Modern Science, Metaphysics & Mathematics

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Oswald Spengler , Wolfgang E. Detlef Felken - Frits Boterman - Klaus P. Fischer - Stuart Hughes - - New York: Scribner. Lesko - - Filozofia 61 5 Oswald Spengler, Technology, and Human Nature. Spengler Heute 6 Essays.

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Peter Christian Ludz - Barbara Besslich - Added to PP index Total views 8 , of 2,, Recent downloads 6 months 3 , of 2,, How can I increase my downloads? Sign in to use this feature. In he was appointed professor of philosophy at Harvard University, a position which he held until his retirement in He was the author of many books and articles in the fields of mathematics, logic, and metaphysics. Already the recipient of many honorary degrees from English and American universities, he was awarded in the British Order of Merit, one of the highest honors which England bestows upon her subjects.

It has been the task of the contributors to this volume to estimate the significance of Whitehead's role in English and American philosophy. Few contemporary thinkers, I am sure, would subscribe to the extravagant claim, sometimes seriously made, that he is the greatest philosopher of all time. Yet no one, I am equally certain, would deny that he made a deep impression on contemporary philosophy. Whereas many authorities would not be willing to admit that Whitehead always expressed his ideas with both clarity and elegance, most of those who have read his writings with sympathetic understanding agree that his views are characterized by a breadth of experience and a depth of insight which are the envy of all aspiring.

Concepts such as causation or laws of nature , although relevant for science, are rarely the subject matter of science itself. For example, if science manages to find out the different variables and constants that determine how things in the world hang together, why do we also need to know what the general characteristics of a law of nature are or how that notion can be analyzed in terms of other notions? Clearly, scientists do not need metaphysicians to tell them about causation or dispositions in order to perform their research. Nevertheless, metaphysicians of science believe that questions regarding the existence and nature of causation, natural kinds, and necessity are valuable in their own right.

At the very least, they are pressing questions that cannot be ignored by those who yearn to thoroughly understand the world we live in. By way of example, consider the dispute between defenders of Humean supervenience and antiHumeans, which revolves around the question of whether there are necessities in nature or not. See 4a for a brief account of the debate. Clearly, this is not a question that can be answered by purely scientific methods, but it is one that metaphysicians will nevertheless take to be meaningful and profound.

Some of the issues discussed in Metaphysics of Science are also relevant for practical contexts. For example, failure to render assistance in case of an accident, a medical emergency, or the like can lead to prosecution or social repercussions due to immoral behavior. However, you can only be held legally and morally responsible for events you are also causally responsible for. Accordingly, both ethics and law require a concept of causality that accounts not just for positive but also for negative causation, that is, causation by the absence of an event or act.

If you pass an unconscious person lying on train tracks and fail to alert the authorities or pull him off the tracks, then you are partly causally responsible for his death if he is later killed by a train. Thus, although many questions within Metaphysics of Science are primarily aimed at complementing science, its debates may have far-reaching consequences in other fields as well.

To more fully understand the difference between the scientific and the metaphysical approach to the key scientific concepts that constitute the subject matter of Metaphysics of Science, it is helpful to consider samples of actual work in Metaphysics of Science section 4 and to take a closer look at the methodology employed section 5. As Metaphysics of Science is the study of the key concepts of science, its subject matter depends directly on what the sciences study and which concepts they employ.

Because there are many different branches of science, there are also many potential topics for metaphysicians to discuss. It is impossible to name them all in a survey article, much less discuss them in detail. However, it is practically impossible to fully grasp what Metaphysics of Science is from general definitions only. The same is true of metaphysics in general.

No layperson will understand what metaphysicians do from hearing that metaphysics is the study of the fundamental structure of reality. In order to give the reader an idea of both the scope of Metaphysics of Science and its practice, this section briefly and tentatively introduces seven debates which have preoccupied metaphysicians of science in the past: counterfactuals and necessities, dispositions, laws of nature, causation, natural kinds, reduction and related concepts, and space and time.

