- 2. Action and Mind
- Faith and Reason
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- The Significance of Unity and Diversity for the Disciplines of Mathematics and Physics
If I intend to be shaking in order to signal my confederate, and this intention makes me nervous, so that I shake, I am shaking because I intend to do so—though not intentionally. There is a failure of intentional action only when intermediaries are of the wrong kind. Reactions to causal deviance vary widely. Some are convinced that the problem is hopeless Anscombe , pp. See Thalberg ; Mele , Ch. A recent development finds a problem of causal deviance in the manifestation of dispositions, even when they are dispositions of inanimate objects.
Suppose I attach a fragile glass to an explosive device that detects whether it is attached to something fragile and if it is, shatters the object when it is struck. When the glass is struck, it will break in part because it is fragile without manifesting its fragility: the causal connection is wrong. Because the phenomenon deviance is in this way general, there is reason to hope we can solve it for intentional action by appeal to resources we need elsewhere. See Hyman on dispositions and desires. It is in any case unclear how the dispute about causal deviance bears on the project of explaining intentional action through intention as a mental state.
Like the theory of intending as being embarked upon intentional action, the disjunctive conception agrees with Aristotle that action is, or can be, the conclusion of practical thought. Corresponding issues have been pursued in the philosophy of perception, where causal and disjunctive theories are often opposed as by Snowdon —1 , and in epistemology more broadly.
Instead of explaining knowledge as belief that meets further conditions, some epistemologists treat knowledge as basic, explaining mere belief as its defective form McDowell ; Williamson A question for this view is how the state of intending can be a form of something dynamic: the event or process of acting. To answer this question, we need to say more about the kind of state intention is. If intention is a mental state in relation to which doing A amounts to doing A intentionally, or with the further intention of doing B , that fact would unify the modes of intention with which we began.
It would, however, tell us little about intending itself. Does this state involve desire? Belief about what one is doing or what one is going to do? Evaluative judgement? Similar questions arise for those who deny that intention is a mental state and explain it as being on the way to intentional action. Must I want to perform an action I am thus embarked upon? Believe that I am engaged in it? Hold it to be in some way good? He made two further refinements. If the judgement is merely that a given action is no less desirable than others, it permits me to intend A and intend B , even if I know that they are incompatible.
A related objection is that we can fail to act, or intend, in accordance with our evaluations. In a typical case of akrasia , I conclude that I ought to quit, but decide to continue smoking instead. All things considered judgement is the special case of this in which r includes all the considerations one holds relevant. There is no inconsistency in judging that the sum of these particular considerations favours A over B while judging that B is better than A , perhaps in light of other considerations one has not specifically considered.
Since it is the latter judgement that constitutes intention, one can act intentionally against the former. This is how Davidson makes sense of my continuing to smoke. A recent critic is McDowell Or fail to intend in accordance with one? He may intend this to be trivial, counting that fact that A is better than B among the relevant truths. But it is both plausible and non-trivial to claim that A is better than B , in the relevant sense, if and only if the balance of reasons favours A over B , where the reasons are distinct from that evaluative fact.
A consequence of this fact is the need to distinguish weakness as akrasia from weakness as failure of will; see Holton , Ch. Whichever way we go, we will need to motivate the evaluative theory. What is it about the role of intention in intentional action, or in practical reasoning, that requires it to take an evaluative shape? What is missing from theories of intention on which it does not?
For Bratman , intention is a distinctive practical attitude marked by its pivotal role in planning for the future. The plans for action contained in our intentions are typically partial and must be filled out in accordance with changing circumstances as the future comes. Among the advantages of being able to commit ourselves to action in advance, albeit defeasibly, are: i the capacity to make rational decisions in circumstances that leave no time to deliberate, or lend themselves to deliberative distortion; ii the capacity to engage in complex, temporally extended projects that require coordination with our future selves; and iii the capacity for similar coordination with others.
