you're sawing off the limb on which your argument rests.

charles ferraro February 10, 2021 at 00:32 #498302
Reply to Wayfarer

I believe there was a time when it was thought that someone would be "crossing the line" if they asked the "foolish" question as to whether, or not, it could be empirically verified that Euclidean geometry was applicable to the physical world we experience. I mean, after all, hadn't Kant demonstrated that this had to be the case?

I'm sure, even then, there were those persons who argued vehemently that it was true "in principle" that only Euclidian geometry could apply to the physical world.

But then, lo and behold, the purportedly "inviolable" Newtonian paradigm shifted to the Einsteinian and, as a direct consequence, it was proven empirically, through several rigorous experiments, that the physical world we experience obeyed, instead, a form of non-Euclidean geometry.

Thank heavens empirical science always encourages investigators to challenge and progress beyond the purportedly inviolable tenets and limits set by the current theory.

Who knows what impossibilities the next paradigm shift will make possible?
Wayfarer February 10, 2021 at 00:43 #498304
Reply to charles ferraro It really doesn’t have any bearing on the discussion. Einstein relied wholly and solely on reason to establish principles which couldn’t even be verified empirically at the time and in many cases not for decades afterwards.
Wayfarer February 10, 2021 at 00:56 #498306
Furthermore, nothing Einstein said invalidated Newton. It simply showed that Newtonian laws have a limited range of applicability.
charles ferraro February 10, 2021 at 01:46 #498313
Reply to Wayfarer

Absolutely it has a bearing.

It's simply dead wrong to assert that Einstein relied wholly and solely on reason.

He also relied on the experimental results of physicists who preceded him and he was known for performing mental experiments, but he also eagerly awaited and valued the results of experiments performed by contemporaries to test predictive hypotheses generated by his theories.

He was alive when some major experiments were performed; e,g., when the bending of light rays during a total solar eclipse was verified. Nuclear fission verified his famous equation.

No theory created by human thought has had a perpetual lock on truth. In this sense, I think every theory is subject to invalidation. But this, I submit, is simply an issue of semantics
Antony Nickles February 10, 2021 at 01:59 #498318
Reply to charles ferraro Quoting charles ferraro
[our] creative act is open, at every moment, to the possibility of complete cessation.


The word itself is dead before it is brought alive into time and context--pedestrian, mundane, banal, or contrary, unexpected, mad. Our very expressions begin and end. But, even in sight of its death, some writing holds itself responsible as we are when we speak: to answer for our expression, stand by it, be seen in it, to make ourselves intelligible, known.

If we turn Descartes around (as Plato, Heidegger, and Wittgenstein suggest for ourselves) he is not as worried about "existence" as knowledge, worried about its certainty to ensure his world (a piece of wax) and even himself.

So we can hope to find a kind of knowledge (thought) that will take the responsibility for ourself away, or we can ensure that we are known by our thoughts. We can look for certainty, or we can be certain, specific, thorough, diligent, resolute.

Quoting charles ferraro
this perpetual openness to and oppressive, arbitrary, unrelenting subjection to the possibility of complete cessation clearly indicates, to me, that the contingent Cartesian thinking and the indubitably certain contingent Cartesian existing don't really matter that much, even if they are man's own creation.


Our desire for a certainty in knowledge kills what it seeks before it begins. Emerson suggests we live open in front. If we are to let ourselves matter, is it our being subject to doubt at every turn that stops our first step? or will we exist only so far as we know?
Wayfarer February 10, 2021 at 02:01 #498319
Reply to charles ferraro Yes, Einstein took into account observations, and relied heavily on thought experiments. But he had no data for many of the predictions that were made by theories, which were, in that sense, the product of reason before observation. Reason plays a critical role in Einstein's thought, as in all science generally. What I'm arguing is that basic principles of thought and logic, such as arithmetic proofs and logical laws, are not contingent - they're what philosophy calls 'metaphysical primitives' or 'basic facts', which cannot or need not be explained with recourse to empirical demonstrations. They are assumed to be functional for the purpose of any reasoned argument. This is not 'a theory' but a principle, and I don't believe you've shown it not to hold.

jgill February 10, 2021 at 05:41 #498349
Quoting Bartricks
?jgill
Presumably you think Newton's most important contribution was the sterling job he did as head of the Royal Mint


I'm humbled by your perceptive reply. :roll:
counterpunch February 10, 2021 at 05:58 #498354
Quoting Wayfarer
It's like you're asking 'but why does two plus two equal four? You can't prove it.'