See the respective articles for more information on modal logic and modality , laws of nature , reductionism , emergence , and time. Some objects have dispositional properties. For example, sugar is soluble, matchsticks are inflammable, and porcelain vases are fragile. For example, for a sugar cube to manifest its solubility by dissolving, it must be placed in water. Not all properties are like that. So-called categorical properties need no stimulus; they are always manifest.

Just think of the properties of being solid , having a certain molecular structure for example, being H 2 O , being rectangular , and so on. The distinction between categorical and dispositional properties is often drawn with the following three features in mind:. For example, from looking at some sort of powder, we cannot tell whether it is soluble or not.

Looking at a football, we immediately see that it is round. Categorical properties are not usually conceived of in this way. Usually, no such productive, causal force is directly associated with categorical properties. Dispositional properties are not just a phenomenon we encounter in everyday contexts, but in science as well. Dispositionality has hence been of interest to Metaphysics of Science since its very beginning.

In fact, the failure of Logical Empiricism to properly account for dispositional properties played a seminal role in the emergence of the discipline see section 2a. Because of their shared belief that all of our knowledge ultimately reduces to observational experience, Logical Empiricists like Rudolf Carnap attempted to account for dispositional properties in terms of observational properties using a simple conditional to connect the trigger to the manifestation: to say that a sugar cube is soluble just means that if we put it in water, it will dissolve.

This and similar attempts at reduction fail, however, as they do not account for the modal behavior of disposed objects. For example, they do not supply a basis on which to ascribe or not to ascribe solubility to objects which have never been placed in water. This strikes us as odd, as it does not correspond to our everyday practice. In order to adequately capture the modal nature of dispositions, philosophers soon suggested that we employ a counterfactual connective instead of the simple conditional. To say that some object has a disposition, they argued, means just that if the object were exposed to the trigger conditions, the disposition would manifest.

This approach faces at least two problems. First, it requires a theory that specifies truth conditions for counterfactual conditionals see section 4b. Although early attempts at reducing dispositions to categorical properties have failed, problems like the above have convinced some philosophers that we should strive for a reductive analysis after all. David Hume famously observed that necessary connections, like those between causes and their effects, cannot be detected empirically.

Hence, Hume concludes, we have no reason to assume that any sort of productive, necessary, or modal connection of events in nature exists. Twenty-first century Humeans, too, claim that there are no necessary connections in nature.


Consequently, they deny that there are irreducible, metaphysically fundamental dispositional properties that seem to imply some sort of necessary or modal connection between the trigger and the manifestation. However, as reduction proves to be notoriously complicated, other philosophers opt for dispositionalism instead, which is, in its most radical form pan-dispositionalism , the view that all properties are of a dispositional nature. Both categoricalism and pan-dispositionalism are monistic theories, as both claim that there is, at the fundamental level, only one type of property.

It is also possible for philosophers to hold a neutral or dualistic view, according to which there are both categorical and dispositional properties at the fundamental level of reality. The debate over dispositions has had substantial impact on other debates within Metaphysics of Science and vice versa.

Other philosophers see the direction of dependence exactly the other way around: dispositions depend on laws of nature, because if the laws of nature were different, objects might have different dispositions. For example, if the laws of ionic bonding were different, salt might not dissolve in water.

Similarly for causation: maybe salt has its disposition to dissolve because its ionic structure is a potential cause of dissolving. Hence, the debate over dispositions should not be viewed in isolation. A plausible candidate for understanding the nature of this modal relationship is counterfactual dependence. If a sugar cube is soluble, then that means, at least in part, that if it were placed in water, it would dissolve.

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The reason is easily understood: counterfactual conditionals describe counterfactual situations, which means that both the antecedent and the consequent are usually not currently true. How then can we evaluate the truth of counterfactual conditionals, given that the truth or falsity of its components is not decisive?

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An idea proposed by Nelson Goodman , and Roderick Chisholm is to have the truth of a counterfactual conditional depend on both the laws of nature and the background conditions on which they operate. Some further conditions must be met, like that the background conditions must be logically compatible with p. Lewis a. According to Lewis, our actual world is only one among a multitude of possible worlds. Robert Stalnaker proposed a similar account but without defending modal realism that is, realism regarding possible worlds. To him, possible worlds are tools, and as such no more than descriptions of worlds that do not exist.