Bratman , Ch. This conception is, on the one hand, too weak, since it treats the fact that I have settled on doing A as just one consideration among many in favour of doing it, whereas means-end coherence is a strict or peremptory demand. And it is, on the other hand, too strong, since it permits a form of illicit bootstrapping in which an irrational decision can generate a reason that tips the balance in favour of acting on it.
Do intentions ever provide reasons? Many deny this; see, for instance, Broome ; Brunero ; Cullity ; Kolodny For versions of this point, see Chang ; Ferrero ; Smith But it faces problems of its own. This structure prompts a serious dilemma. If reasons for adopting a practice or pattern of reasoning transmit to the actions or inferences that fall under it, as Rawls once argued, the problems of bootstrapping and peremptoriness return. All we have is a theory of why intentions provide reasons. Neither option is appealing. By the same token, there is no need to admit that intentions provide reasons for acting.
We thus avoid both horns of the dilemma sketched above. How far this strategy succeeds is a matter of ongoing dispute Setiya b; Bratman b; Brunero ; Way A further objection to the demands for consistency and coherence in intention turns on an implication that Bratman , Ch. According to the Simple View, doing A intentionally involves an intention whose object is A. As Bratman argues, however, it is sometimes rational to attempt both A and B , hoping to achieve one or the other, when I know that I cannot do both. Considerations of symmetry imply that I also intended to do B. But then my intentions are not jointly consistent with my beliefs.
Bratman concludes that the Simple View is false, since it would be irrational to have such intentions. Instead, I intend to try doing A and to try doing B , knowing that I can make both attempts, though both cannot succeed. But he finds this phrase ambiguous. On one reading, it ascribes the intention to do A , but in the present case it does not. What is more, there are natural alternatives. One equates intention with guiding desire, defends the Simple View, and finds the requirement of consistency defeasible.
2. Action and Mind
There is rational pressure to conform to it, in general, but this pressure can be outweighed, as when it makes sense to intend both A and B , despite their manifest inconsistency, hoping to achieve just one. The question is whether such accounts reveal the unity of intentional action, intention for the future, and intention-with-which. The more basic objection is about the role of intention in intentional action. But it is open to question how deep the envisaged unity goes. Why must there be intention in intentional action, if intentions are plans? A partial answer cites the need for direction and guidance in doing anything that takes time or requires the selection of means.
But it is not clear that such guidance requires intention see Bratman , pp. Why must reasons attach to what I am doing by way of plans or guiding desires?
One response is to admit that they may not: there can be intentional action without intention see Bratman , pp. But if we hope to unify intention with intentional action, we cannot accept this. Intention must figure in the correct account of acting for a reason, and thus intentionally. In order to avoid disunity, the theory of intentions as plans or as guiding desires needs such an account. Acknowledging these problems, some philosophers turn back to Davidson and the project of reducing intention to desire and means-end belief see, especially, Ridge ; Sinhababu ; and, for discussion, Mulder But others see a promise of unity in the idea—influentially proposed by Elizabeth Anscombe , pp.
What is more, acting for a reason, in a sense that contrasts with mere purposive behavior of the sort characteristic of other animals , essentially involves such knowledge: in acting for a reason, I know an explanation of what I am doing that cites that reason, and therefore know that I am doing it. Intentional action turns on knowing the answer to that question. This picture raises many difficulties, and needs considerable refinement and defence.
Some will resist the claim that acting for a reason is acting with self-knowledge—though it is important to stress that the knowledge attributed here need not involve conscious belief. There is also disagreement about the kind of explanation involved in giving the reasons for which one acts Wilson , Ch. But if the picture is basically right, it suggests that the unity of intention can be found in knowledge or belief about action. Assuming that knowledge entails belief, the basic thought is that intention in action involves the belief that one is doing A. And prospective intention, or intention for the future, involves a belief about what one is going to do and why.
The idea that intention involves belief is what unifies intentional action, prospective intention, and intention-with-which. See the treatment of mistakes below. The claim that intention entails belief—most commonly, that if one intends to do A , one believes that one is going to do it—is widespread among those who draw no particular inspiration from Anscombe. See Audi ; Harman ; Davis ; Ross As Grice , pp.