I can. Let's use apples, no, oranges. No, wait - apples.

Take two apples - put them in an empty bag.
Take two apples - put them in the same bag.
How many apples are in the bag?

It's not a mere convention that there are four apples in the bag.

One could use a different word to represent the number four, but the integer exists in reality - insofar as the universe is not considered a whole, and everything in it an indivisible part of that whole, individual objects exist - so numbers exist, and because one object and one object is two objects, then 2+2=4.
Wayfarer February 10, 2021 at 06:40 #498361
Reply to counterpunch Fair enough, and of course I agree, but the point was that there is no need to prove such simple facts. And I’m a Platonic realist about numbers, so I also agree that the integers are real.
counterpunch February 10, 2021 at 07:22 #498367
Reply to Wayfarer Quoting Wayfarer
Fair enough, and of course I agree, but the point was that there is no need to prove such simple facts. And I’m a Platonic realist about numbers, so I also agree that the integers are real.


I was just looking to prove that 2+2=4, but it seems like I've cracked open a whole other can of worms. I've read a couple of short essays, and I'm not sure now where I stand on the question of whether numbers are real. At the very least, there is a question - as to what a number actually is, and in what sense it can be said to exist? Apples isn't the answer - because apples are a number of objects, as opposed to numbers as objects in themselves.

Platonism assumes the existence of ideal forms - but you qualify that with realism? So, what - no ideal forms for you?
Wayfarer February 10, 2021 at 07:29 #498370
Reply to counterpunch Hey there’s a really good current essay on this subject....quick google....here, I’ve been meaning to start a thread on it, perhaps I will, it’s a bit tangential to this one, but have a read.
Banno February 10, 2021 at 07:34 #498372
Quoting counterpunch
because one object and one object is two objects, then 2+2=4.


Watch raindrops, sliding down a window.

One plus one equals one.
counterpunch February 10, 2021 at 07:45 #498373
Reply to Banno

Quoting Banno
Watch raindrops, sliding down a window. One plus one equals one.


Twice the size!

Quoting Wayfarer
Hey there’s a really good current essay on this subject....quick google....here, I’ve been meaning to start a thread on it, perhaps I will, it’s a bit tangential to this one, but have a read.


I read the essay, and the answer came to me. Numbers exist in the relations between objects. One apple is one apple. One apple and one apple is two apples. The number exists in the relation of one apple to another; not in the apple itself, not in some platonic ideal beyond time and space - but in the relation between objects. It's too simple, too obvious. Why ain't it that?

counterpunch February 10, 2021 at 07:56 #498374
"Thinking about geometric objects is perhaps the clearest way to think about abstract objects. A line segment (a true, geometric line segment) is a perfectly straight, one-dimensional object with a determinate length. There are no such objects in space-time. Every object you could possibly interact with is three-dimensional — no matter how thin a piece of, say, plastic you create, it always has a height and a thickness, giving it three dimensions. Nothing, therefore, in the concrete world, is a real geometric line segment. We have things that approximate line segments — very straight, very thin objects. But none of those things will ever be perfectly straight and with zero thickness. So if there does, somehow, exist a true line segment, it certainly isn’t in the concrete world, and therefore it must be in some sort of abstract realm."

Neither does a unicorn, or a griffin exist in the concrete world - yet we can imagine them, and draw them - because we know what a horse looks like, or what a lion and a eagle look like, and can conflate them. So, perhaps a true geometric line segment is like that - an abstraction from the relations between real objects; then the idea of numbers as existing in the relations between objects holds up.
Wayfarer February 10, 2021 at 08:17 #498378
Reply to counterpunch Perfectly true - but only a rational mind can see it.
counterpunch February 10, 2021 at 08:47 #498379
Reply to Wayfarer If you were able to somehow go back in time, and map every mathematical thought in chronological order, surely it would begin with the relationship of one apple to one more apple, and get increasingly abstract.