Some possible worlds are more similar to ours than others. But these worlds do not interest us; this is clearly not what we mean by saying that had David not overslept, he would have made it in time. To judge whether the counterfactual conditional is true regarding our world, we need to consider only worlds where the laws of nature remain the same and everything else is rather normal—that is, similar to what actually did happen—except for the fact that David did not oversleep and maybe some minor differences.

Lewis and Stalnaker suggest that an ordering of worlds with respect to similarity to our world is possible. Naturally, worlds where many facts are different from the facts of our world, and worlds with different laws of nature, count as particularly dissimilar. Counterfactual truth can then be determined as follows: of all the possible worlds where p is the case for short, the p -worlds , some will be q -worlds and others non- q -worlds that is, worlds where q is true or not true, respectively.

So to find out whether it is true that David would have gotten to work in time had he not overslept, we look at possible worlds where David did not oversleep and check whether the worlds where he makes it into work are more similar to the actual world than worlds where he does not because, say, all buses disappear or the floor is sticky. According to this analysis, the consequent need not be true in all possible worlds but only in similar p -worlds in order for a counterfactual to be true.

For example, had David overslept in a world where objects can be transported via beaming, he might still have made it to work in time. But as it is doubtful whether this technology will ever be available in our world as it is not clear whether it is compatible with our laws of nature , the world where beaming has been invented is not relevant for the evaluation of the counterfactual conditional.

Related to what has just been said, we can point out a welcome feature of counterfactual conditionals: it can be true both that if David had not overslept, he would not have been late for work; and that if David had not overslept, yet the bus had had an accident, he would still have been late for work. This is a feature that necessary conditionals and mere material implications cannot well accommodate or only with the undesirable implications that it is impossible for David to oversleep together with the bus having been involved in an accident.

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In addition to providing a way of understanding counterfactual conditionals, possible world semantics allows us to spell out the modal notions of necessity and possibility in terms of quantification over possible worlds. If p is necessarily true, there is no way that p could be false; that is, there is no possible world where p is false. Necessity is thus expressed in terms of universal quantification over all possible worlds, whereas possibility is existential quantification over all possible worlds. Like the general and existential quantifiers, necessity and possibility, too, are interdefinable: if p is necessary, then it is impossible that non- p , and if p is possible, then it is not necessarily the case that non- p.

Note that there are different sorts of necessity which can be easily accounted for if we conceive of necessity and possibility in terms of quantification over possible worlds: Logical, metaphysical, and nomological necessity can be defined by restricting the scope of worlds over which we quantify. For nomological necessity, for example, we restrict quantification to all and only worlds where our laws of nature hold.

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Possible world semantics faces several problems, however. For example, it is unclear just how we can know about what is or is not the case in other possible worlds. How do we gain access to possible worlds that are not our own? However, possible world semantics is a valuable tool for understanding some of the most central issues in Metaphysics of Science, such as dispositions and causation. In addition, necessity is a crucial element in theories of laws of nature, essences, and properties.

The modalities of necessity, possibility, and counterfactuality are also important in their own right: after all, knowing what would happen if something else were the case or what can or must happen is key to scientific understanding. Here are some intuitions philosophers have about laws of nature: laws are true or idealized, objective, universal statements. Laws of nature support counterfactuals, are confirmable by induction, and are explanatorily valuable as well as essential for predictions and retrodictions. Laws have modal power in that they force certain events to happen or forbid them from occurring.

Any analysis of the concept will attempt to account for at least some of these features. Roughly, there are five types of theories of laws of nature: regularity accounts, necessitation accounts, counterfactual accounts, dispositional essentialist accounts, and accounts which take laws to be ontological primitives. Whether a given generalization is true is, of course, an empirical matter and must be determined by the sciences, but what it means for a statement to be lawlike is left for metaphysics to define. Not all general statements are lawlike. The main challenge for regularity theories is figuring out what makes a universal statement lawlike without appealing to any sort of connection between events other than regularity.

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The Best Systems Account Lewis a is an example of a sophisticated regularity theory. It asks us to imagine that all facts about the world are known, such that you know of every space-time point what natural properties are instantiated at it. There are many different ways of systematizing this knowledge by using different sets of generalizations.

