Sunday, December 30, 2012

Reconciling Rationalism and Empiricism: the Infinite, Finite and Indefinite

Considering the relation between the infinite, finite and indefinite can help overcome the difference between the Rationalists and the Empiricists. This is a rough exploration of this possibility.
A well known way of thinking about the indefinite is to consider a series that has no end, for example, the series of all natural numbers. We can imagine counting this series without having to stop. What does this "without having to stop" consist in?
In some way, it is a characteristic of a natural number is that they are finite. Because of this quality finitude, when we think a number we can always think a larger which will also have the quality of finitude. Since finitude is figured into every natural number in advance, it would be a contradiction to suppose any largest in the series.
From the above, Empiricism concludes that there can not be an absolute largest in the series of natural numbers. We are restricted to experience in our discovery of natural numbers, but we can think no reason the series could end, so we can say the series of natural numbers is indefinite, but not infinite.
This can appear to be a sufficient refutation of various Rationalist arguments that employ the infinite to prove the existence of absolute substances, causes, ideas, &c. We have no justification for saying that the series terminates in an absolute, since the series does not admit of any absolute member.
For example, Leibniz' Principle of Sufficient Reason demands a ground (reason) for everything. Leibniz uses this to argue that in order to have something there had to be an absolute (infinite) ground. From the perspective of a series, this is faulty reasoning, since we cannot see how any particular thing supposes a ground that is absolute rather than finite, and so an Empiricist would reject Leibniz' Principle of Sufficient Reason.
However, if we adjust our view we might see a different way of understanding Leibniz' principle.
When we count our series of natural numbers we can understand that we can count on forever without finding a largest. What grounds this feeling of being able to count on forever? If we turn to the individual numbers, and say that with a natural number we already understand that they are finite, and that we can count higher, we are not in a better position, since we can still ask: what grounds are there for thinking this quality of finitude?
If we understand the discussion of the infinite (absolute) as trying to understand how finite things attain this quality of finitude rather than how they appear in a series, then we can understand the discourse on the infinite as simply saying, we think the finite in contrast with the infinite. In this case, we are not thinking infinite as the largest finite thing - which is a contradiction - but rather we think the infinite strictly as the ground for thinking the quality of finitude distinctly (distinctness has to do with thinking something with a specific different).
If this possibility is employed in understanding the Principle of Sufficient Reason, then we see that the absolute (infinite) ground does not need to be thought in terms of the cause furthest in the past, or first in the series, but rather the absolute ground is that through which we comprehend the finite aspects of the series.
Kant thinks along similar lines in the Critique of Pure Reason.In the resolution to the Third Antinomy - which concerns the thesis, "there is a first cause", and the anti-thesis, "there is no first cause" - Kant concludes that both are true, if you allow yourself to think of them as operating in different ways.
Kant thinks cause in the following way: whenever something happens, something is always presupposed that came before. From this it is easy to see the necessity of an always prior happening. However, Kant asks if we are required to think of the prior thing in terms of a happening. His conclusion is that there is no such requirement, and so we can think the prior thing in a different way. Whenever we think the coming before in terms of happening, we also suppose a further coming before. But, when we do not think the coming before in terms of happening, then we do not suppose an earlier happening, but an intelligible ground. In the first case, cause is thought temporally as happening, and in the second as ground, which is not temporal.
To illustrate thinking a prior thing without thinking it as a happening, consider a basic natural law, such as gravity. When we see an object move towards the Earth, we see it in terms of the series of happenings, this series is an expression of the law of gravity. But in thinking gravity as a ground, we think it as 'something' spontaneous - not in time.Gravity, as a ground, is not an appearance, or a happening; we can't posit existence for it, but it is intelligible.
Applying this back to Leibniz, we can see that his manner of thinking the absolute (infinite) ground could be seen in terms of a law thought as an intelligible something, and not in terms of a most prior element in the series of happenings. According to Leibniz, then, in order to think any element in a series in its particular dependent way, we also think of merely intelligible thing which grants it this dependent status. An element of a series is dependent upon its prior cause in one sense, but in another sense it is dependent on the particular way it is conceived of as dependent.
(Generally, I think a resolution between the Empiricists and Rationalists using a syllogism as a model:
Major Premise
Minor Premise
Empiricists seem generally concerned with the validity of conclusions. Rationalists seem to be concerned with how the major premise (rule) can apply to the minor premise (case).
Asking into the validity of this or that conclusion is asking into the a posteriori. The accounting for the connection of the rule to the particular is asking into the a priori. The former considers cause in terms of the series of events, the latter considers the cause from the perspective of how the rules are applicable at all a priori - in terms of 'logical' ground.)