Also, it's said that phylogeny recapitulates ontogeny - and you don't start kids out learning math with abstract objects. You begin with one apple and one more apple - and build toward abstract objects. So, all in all - maybe this is a wrong end of the telescope problem.

Maybe numbers do exist, primarily in the relations between objects. Then, expert mathematicians forget their infant education, and talk about numbers existing as abstract objects, and cite highly derived ideas, like geometric line segments and set theory, as proof of an abstract realm created through logical manipulation of those basic, real numerical relations.
Wayfarer February 10, 2021 at 08:53 #498380
Reply to counterpunch the point is, they’re the same for all who think, and they can be used to encode ideas which are universally applicable. So, they’re real. But they don’t exist - there are no numbers ‘out there somewhere’. They’re purely and simply objects of rational intellect, but they’re real. That’s the inconvenient truth for empiricists.
counterpunch February 10, 2021 at 09:03 #498382
Reply to Wayfarer Why would it be a problem for empiricists? If you see two apples and I see two apples - there are, empirically speaking, two apples.

Assuming two exists only as the relation of one apple to the other, it becomes an adjective, and it makes as much sense to say 'two' exists, as it would to say high, or long, or lazy - exist as some abstract ideal.
charles ferraro February 10, 2021 at 16:56 #498449
Reply to Wayfarer

Descartes' use of hyperbolic doubt and, in particular, the constant deception caused by the "evil genius," postulated conditions under which it would be possible to conceive that even the necessary "a priori" truths of logic and mathematics, his "clear" and "distinct" ideas, would be false in this world and in all possible worlds. That's why he desperately, and I think unsuccessfully, tried to argue for the existence of a "good" Deity that would, nevertheless, guarantee their truth.

Thus, only the Cogito Sum, which survived hyperbolic doubt, would be an indubitably certain first principle in this world and in all possible worlds. But it would still be contingent in this world and in all possible worlds.
Wayfarer February 10, 2021 at 21:09 #498498
Reply to charles ferraro Contingent upon his existing, for sure.
charles ferraro February 11, 2021 at 00:19 #498533
Reply to Wayfarer

In other words, for any human who performs the Cogito Sum in the first person, present tense mode, be it performed either in this world or in any possible world, the Cogito Sum would always be both indubitably certain and contingent; not so much in the sense of dependency, but in the specific sense that both the Cogito (I think), and the Cogito generated Sum (I am), would always be experienced as being open and vulnerable to the possibility of complete cessation.
Wayfarer February 11, 2021 at 00:32 #498535
Reply to charles ferraro Sure. But I still don’t see why the possibility of cessation is a consideration. Descartes never set out to prove the immortality of the soul, only an indubitable foundation for thought.
charles ferraro February 11, 2021 at 01:29 #498553
Reply to Wayfarer

Precisely because contingency is an essential characteristic exhibited by the human Cogito Sum that is equal in importance to its indubitable certainty and, therefore, should not be dismissed out of hand.

Also, I think the notions of contingency and necessity, as I defined them, play a crucial role in understanding whether, or not, Descartes' Ontological Argument for the Existence of God works.

I am taking the liberty of forwarding to you a piece I wrote to verify this contention. It's lengthy, but I hope you will enjoy it.

CRITIQUE OF DESCARTES’ ONTOLOGICAL ARGUMENT FOR THE EXISTENCE OF GOD

That the existence of God may be rightly demonstrated from the fact that the necessity of His existence is comprehended in the conception which we have of Him.

Rene Descartes

The (ontological) argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies

Bertrand Russell

It is this author’s contention that Renee Descartes should have rejected the validity of all ontological arguments for the existence of God and that his philosophy would have provided him with a unique and sound rationale for explaining why such arguments had to be false. Descartes should have realized that his version of the ontological argument, as well as the version formulated before him by Anselm, was simply incompatible with the new philosophical methodology and criteria he established for determining indubitably certain existence.

It was not sufficient for Descartes and Anselm before him merely to present the individual with the idea, or definition, of a necessary being and then, by performing a detailed analysis of the idea, or definition, try to claim to have demonstrated successfully the necessary existence of such a being.