Faith and Reason
See Davidson , pp. So far, we have only the fragment of a theory, an alleged condition of intending, not an adequate account of what intention is. Here there are several possibilities. On the simplest proposal, to intend an action is to believe that one will perform it and to have an appropriate guiding desire Audi , p. But a mere conjunction seems insufficient: the desire and belief could be utterly unrelated Davis , pp. This prompts the suggestion that, when S intends to do A , his belief rests on his desire: to intend an action is to believe that one will perform it on the ground that one wants to do so Davis , p.
The principal defect of this account is that it makes the belief component of intention epiphenomenal. Something similar is true on more subtle theories that divorce the motivational role of intention from belief; as, for instance, Ross , pp. For objections of this kind, see Bratman , pp. There is variation even among those accounts that give a motivational role to belief.
Such expectations interact with a general desire for self-knowledge to motivate action by which they are confirmed. More recently, Velleman has replaced the desire for self-knowledge with a sub-personal aim or disposition Velleman 19— Either way, his view threatens to generate what Bratman , pp. A different proposal, due to Harman , p. But it seems possible to intend an action spontaneously, for no particular reason.
In later work, Harman looks downstream of intention, rather than upstream: an intention is a belief about what one is doing or what one is going to do that has the power to guide and motivate action through practical thought Harman , pp. In the bad case, one merely intends to act. If not its causal role, however, what distinguishes knowledge in intention from knowledge of other kinds? Intention sets a standard of success for what does. For discussions of this point, see Frost ; Setiya a; Campbell a; Campbell b. Intention is justified by the former, not the latter: by practical not theoretical reasoning Anscombe , pp.
It is often regarded as a virtue of such cognitivism that it explains why there should be an indefeasible requirement of consistency among intentions and beliefs Ross , pp. It has also been argued that the requirement of means-end coherence follows from requirements of theoretical reason on the beliefs that figure in our intentions Harman , p. If I intend to do E and thus believe that I will do it, and I believe that doing M is a necessary means to doing E , but do not intend or believe that I am going to do M , I fail to believe a practically salient logical consequence of what I believe.
The principal challenge for a cognitivist account of means-end coherence is to explain why one must avoid such theoretical failures by forming the relevant intention, not just the corresponding belief Bratman a. But once again, one need not defend cognitivism, even in its less ambitious form, in conceiving intention as a kind of belief. There are two main arguments against this conception. The first turns on apparent cases of intention without belief. Or imagine I am recovering from paralysis, and movement slowly returns to my hand.
At a certain point, I am not sure that I can clench my fist. As it happens, I can. But if I try to do so behind my back, under anesthesia, I may not believe that I am clenching my fist, even though—on the face of it—I am doing so intentionally, and that is just what I intend Setiya , pp. Something similar crops up in planning for the future. Such examples can be dealt with in various ways. One strategy insists that, when I do not believe that I am clenching my fist, or that I will mail the bills, I do not intend the corresponding actions, I merely intend to try Harman , pp.
But do I really act as I intended if I try and fail? See Pears , p. And when I know that I am forgetful, do I even believe that I will try to mail the bills? A more radical theory points to the simplifying assumption, often made in epistemology, that belief is binary and does not come by degree. On that assumption, it may be harmless to claim that intention involves belief. But the truth is bound to be more complex: that in forming an intention one becomes more confident than one would otherwise be Setiya , pp.
A final response casts doubt on the examples. It is not a condition of being embarked on intentional action that one will in fact succeed. The same might be said when I am clenching my first, if what I know is merely that I am in progress towards doing so, in some liminal way.
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This points back to the theory of intending as doing, discussed in section 1. This strategy struggles with prospective intention and the belief that I am going to act. But its advocates may insist that the content of prospective intention is also imperfective Thompson , pp. We have practical knowledge only of what is in progress, not what has happened, or what will. The second objection is epistemic. If forming an intention is, among other things, coming to believe that one is doing A , or that one is going to do A , what entitles us to form such beliefs?