Wednesday, December 26, 2012

Reflecting on Kinds of Nothing in Kant and Leibniz

Recently I have been working on getting a handle on 'nothing' in order to to more fully appreciate Heidegger's question in Introduction to Metaphysics: Why is there something rather than nothing? I wish to understand this question not simply to understand Heidegger - he can speak for himself well enough - but to help understand some of the history of philosophy where Heidegger drew the question from. And this goal itself is only a stop along the way to unlocking the significance of 'nothing' for continued genuine questioning.
So far I have considered Leibniz and Kant. The reason for considering Leibniz is that he asks and answers our guiding question in a manner that Heidegger is aware of and reflective about. My reason for selecting Kant was my familiarity with him, and that his passage on nothing has a straightforward introduction to some difficulties of the subject; a secondary consideration was that the section that Kant's discussion of 'nothing' appears in - the Amphiboly - is one which Heidegger calls decisive, even if he does not (to my knowledge) directly reference the discussion of 'nothing'.
I also plan to consider 'nothing' in Parmenides, but before I do I want to take an opportunity to reflect on the considerations so far and to add some remarks and refinements.
One thing that has come up in the interpretation so far has been different kinds of nothing. For Leibniz, I attempted to understand nothing as the simple negation of the actual, as well as nothing as a privation (of goodness); in Kant, there was also nothing as a negation of the different ways of being judged objectively, as well as a nothing that was indistinguishable from being: the problematic object, theoretically indeterminable whether it 'is' something or nothing. To help to understand these different types of nothing I will consider the negation of a specific thing (any thing, say, a cup).
For Leibniz, the denial of the actuality of a specific thing means that it is contradictory with whatever is actual and better (more good). The negated object is still a possible object, but it has specific reasons relative to what is actual for not being actual (even if we do not know them). Simply not being actual still allows us to consider why this is so, and so blurs the difference between nothing as not-actual and as privation. If an object is self-contradictory, however, then we get a different sense of nothing for Leibniz which we should consider.
For Kant, the negation of a specific object reveals no other determination about it, but this also does not mean an object is nothing, but simply that we think it as an object of possible experience. A cup is not impossible, and so is not properly nothing, just as in Leibniz we can say that the negation of the actuality of the cup is not nothing.
For Kant, 'nothing' is determined by impossibility of the object being given in any possible experience, and there are four ways of being such an impossible object. However, the impossibility of the object is ultimately determined by its inability of being temporalized. So, for Kant, 'nothing' is relative to the constitution of our experience. On the other hand, the problematic is the positive expression of the limits of our cognition, and reveals some new options.
If something is problematic for us, and intelligible, then it is at least not self-contradictory, but we still cannot say that it is possible or impossible, since it does not relate to a possible experience. Freedom is such a concept as this, which we can think without contradiction, but also cannot be made an object of a possible experience. We can also consider the problematic in stronger terms, according to what is not even intelligible; here, even self-contradictory concepts, such as square circles, are considered problematically. Perhaps there is a being which 'experiences' square circles, and for whom a round circle is a contradiction. This is meaningless for us apart from the recognition that our form of experience is not itself necessary.
In Kant, then, we have, first, the negation of a thing, which still leaves it as possible - the imaginable; second, the nothing, which means something impossible - inability to temporalize; third, the problematic intelligible object, which is also atemporal, and is thought without contradiction - the positive expression of the limits of theoretical reason; fourth, the unintelligible problematic object which is atemporal and self-contradictory, which we can think as possible for some being constituted differently than us - the positive expression of the limits of all human reason.
We may be tempted to consider a fifth: the absolute problematic - a positive expression of the limits of any kind of reason (not only human). But the only reason that this cannot really be considered, is that it is actually just an instance of something unintelligible problematic. The contradiction of absolute limitation is that limitation is always of something, and so a non-relative limitation cannot be thought by us. However, just because it is unintelligible to us, does not discount it absolutely, since it is still unintelligible problematically.
Leibniz considers the self-contradictory to be exactly the absolute problematic (the unconditioned limit), but because this absolute limit is intelligible, it must be different from our determination above. For Leibniz, the absolute limit is self-contradiction, which is even a limit for the absolute being - God. In Kant's terms, Leibniz only goes as far as the intelligible problematic, but this intelligible problematic is determined to exist by Leibniz, and not just as intelligible. From Kant, we see that practical reason is what first gives the (intelligible) problematic determinations beyond self-consistency, such as existence, and on such practical foundations we make further determinations within the problematic. This shows more clearly the moral outlook already unconsidered in Leibniz' position.
Since Leibniz determines the absolute being as existing, and so as having a (theoretical) thingly character, we can see a choice had to be made between how we think God and objects: either the objectivity of objects must be expanded to be moral, or the nature of God must be reduced to conditions of appearance so that he can be determined theoretically. (Perhaps we can see a glimpse of Spinoza's pantheism here.) We know that Leibniz expands on the objectivity of the object, making goodness the determining factor of the actual. But, in order to have real possibilities - actual possibilities - these also must be good, and so a consideration of degrees is employed.