I submit that Descartes’ own well-defined methodology and explicit criteria for determining indubitably certain existence should have prompted him, instead, to explain (a) the difference between contingent thinking activity and necessary thinking activity, and (b) the corresponding difference between contingent personal existence and necessary personal existence. The specific definition of the terms contingent and necessary, as used in this paper, will be made clear during the following discussion.

In Meditation II, Descartes presented the reader with a detailed explanation of the human Cogito Sum along with the method the reader could use to realize it. He claimed that a person attempting to doubt his own existence, even under the most extreme (hyperbolic) of scenarios (the dreaming doubt and the malicious demon doubt), would ultimately and inevitably realize or intuit, during his doubting activity, that his existence was an indubitably certain existence. A simultaneous intuition or realization would occur that not existing while doubting or thinking was impossible for the thinker. Or, phrasing it positively, a simultaneous intuition or realization would occur that existing while doubting or thinking was indubitably certain for the thinker. As Descartes put it: “I am, I exist. This is certain. How often? As often as I think.”

However, Descartes did not say that his existence was necessary-in-itself. He said only if, and when, he doubted, only if, and when, he thought, only then, during the time of their occurrence, did he simultaneously intuit his existence to be indubitably certain. If he ceased to think for an instant of time, then Descartes claimed that he would have no ground for believing that he could have existed during that instant. As Descartes cautioned: “For it might indeed be that if I entirely ceased to think, I should thereupon altogether cease to exist.”

So, then, according to Descartes, a person’s thinking activity is contingent in the specific sense that it is experienced by the person as always being open to the possibility of complete cessation and non-existence. In other words, the Cogito portion of the Cogito Sum is experienced by the person, in the first person, present tense mode, to be contingent thinking activity (a contingent Cogito), since it is experienced as always being open to the possibility of complete cessation and non-existence.

Search as one will, there is no separate or concomitant intuition available which would also assure the person, beyond all reasonable and hyperbolic doubt, that his doubting or thinking is an activity impervious to the possibility of complete cessation and non-existence. And the force of this realization would apply equally to all the many different modes of the person’s thinking activity such as perceiving, inferring, deducing, imagining, remembering, conceiving, speculating, calculating, hypothesizing, etc.

Descartes showed how the performance of a human Cogito Sum did, in fact, yield the intuition of an indubitably certain, yet contingent, personal existence (the contingent human Sum) based upon, emerging from, and restricted to the human person’s simultaneous experience of the occurrence of its contingent thinking activity (the contingent human Cogito). Or, stating it more succinctly, a person’s contingent thinking activity (the human Cogito), during the time that it is experienced by the person, always provides the person with a simultaneous intuition of the indubitable certainty of that person’s contingent personal existence (the human Sum).

Surprisingly, in none of his subsequent meditations did Descartes attempt to present the reader with a detailed explanation of the divine Cogito Sum which would have paralleled nicely the detailed explanation of the human Cogito Sum he offered in Meditation II.

Preoccupied as he was with the urgent need to provide a divine guarantee for his clear and distinct perception criterion of truth, in Meditation III Descartes decided to present the reader with a series of more, or less, traditional a posteriori arguments for the existence of God and, in Meditation V, he decided to present the reader with his a priori ontological argument for the existence of God based, curiously enough, upon his clear and distinct perception criterion of truth.

Nevertheless, had he intended to do so we suspect Descartes could have provided a detailed explanation of the divine Cogito Sum along the following lines.

If one assumes the divinity thinks, then its thinking activity (the divine Cogito) would be necessary in the specific sense that it would be experienced by the divinity as always being closed to the possibility of complete cessation and non-existence and, as such, it would always provide the divinity with an intuition of its indubitably certain necessary personal existence (the divine Sum).

In other words, he could have explained how the performance of a divine Cogito Sum would have provided an intuition of indubitably certain necessary personal existence (the divine Sum) based upon, emerging from, and restricted to the divine person’s experience of the occurrence of its necessary thinking activity (the divine Cogito).

The divine person’s necessary thinking activity (the divine Cogito) would provide the divine person with an intuition of the indubitable certainty of the divine person’s necessary personal existence (the divine Sum).