Not, or not ordinarily, that we have sufficient evidence of their truth. Forming an intention is not predicting the future on the basis of what one takes to be, or what ought to be, adequate grounds. Even though he hopes to reduce practical to theoretical reasoning, and holds that intention involves belief, he denies that intentions are formed on the basis of sufficient prior evidence. Anscombe and Velleman concede that knowledge in intention often rests in part on observation; the claim is that it goes beyond what observation, or inference from prior evidence, can support.
For differing views of the role of perception in practical knowledge, see Pickard ; Gibbons ; Schwenkler ; Ford The postulation of beliefs formed without sufficient prior evidence is sometimes taken as a fatal flaw. In a memorable formulation, Grice , p.
The Significance of Unity and Diversity for the Disciplines of Mathematics and Physics
Instead, we know what we are doing, or what we are going to do, by inference from the condition of our will, along with premises about our own abilities Grice , pp. The condition of the will cannot itself involve belief. Reactions to this problem vary widely. Those who restrict the content of intention to what is in progress and emphasize how little is involved in being embarked on intentional action may suggest that the beliefs in question verify themselves.
It is sufficient for doing A intentionally, in the relevant sense, that one intends to do it. As we saw in section 1, however, there are reasons to doubt this sufficiency. And the view seems to deflate the interest of practical knowledge. Non-reliabilists may dismiss the need for prior evidence, holding that we are entitled to form a belief if we know that it will be true, and that we will have sufficient evidence for its truth, once formed; this condition can be met when we form an intention to act Harman , p.
So long as I know what I intend, and that my intention will be effective, I have sufficient evidence for what I am doing, or what am I going to do, even though this evidence did not precede the forming of my intention. Critics may object to the necessity of these conditions.
A more common objection is that the conditions are not sufficient. They assimilate intention to faith, as when I form the belief that I can leap a great chasm even though I have no evidence of my ability to do so, knowing that the belief itself will ensure success. On an alternative view, there is a general demand for prior evidence in forming beliefs, but our intentions are sometimes exempt from it, as perhaps when we know how to perform the relevant acts Setiya ; Setiya ; Setiya It is know-how that explains why the execution of our intentions, and thus the truth of the beliefs that they involve, can be credited to us.
Is practical knowledge exempt from ordinary requirements of evidence because there is a mistake of performance, not of judgement, when its object is false? See Anscombe , pp. Would it then amount to knowledge of what is not the case? Anscombe may seem to suggest as much Anscombe , p. Implicit these debates is a question about the scope of groundless non-perceptual, non-inferential self-knowledge. A blanket objection to beliefs formed without sufficient prior evidence cannot be sustained: I often know what I believe without having come to know on the basis of perception or inference.
Is groundless knowledge of this kind restricted to our mental states? Or can it extend to what we are doing and what we are going to do? Why should that not be true of intentional action? If she failed in that endeavour, she at least prescribed a task for future work: to say whether it is indeed a prejudice or a decisive obstacle to the possibility of practical knowledge and the theory that intention involves belief. Intending as Doing 2.
Intention in Action 3. Intention and the Good 4. Intentions as Plans 5. Intention in Action If prospective intention cannot be explained in terms of intentional action, or both in terms of being in progress, how can we preserve the unity of our three divisions? Intention and the Good If intention is a mental state in relation to which doing A amounts to doing A intentionally, or with the further intention of doing B , that fact would unify the modes of intention with which we began.
Intention and Belief Acknowledging these problems, some philosophers turn back to Davidson and the project of reducing intention to desire and means-end belief see, especially, Ridge ; Sinhababu ; and, for discussion, Mulder Bibliography Alvarez, M. Anscombe, G. Geach and L. Gormally eds. Archer, A. Audi, R. Baier, A. Bratman, M. Sobel and S. Wall eds. Robertson ed. Broome, J. Morris and A. Ripstein eds. Wallace, et al. Brunero, J. Burge, T.