Monday, December 24, 2012

Understanding the Question, "Why there is something rather than nothing?", Part II: Kant

When considering the title question with regards to Leibniz, I found that the Twenty-Four Statements (as titled by Heidegger) supported two different ways of thinking 'nothing'. There was one sense that concerned just that something is actual or not. The other sense of nothing was the privation of goodness in things that were possible; the best of the possibles were the ones that became actual.
The cause (= real ground) of there being something rather than nothing in Leibniz is an absolute being (God), and this being is necessary simply given that there are actual things. There is nothing higher than the absolute being, and so nothing is just privation of what brings something into actuality - relative goodness. Kant determines the thingness of things in a different manner than Leibniz - a manner that does not involve the ethical aspect of life, and the result is very different. For Kant, we are constrained to objects of a possible experience. I will consider, now, how Kant thinks the question of why there is something rather than nothing in terms of the object of possible experience.
In the end of the Appendix to the Analytic of Elements in the Critique of Pure Reason there is a short passage concerned with 'Nothing'. This section begins with the following:
"Before we leave the Transcendental Analytic we must add some remarks which, although in themselves not of special importance, might nevertheless be regarded as requisite for the completeness of the system. The supreme concept with which it is customary to begin a transcendental philosophy is the division into the possible and the impossible. But since all division presupposes a concept to be divided, a still higher one is required, and this is the concept of an object in general, taken problematically, without its having been decided whether it is something or nothing. As the categories are the only concepts which refer to objects in general, the distinguishing of an object, whether it is something or nothing, will proceed according to the order and under the guidance of the categories." (A290 B346)
We can let Kant's discussion of the kinds of nothing stand on its own here, but take up the investigation of the problematic - the merely intelligible object in general which is divided conceptually into the possible and the impossible. The possible is already a something, while the impossible is already a nothing.
The determination of something or nothing is along with the Categories, and the Categories have significance, as we learn in the chapter on the Schematism, as a priori time determinations. The category of possibility means: "the agreement of the synthesis of different representations with the conditions of time in general." (A144 B184) So, if we consider the difference between something and nothing the problematic object which these are divided from, we can see that it is temporality generally that divides them. The problematic object is intelligible while not being in time.
If we ask the question, "why is there something instead of nothing at all?", and try to answer with Kant's conception of nothing, we only get the difference between a thing and the kinds of negations of determinate negations of temporality. There is no answer here. But, as with Leibniz, we can allow ourselves a sense of nothing as negation of 'actuality', and another sense of nothing beyond this sort of negation of something.