He could have gone on to explain that IF the human person were also able to experience the occurrence of such necessary thinking activity (the divine Cogito), then the human person, too, would be able to experience it as always being closed to the possibility of complete cessation and non-existence.

But that since the human person is, in fact, simply not able to experience the occurrence of necessary thinking activity (the divine Cogito), in the same way as the human person is able to experience the occurrence of contingent thinking activity (the human Cogito), the human person is, therefore, prohibited from ever having direct access to an intuition of indubitably certain necessary personal existence (the divine Sum).

This Cartesian-based distinction between the impossibility of having a personal experience of necessary thinking activity and the possibility of having a personal experience of contingent thinking activity should not be confused with the traditional distinction between an essence that contains within itself the reason for its existence (necessary being) and an essence that does not contain within itself the reason for its existence (contingent being). The Cartesian-based distinction is grounded in, and can be verified through, a person’s experience, whereas the traditional distinction is grounded in a person’s abstract thinking but cannot be verified through a person’s experience.

From a Cartesian-based perspective, the central issue is the possibility of having a personal experience of thinking activity that can cease to occur and can go out of existence versus the impossibility of having a personal experience of thinking activity that can never cease to occur and can never go out of existence.

Human thinking activity is contingent being because the human person experiences his thinking activity can cease to occur and can go out of existence – nothing more, nothing less. The human person’s, alone, is the I think contingently, I exist contingently (Cogito contingenter, Sum contingenter).

By contrast, divine thinking activity is necessary being because the divine person experiences that its thinking activity can never cease to occur and can never go out of existence - nothing more, nothing less. God’s, alone, is the I think necessarily, I exist necessarily (Cogito necessario, Sum necessario).

It is simply impossible for a human being to have a personal experience of thinking activity that can never cease to occur and can never go out of existence (the divine Cogito).

However, from a Cartesian perspective, it is precisely this impossible experience which is the indispensable prerequisite that would enable a human being to have a performative intuition of the indubitable certainty of necessary personal existence (the divine Sum), i.e., the existence of God.

But, unfortunately, all ontological arguments lack this indispensable experiential prerequisite. And, in response to Russell, this is precisely where the fallacy of the ontological argument lies!

For whatever reasons, the preceding line of thought is what Descartes chose neither to pursue, nor to explain.

Nevertheless, from a Cartesian point of view based upon a well-defined Cartesian methodology and explicit criteria for determining indubitably certain existence, I would submit (a) that the occurrence of necessary thinking activity (the divine Cogito) is precisely what a person would have to be able to experience in order to make a legitimate claim to having an intuition of indubitably certain necessary personal existence (the divine Sum), and (b) that this Cartesian-based explanation of what would be required for a human person to successfully execute an intuition of indubitably certain necessary personal existence (the divine Sum) is far superior to Descartes’ ontological argument and that of his predecessor, Anselm.

This Cartesian-based critique specifies precisely what is fallacious about Descartes’ ontological argument, Anselm’s ontological argument, and all other ontological arguments for the existence of God in a manner uniquely different than the critiques proposed by St. Thomas Aquinas, David Hume, Immanuel Kant, Arthur Schopenhauer, and Gottlob Frege.

Ontological arguments, being conceptually abstract through and through and remaining completely detached and isolated from the empirical realm, lack the requisite foundation of a personal human experience of necessary thinking activity (the divine Cogito). Only the possibility of having such a personal experience would also permit a human person to have an intuition of indubitably certain necessary personal existence (the divine Sum).

It is of interest to note, too, that all the critiques cited above are essentially as conceptually abstract as the ontological arguments they seek to contest. The total inability of a person to experience the occurrence of necessary thinking activity is never made the central issue of contention. For all these critics, the perennially unresolved central issue is simply the logical validity, or invalidity, of the abstract reasoning involved in the ontological arguments. Without exception, this is their exclusive, limited focus.

I submit that the Cartesian-based critique succeeds in altering this traditional focus since it offers a unique, experientially grounded explanation for why, ab initio, all ontological arguments for the existence of God must be false.