Campbell, L. Chang, R. Cullity, G. Dancy, J. Davidson, D. Davis, W. Mele ed. Although Paul Bernays, the co-worker of the foremost mathematician of the 20 th century, David Hilbert, and the author of a distinct variant of modern axiomatic set theory, did not develop the necessary theoretical distinctions advanced in this account of the inter-modal meaning of the at once infinite actual infinity , he does have a clear understanding of the futility of arithmeticistic claims.
He writes:. It should be conceded that the classical foundation of the theory of real numbers by Cantor and Dedekind does not constitute a complete arithmetization. The claim that the field of investigation of mathematics purely emerges from the representation of number is not at all shown.
Much rather, it is presumably the case that concepts such as a continuous curve and an area, and in particular the concepts used in topology, are not reducible to notions of number Zahlvorstellungen. An understanding of modern physics is crucially dependent upon a clear distinction between the four most basic aspects of reality, namely: number, space, movement, and the physical aspect. The uniqueness and coherence of these fundamental aspects of reality are indispensible in an assessment of the implications of a non-reductionist ontology for the foundation of the discipline of physics.
The latter conviction! However, without an implicit trust or faith in reason this postulate itself cannot be maintained. All human beings are endowed with the capacity to think and to argue rationally, but they do this from one or another diverging direction-giving orientation. Consequently, despite the fact that positivism acknowledged that there are universal structural conditions for theory making, it never allowed that deep, extra-scientific convictions could be among them.
An analysis of the structure of scientific activities therefore does not aim at securing a domain of the good by protecting it from the evil influence of direction-giving ultimate commitments, for any such analysis can only advance by implicitly proceeding from a particular life-orientation. Whatever the life-orientation of thinkers may be, they all equally share in the dimension of rationality or: logicality and all of them are inevitably in the grip of a more-than-rational ultimate commitment. We have seen that the Pythagoreans held the view that everything is number, but that after the discovery of irrational numbers they reverted to a spatial approach.
In respect of the nature of material things the most important consequence of this switch is that the Greek-Medieval legacy only acknowledges concrete material extension. Extension characterizes the nature of material things. In line with the Aristotelian tradition it was believed that celestial bodies obey laws that are different from those that hold for entities on earth. In addition it was believed that the movement of anything required a cause. The problem of motion increasingly acquired a more prominent position, although it did not mean that the powerful influence of the classical space metaphysics immediately lost its hold.
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The power of this spatial orientation is indeed still evident in the thought of Descartes and even Immanuel Kant. In their understanding of nature both these philosophers continued to assign a decisive role to spatial extension. When our understanding leaves aside everything accompanying their representation, such as substance, force, divisibility, etc.
It should not surprise us therefore that Descartes straightaway applied the feature of mathematical continuity to material things and even to atoms which since Greek antiquity, were supposed to be the last indivisible material particles. He holds that there cannot be atoms or material particles that are inherently non-divisible.
In this context XX he even introduces the idea of God in order to make acceptable the infinite divisibility of matter. He argues that although God can make a particle small enough such that no creature can divide it, this does not set any limits to the Divine capacity to divide. Therefore it should be assumed that matter is indeed infinitely divisible. The truly modern era in physics begins with Galileo, who formulated his law of inertia. Galileo formulated his law of inertia with the aid of a thought experiment.
Suppose a body moves on a friction-free path extended into infinity, then this movement will simply continue endlessly. Opposed to the traditional Aristotelian-Scholastic conception according to which the movement of a body is dependent upon a causing force , the law of inertia implies that motion is something given and that therefore, instead of trying to deduce or explain it, it should be accepted as a mode of explanation in its own right.
Motion is original and unique, and indeed embodies a distinct mode of explanation different from those used by the Pythagoreans number and the Eleatic school of Parmenides space. If motion does not need a causing force, then at most it is possible to speak of a change of motion acceleration or deceleration —and this does need a physical force. The idea of a uniform rectilinear motion on the one hand expands the inherent limitations attached to number and space as modes of explanation, and on the other it opens the way to consider another problem that already captured Greek thought.
This problem concerns the relation between persistence think about the nature of inertia and dynamics consider the change of motion requiring a physical force. The important insight of Plato is that change can only be established on the basis of constancy persistence —i.