For Kant, the problematic is a nothing in more than the sense of negation of something, but in terms of the limits of our theoretical cognition. We could also remark that from the perspective of theoretical reason, Leibniz' 'real ground' would be just as likely absolute Being as it would be absolute Nothing.
If we consider how the problematic can give us an account of question, we can be sure that theoretical reason will have nothing to do with it. Theoretical reason will always send you looking for prior causes forever, which is something we should do, but also cannot answer our question. To get a handle on the answer for our question, we must constrain ourselves to think the problematic in one way or another. Kant gives us the manner in which we do this in his discussion of freedom in the resolution to the third antinomy.
In the third antinomy, Kant is addressing the conflict between a supposed first cause, and the necessity of there always being a prior cause. Kant's resolution is that both sides of this dispute can be true. While we must think everything that happens in terms of something that comes prior, it is not necessary that we think the prior as only appearance. Therefore, we can think something prior in a temporal way - according to an order of nature - and an a-temporal way - according to an order of freedom. But, we cannot arbitrarily decide when to think according to the temporal or not, since cause is a necessary a priori connection of representations. When are we constrained to think in accordance with a cause outside of time? Kant's answer for this is - when we think the moral: when something ought to be.
For Kant, then, the transition to Practical Reason first gives us a determination of the problematic. For theoretical reason, the problematic was indeterminate concerning its being or non-being, but with practical reason we are constrained to think the problematic in terms of being, and so to employ our temporal/theoretical scheme back onto the absolute in order to make it intelligible as a being. This illustrates how the practical determines the noumenal realm in a certain way due to the constraints of our faculties, and so shows how we must operate in relation to the absolute, but at the same time denying any real knowledge of it.
For Kant, the question "why is there something rather than nothing?" is entirely senseless for theoretical reason, but under the constraints of practical reason, the question takes on a significance for us. I not look at the answer that Kant gives to this question, but would rather take some time to consider Leibniz' and Kant's approaches to the question.
For Leibniz, the question already had moral significance, while Kant was restricted at first to a purely theoretical view, from which point the question was senseless, and then showed the transition to the moral view wherein the question takes on sense again. In terms of the ethical being involved in the question, both Kant and Leibniz are in agreement. However, for Leibniz, who didn't clarify the being of beings theoretically, the actual was constrained to be whatever was already the best (highest good), while for Kant, the actual had nothing to do with the good, but rather it was the moral demands placed on us that first allow us to think to the problematic in a determinate way. Kant shows how a system like Leibniz' can first be thought up, which first grounds it critically. I will leave off the fruitful comparison between Kant and Leibniz here.

Thursday, December 20, 2012

Understanding the Question, "Why is there something rather than nothing?", Part I: Leibniz