Certain assumptions shared by Descartes’ arguments for the existence of God, be the arguments a posteriori or a priori, are that the ideas of the infinite and the perfect are ontologically prior to the ideas of the finite and the imperfect, and that the ideas of the infinite and the perfect are innate to the human mind because they are implanted there by God.

For example, for Descartes my idea that I think contingently (which is my idea of a finite and imperfect activity) presupposes an ontologically prior, innate idea of what it means to think necessarily (which is my innate idea of an infinite and perfect activity).

Or, to understand that I think contingently (a finite and imperfect activity) requires that I must have some ontologically prior, innate understanding of what it means to think necessarily (an infinite and perfect activity). However, as this line of reasoning relates to the central theme of this essay, I would submit, contrary to Descartes’ position, that my understanding of the idea of necessary thinking activity (an infinite and perfect activity) is not innate to the human mind and is not implanted there by God.

Neither is the idea of my contingent thinking activity (a finite and imperfect activity) obtained, as Descartes would claim, by my limiting or bounding, in some way, the ontologically prior, innate idea of necessary thinking activity (an infinite and perfect activity). Instead, my idea of necessary thinking activity is a direct result of my deliberate attempt to try to remove, albeit unsuccessfully, that characteristic from the idea of my contingent thinking activity which limits and constrains it; viz., its vulnerability to the possibility of complete cessation and non-existence. This, I submit, is the genuine way in which I arrive at an understanding of the idea of necessary thinking activity (an infinite and perfect activity).

Nevertheless, it does not necessarily follow, either from the former interpretation of Descartes or from the latter interpretation of this author, that I can have a direct personal experience of necessary thinking activity (an infinite and perfect activity) in the same way as I do, in fact, have a direct personal experience of contingent thinking activity (a finite and imperfect activity).

As I see it, the central issue is not a matter of the possibility of my being able to have, or not to have, an idea of perfect thinking activity or an idea of perfect being – be those ideas innate, adventitious, or factitious. Instead, the central issue is a matter of the possibility of my being able to have, or not to have, a direct personal experience of that perfect thinking activity or of that perfect being.

Or, approaching it from a slightly different direction, doubts and desires may come from an understanding that I lack something, and that I would not be aware of that lack unless I was aware of a more perfect being that has those things which I lack. However, my ability to have an idea of, or conception of, or understanding of, or awareness of a more perfect, or infinite, being that possesses all those things which I lack (inclusive of necessary thinking activity), does not mean that I am also able to have a direct personal experience of that being and its necessary thinking activity in precisely the same way as I am able to have a direct personal experience of my being and my contingent thinking activity.

Certainly, I can postulate the existence of a being that thinks necessarily and exists necessarily, but I cannot have a direct personal experience of the necessary thinking activity which would simultaneously yield an intuition of the indubitably certain existence of such a necessary being. Again, I can perform the “Cogito contingenter, Sum contingenter,” but I cannot perform the “Cogito necessario, Sum necessario.”

Descartes’ a priori ontological argument for the existence of God is not an experientially grounded performative argument like the one he formulated that successfully and persuasively proved the existence of the human self. His ontological argument, lacking the crucial, indispensable experiential foundation of necessary thinking activity, is destined to fail from its very inception. It is a non-persuasive, quasi-intuitive argument espousing a so-called self-validating idea of God which is given in consciousness and which represents God as existing, but which, in fact, completely misses the mark.

In fact, one could assert even further that the ultimate test of the efficacy of any argument for the existence of God, be that argument a priori or a posteriori, does not consist in the ability of that argument to provide the meditator with a clear and distinct idea of God’s necessary personal existence. Instead, one could assert that the efficacy of any such argument is determined, first and foremost, by whether, or not, it can engender in the meditator a direct personal experience of necessary thinking activity (the divine Cogito). And even assuming such an argument can engender in the meditator a direct personal experience of necessary thinking activity, then can it also engender in that meditator a simultaneous intuition of indubitably certain necessary personal existence (the divine Sum)?

However, in conclusion, this author knows of no traditional, professionally recognized, a priori or a posteriori argument for the existence of God that has succeeded in providing the meditator with the requisite foundation of a direct personal experience of necessary thinking activity (the divine Cogito) while also engendering in the meditator a simultaneous intuition of indubitably certain necessary personal existence (the divine Sum).