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Of course this insight does not force us to join the specualative account which Plato gave for it in his metaphysical theory of static, super-sensory ideal forms although it is true that his solution did form a lasting attraction for many scholars. Even Frege said that amidst the on-going flow of events something lasting, something with eternal durability must exist for otherwise the knowability of the world would be canceled and everything would collapse in confusion.
From this it follows that Einstein primarily aimed at a theory of constancy —whatever moves, moves relative to this element of constancy. It also implies, by taking into consideration the interconnection between the kinematic and physical aspects, that a more precise formulation of the first main law of thermodynamics the law of energy-conservation ought to be designated as the law of energy-constancy an analogy of the foundational kinematic aspect on the law-side of the physical aspect of energy-operation.
However, a certain ambiguity is still found in the thought of Descartes and his followers for in spite of the fact that they viewed extension as the essential property of matter, they also simultaneously pursued the kinematical ideal to explain everything that exists and happens exclusively in terms of movement cf. Maier, Galileo himself embodies the long history of our understanding of matter up to this phase of its development because he explicitly explores the three modes of explanation thus far highlighted in our discussion. He accounts for arithmetical properties countability , geometrical properties form, size, position and contact and kinematic features motion.
As soon as the kinematic mode of explanation is acknowledged in its own right the necessity to find a cause for motion disappears. Stafleu, Unique and irreducible modes of explanation are not opposites —for they are mutually cohering and irreducible. The last prominent physicist who consistently adhered to the mechanistic approach was Heinrich Herz. As soon as the physical aspect of reality surfaced it opened up the way for 20 th century physics to explore it as a distinct mode of explanation and to arrive at an even more nuanced understanding of reality.
For example, in his protophysics Paul Lorenzen distinguishes four units of measurement reflecting the first four modes of explanation: mass , length , duration and charge Lorenzen, ff. Writing on the foundations of physics, David Hilbert refers to the mechanistic ideal of unity in physics but immediately adds the remark that we now finally have to free ourselves from this untenable ideal cf.
Hilbert, The conception of nature that rendered the most significant service to physics up till the present is undoubtedly the mechanical. If we consider that this standpoint proceeds from the assumption that all qualitative differences are ultimately explicable by motions, then we may well define the mechanistic conception as the conviction that all physical processes could be reduced completely to the motions the italics are mine—DFMS of unchangeable, similar mass-points or mass-elements. Eventually the distinction between the kinematic and physical aspects of reality thus became common knowledge.
According to Janich the scope of an exact distinction between phoronomic subsequently called kinematic and dynamic arguments could be explained in terms of an example. Modern physics has to employ a dynamic interpretation of the statement that a body can alter its speed only continuously. Given certain conditions a body can never accelerate in a discontinuous way, that is to say, it cannot change its speed through an infinitely large acceleration, because that will require an infinite force. The idea of an attracting force, initially conceived of in connection with magnetism, eventually brought Newton to the insight that magnetism is a force that cannot be explained through motion, although in its own right, foundational to the physical aspect, motion is a mode of explanation.
Stafleu points out that the rejection of the Aristotelian distinction between the physics of celestial bodies and the physics of things on earth paved the way, in the footsteps of Galileo and Descartes, to realize that the same physical laws apply to both domains, i. He also remarks that Newton just as Kepler indeed already appreciated force positively as a principle of explanation that is distinct from motion as an original principle of explanation see Stafleu, Stafleu summarizes this process through which the physical aspect emerged as an equally original mode of explanation as follows:.
In Newtonian mechanics, a force is considered a relation between two bodies, irreducible to other relations like quantity of matter, spatial distance, or relative motion. Though an actual force may partly depend on mass or spatial distance, as is the case with gravitational force, or on relative motion, as is the case with friction, a force is conceptually different from numerical, spatial or kinematic relations Stafleu, Since the introduction of the atom theory of Niels Bohr in , and actually already since the discovery of radio-activity in and the discovery of the energy quantum h , modern physics realized that matter is indeed characterized by physical energy operation.