I have been struggling with finding access, by my own means, to the question Heidegger poses in Introduction to Metaphysicsthrough the history of Philosophy. The question is not an innovation of Heidegger's, but is asked, and often answered, in the history of Philosophy.
Leibniz answers the question in what Heidegger calls the Twenty-four Statements, since, he says, there ought to be a ground for the fact that there is something. For Leibniz, it seems for there to be something requires the possibility of bringing possibilities into actuality. Since there are actual things, it is necessary that these possibilities are brought into actuality, and that whatever is the cause (the 'real ground') of this stepping into reality (coming into existence) is also the necessary ground of the fact of actualities. Of course, this ground is none other than God.
Here is an illustration of Leibniz's work here in terms of the elements involved: 1) the actual that is, and which is known; 2) the demand that we account for the actual's being instead of nothing; 3) the possible from which the actual steps into existence; 4) that which is necessary in the face of the fact that the possible does step into existence.
Any of the actual things could just as well have been nothing, and, for Leibniz, many of possibilities did not come to pass. Coming to pass is determined by God on the basis of the most good. (Goodness now is understood in a way mediated first by the fact that something is rather than not, and should be understood in terms of existence, and not our preference.) For something to not come into existence is for it to have contradicted whatever did come to pass, and also not being as good as what did come to pass.
(I must mention, in defense of Leibniz, that it seems highly important to see the choice to place goodness at the root of the decision of what should be is not arbitrary. The highest order decision about what is actual should align with the highest knowledge of it, and so should be knowledge of what is best, and ultimately good. Here, goodness should not be considered in terms of morally good, since it seems ethics is determined by Leibniz at the end of the Twenty-four Statements in terms of coming to understand the goodness of the world, and to situate our minds to not be at odds with the goodness of existence by expecting things out of it that we should not. This means that the way things are opposed to our desires should have a regulative impact on us so that we come to understand the world better and change ourselves to not be at odds with it.)
So something is, in which case it is the most good, or something is not, which is to say it contradicts the good or is less good. What does nothing mean here? Nothing is not the contradictory, or the less good, since these are still possibilities. Nothing must be understood as something else. Things have less reality if they are less likely to come into existence, and so nothing would seem to be a privation, in some degree, of goodness. So nothing here is not a mere not being actual but a privation. If this is the case, then when we look out and see that there are actual things, we can't suppose that it could have been nothing, since nothing is just privation of what is. This may give us some right to understand nothing is another sense, that is, whatever is not actual is nothing.
The dual notion of nothing we have is first, nothing as privation of goodness or contradiction with what is good, and second, nothing as not being actualized. It appears that the second approach to nothing dominates the question Leibniz answers of why there is something rather than nothing. Because he is focused on the second sense of nothing, he can see the actual in opposition to its alternative, and not just different in degree. The dividing line between something and nothing, then, is determined on the basis of there being goodness (which is our highest way of thinking the best and so the highest kind of knowledge we tend towards). But this goodness is decided on the basis of what simply is (which could have still been anything). This establishes a kind of circle that is driven by the pursuit of the highest kind of knowledge for us.
Looking at the four-fold division above, then we can note that (2) the demand that we determine the question is driven by the demand to know the highest, and so the direction of (4) how we determine what is necessary is established in this practical manner (rather than upon an analysis of the 'objectivity of the object', which is an alternative approach).

Wednesday, December 19, 2012

Understanding Destiny Transcendentally

   I have been inquiring into 'destiny' as part of a general study of 'problematic' concepts and how they are grounded in the human experience in such a way that can provide insight into the human condition, as well as works of thought in the history of philosophy.  The result is an understanding how we are destined transcendentally.  These reflections should serve as a starting point rather than an end.  In order to understand our transcendental destiny it will be good to start with a more familiar picture of destiny.
   Where there is destiny there is a story wherein something or someone is destined.  The nature of the destined is such that it is established towards something.  Sometimes things are at the end of their destiny, and the story surrounding the thing is arranged by the destiny; other times the destiny is still to be fulfilled and stretches forward arranging and canceling possibilities.
   Destiny does not mean that something will happen according to mere mechanism, but rather according to a purpose or plan; such purposes or plans are thought on analogy with something willed by an intelligence.  (This is mentioned not to say that we must grant ourselves knowledge of some intelligence that is determining destiny, but simply to characterize the way we think destiny.)  When I meet my beloved, it may feel like some being intended for this to happen; when things are shaping up poorly I may wonder if it was planned that the difficulties would emerge at precisely the decisive moment.  
   We may feel like we are being rewarded, or punished by destiny, or even that we no longer have a destiny (that we are abandoned by the gods).  But no matter what specific case of being destined, we can be sure that there is also a pure mechanism that accounts for the entire sequence of appearances, and so the destiny is not necessary for the occurrence of the events that we feel are destined.  But we may still ask what it would be for a destiny to be necessary, and from that take a view to what things may count as such a destiny.
   For a destiny to be necessary it is not enough to just say that the destiny corresponds with whatever happens in nature mechanically.  Instead, what is destined must be thought apart from the mechanism of nature.  This is why any destiny in nature is also not necessary, since it always can defer to mechanism.  This tells us that in order for a destiny to be necessary, it cannot refer to beings as natural (where nature is understood as the Kantian 'sum total of appearances').  But what can be said to happen outside of nature that is purposive?
   Kant's aesthetic and moral judgments appear to be instances where destiny is at work transcendentally.  With the aesthetic judgment (judgment of taste) we find ourselves with the purpose of thinking a specific yet undetermined thing under a concept; with the moral judgment we are commanded to act in a certain specified way, but the command is given by us, and we are revealed as free.  Destiny in the case of the judgment of taste is the reflection off of the satisfaction in an object which at the same time makes us into thinking beings; destiny in the moral judgment is the reflection off of the moral law which at the same time reveals us as free and self-governing.
   There is a peculiarity of the aesthetic and moral judgments which defy the common view of destiny which makes man appear insignificant and only playing a role set out for them.  With the aesthetic and moral judgment, the human being is first free - free to act in relation to things according to his nature as an intellect, and as an agent.  (Perhaps it is only because the human is transcendentally destined to be free that these weighty elements of our life stories can weigh on us as they do and usurp destiny transcendentally understood.)
   We can also consider Heidegger's question concerning the essence of technology.  What is destining us to order beings in terms of standing reserve?  Well, this destiny is not necessary for us transcendentally speaking - we came into our technological 'frame' only at a certain point in history - but we can understand how a certain blindness to the limitations our 'frame' puts on the world ultimately has a restriction on the way in which we come into contexts with things, and are fated to operate in certain modes with them.  How can we best understand our capacity to conceal the nature of things?

Thursday, December 13, 2012

Towards Orderly Discourse About What Philosophy Is

   A difficulty in discussing philosophy is that there are many conceptions of what it is.  These differences often lead to an inability to begin discussing, since the basic aims of the participants appear at odds with each other.  I am not interested here in arguing for any particular way to use the word 'philosophy', nor am I trying to promote anything other than orderly discourse.  I am interested in presenting general distinctions in the hope that they can be used to avoid conflicts that rest on misunderstandings.
   My approach will be to consider different ways of thinking about goals which I think are helpful for considering different uses of the term 'philosophy', and then illustrate them.  There are two distinctions that I will need to make in order to proceed.
   The first distinction concerns kinds of goals, which are either subjective and objective.  A subjective goal is concerned with a result in the subject (e.g., becoming warm when cold); an objective goal is concerned with some result in objects (e.g., a product as a final result of work).
   The second distinction concerns the kind of result expected by goals, which are either determined or undetermined.  A determined goal is one that has a specifiable state to bring about; an undetermined goal does not specify a particular result.
   I hope to clarify what these distinctions above by considering them in combination as providing different ways of philosophizing.

Determined Objective Goals
   If you philosophize in this way you are concerned with changing something about the world.  Perhaps you want to advance a discipline such as Physics, and so think through the consistency of different theories to advance the correct one; you may also have ideas for social or political changes that you would like bring about.  These would be determined objective goals.