It was also realized that physical processes are irreversible. In itself this observation also justifies the distinction between the kinematic and the physical aspects of reality. Both Planck and Einstein knew that from a purely kinematic perspective all processes are reversible. Einstein refers to Boltzmann who realized that thermodynamic processes are irreversible.
This law accounts for the fundamental irreversibility of natural processes within any closed system. The term entropy itself was introduced by Clausius only in In Thomson explains that according to this law all available energy strives towards uniform dissipation see Apolin, and Steffens, ff. We may now consider the claim of positivism, namely that sensory perception is the ultimate source of scientific knowledge. Let us explore this issue in some more detail. In order to highlight the limitations of the senses in the acquisition of knowledge, we only have to consider the aforementioned sketch of the history of the concept of matter.
We have referred to the fact that the Pythagoreans adhered to one statement above all else: everything is number. After the discovery of irrational numbers we saw that Greek mathematics as a whole was transformed into a spatial mode the geometrization after the initial arithmetization. As a consequence, material entities were no longer described purely in arithmetical terms.
The aspect of space now provided the necessary terms required to characterize material entities. Particularly through the work of Galileo and Newton, the main tendency of classical physics eventually underwent a shift in perspective by attempting to describe all physical phenomena exclusively in terms of kinematic motion.
Since the introduction of the atom theory of Niels Bohr in , and actually already since the discovery of radio-activity in and the discovery of the energy quantum h , modern physics realized that matter is indeed characterized by physical energy-operation. From this brief historical analysis it is clear that different aspects served to characterize matter—starting with the perspective of number, and then proceeding to the aspect of space, the kinematic aspect, and eventually the physical aspect of reality.
The moment we proceed from what has been observed to a description of what has been observed the positivist criterion collapses, because the terms employed in such a description derive from aspects that are not open to sensory perception. Can these modal aspects be observed in a sensory way. Can they be weighed , touched , measured or smelled? The answer must be negative, for they are not things but aspects of things or rather aspects within which concretely existing things function.
In the first place he distinguishes two global basic conceptions regarding the nature of matter, and he points out that currently these conceptions once again, as previously, occupy a prominent place in the discussions. He calls these two basic conceptions the atomistic conception and the continuity conception. Suddenly the question concerning the infinite divisibility of matter once again occupies a central position, thus highlighting anew the important distinction between physical space and mathematical space.
But this is not yet the end of the dependence upon unique modes of explanation. As soon as we do this, the key points of our historical survey of physics are again brought into play a decisive conditioning role in our theoretical reflections. Things function at once within all these modes and yet, in spite of this aspectual many-sidedness, things are never exhausted by any one of these modal aspects. However, he does not realize that although he has a purely physical theory in mind, the meaning of the physical aspect of reality inherently points beyond itself to its inter-modal coherence with other aspects, first of all with those aspects that are foundational to the physical aspect namely the aspects of number, space, and movement.
Even the way in which he phrases his goal cannot escape from terms that have their original seat within some of these aspects. The unity of physical material entities can never be found in one privileged or elevated mode of explanation. Accepting the unity and diversity within creation presupposes both the acknowledgement of God as Creator and the insight that nothing within creation can be elevated to serve as a substitute for God. Reifying or divinizing any aspect always lead to theoretical antinomies.
Only when a non-reductionist ontology is employed is it in principle possible to do justice to the unity and diversity within creation. Jedoch, es ist sehr zweifelhaft, ob eine restlose Arithmetisierung der Idee des Kontinuums voll gerecht werden kann. Einstein, Bernays, P. Abhandlungen zur Philosophie der Mathematik. Darmstadt: Wissenschaftliche Buchgesellschaft. Clouser, R. Descartes, R. Dooyeweerd, H. Lewiston: Edwin Mellen. Einstein, A. Autobiographical Notes.
In: Albert Einstein, Philosopher-Scientist. Edited by P. New York: Harper Torchbooks. Reprint of the Braunschweig edition original edition Relativity, the Special and General Theory. Bristol: Arrowsmith reprint of the first translation. Fraenkel, A.