Determined Subjective Goals
   If you philosophize in this way you are concerned with changing the subject (or other subjects).  Perhaps you want to instill a stoic outlook, or help others to take an interest in something, such as virtue.  These would be determined subjective goals.

Undetermined Goals
   Here there is difficulty addressing the objective and subjective, since it becomes clear that if the goal is undetermined we can not specify if it is one or the other.  However, I hope to say something about the objective and subjective after some exposition.  Also, this kind of goal for philosophy is the hardest to explain (at least for me), and the one I find least understood by those I speak with, and so I am giving myself more space for my exposition.
   With both objective and subjective determined goals for philosophy there is always some demand external to the activity which sets it to work.  If I am advancing a science, or the state, then there are goals to be accomplished that the philosophical activity seeks to satisfy.  An undetermined goal is an end in itself, that is, there is no external demand which the activity depends upon.  
   A peculiarity that we find now is that there is no reason to philosophize in an undetermined way, and so no justification for it; this has historically made this sort of philosophy look ridiculous.  However if we adjust our view, we can see that this kind of philosophizing occurs when we are unexpectedly brought into a kind of activity which may sustain itself in an open-ended way or opens up determined objective or subjective goals that we can pursue.
   We can make achieving an undetermined goal state into a goal, but when we ask if this goal is objective or subjective it seems difficult to answer.  Bringing about this state of activity with an undetermined goal is not clearly met by putting either the subject or objects into a certain specifiable state.  However, this weakness can become an advantage in characterizing this kind of philosophizing:  We can say tentatively that while seeking an undetermined goal state we must work to abstain from all externally determined goals.
   This sort of undetermined philosophical activity is captured in many thinkers in the history of philosophy, both in the process of the thinkers, as well as captured in themes.  Plato writes Socrates questioning the conceptions of his fellow citizens; Descartes tries to empty himself of pre-conceptions to find a necessary foundation; Aristotle discusses the highest virtue as contemplation - thought thinking itself; Kant discusses it in the judgment of taste as the foundation of logic; Heidegger tries continually to open himself, and those at his lectures, to the question posed by Being.

   By suggesting these distinctions I don't mean to decide what anyone should do.  Also, I do not want to suggest that anyone must pick one; we may constantly shift between them.  My goal is that after setting out these three types of philosophizing we can use the division to look at what people are doing at any point under the name of philosophy and consider the best approach to evaluate it and understand it better before disputing it simply because it does not sound like the sort of activity we may be interested in putting under the heading 'philosophy'.

Monday, December 3, 2012

Descartes' Cogito and Heidegger's Dasein

I want to write this just as a small matter of consideration for interpreters of Heidegger and Descartes.
Recently I was considering how doubt concerns the subject and not objects, and that the result of the hyperbolic doubt that Descartes pursues results in no change in the objects as objects, but only in the subject's possible activities with the objects - they become doubtful behaviors. 
I thought it may be interesting to point out that when we doubt an activity, it is not gone for us as a possible activity. I may doubt that I can pick up an object, but this doesn't change the object, nor does it change the possibility of my picking it up (as an action I can try). 
When I doubt all that is possible for me to doubt, as Descartes does, I am left with all the same possibilities, and objects. However, I am not doing anything else with the objects. I am, however, still there in the same circumstances, just having taken a certain stand in relation to them. 
To be a bit cheeky. Heidegger complains about Descartes, but in showing what Descartes overlooked, he also overlooked what both of them overlooked: the Cogito also establishes Dasein (being there) as Being-in-the-World.  Heidegger really does acknowledge this, however, but sees the thing that Descartes as overlooking an inquiry into the 'sum' of the 'Cogito sum'.
(6/9/2015) Heidegger has a very interesting interpretation of Descartes (similar to my own here) in his Nietzsche lectures, Volume 4 (Nihilism) Chapter 16 (The Cartesian Cogito as Cogito Me Cogitare).  Of course, Heidegger doesn't identify Descartes' position with his here.