These generalizations make up competing deductive systems. Defenders of the Best Systems Account hold that a contingent generalization is a law of nature if and only if it is a theorem within the best such system. Which system is the best is determined by appeal to certain criteria: simplicity, strength or informational content , and fit. The Best Systems Account has been criticized for not taking seriously the intuitions that laws of nature are objective, have explanatory value, and hold with modal force.

The Best Systems Account yields regularities, but it does not explain why they obtain. Opponents of regularity theories stress that laws do not merely state what is the case, but enforce or produce what happens. Necessitation accounts are alternatives to the Best Systems Account that endorse this idea. For Armstrong, a law of nature is a necessitation relation N between natural properties. Armstrong speaks of universals. For two natural properties to be related by necessitation means that one of them gives rise to and must be accompanied by the other hence necessitation. Necessitation accounts have some advantages over regularity theories.

For example, they can more easily allow for uninstantiated laws. But how exactly do we know which properties are related by the necessitation relation, and why should we even assume that it exists? Armstrong argues that necessitation can be experienced insofar as it manifests in causal processes. However, not all laws are causal laws.

Defenders of necessitation accounts must work out these issues. The counterfactuals account focuses on a feature related to necessity, namely, the fact that laws of nature are stable under counterfactual perturbations. Versions of the counterfactuals account of laws of nature have been proposed by James Woodward , John Roberts , and Marc Lange In other words, it is more intuitive to hold that the laws of nature support counterfactuals rather than that counterfactuals support the laws.

Another prominent way to account for laws of nature is to appeal to dispositional essentialism. Dispositionalists, like Brian Ellis , Alexander Bird , or Mumford and Anjum , believe that some or even all properties are essentially dispositional. For example, if an object has the property of being electrically charged, that just means that it has the dispositional property of being attracted or repelled by other charged objects nearby. In this sense, the property of being electrically charged is essentially dispositional, because no object is electrically charged unless it is disposed to be attracted or repelled in this way.

This is precisely what many metaphysicians ask of laws: that they bring about or make necessary what happens when something else is the case. Dispositional essentialists thus claim that dispositions ground nomological facts: laws arise from the dispositions things have. Obviously, the dispositional essentialist account of lawhood hinges on non-trivial premises, which must be evaluated in their own right—for example, the premise that dispositions are basic. If analyzing lawhood is so complicated an affair that it requires elaborate theories and intricate tools, why not assume that lawhood is conceptually and ontologically primitive—that is, that the concept of lawhood cannot be defined in terms of other concepts, and that it cannot be reduced to underlying phenomena?

Tim Maudlin argues that scientists do not seek to analyze laws, but rather accept their existence for a brute fact in their daily practice, and that philosophers should do likewise. As lawhood is a primitive concept for Maudlin, he attempts to utilize it in defining other notions, like causation and counterfactual truth.

Causation is obviously intimately connected to the laws of nature , as we would expect at least some laws to govern some causal relationships. Causation, however, is not a straightforward notion. For example, philosophers disagree over which kinds of entities are the proper relata in causal relationships, some potential candidates being substances, properties, facts, or events. There are several approaches to understanding causation: regularity theories, counterfactual theories, transfer theories, and interventionist theories.

According to regularity theories, all that can be said about causation comes down to stating a regularity in the sequence of events. The motivation for regularity theories stems from the fact that instances of a regularity can be observed, unlike the production of one event by another or a necessary relation between events. According to Mackie, an event is a cause if it is an Insufficient but Necessary part of an Unnecessary yet Sufficient condition for the effect to occur.

For example, a short circuit C alone is not sufficient for a house to burn down E ; there must also be inflammable materials nearby A and there must not be sprinklers which extinguish the fire B. Call this a complex condition ABC. As the absence of sprinklers and the presence of inflammable materials is not enough to cause a fire, the short circuit is necessary within this complex condition, which is then sufficient for the fire. For example, a lit candle in a dried-up Christmas tree may also cause the house to burn down.

As the short-circuit scenario ABC is only one of many potential causes of a fire, it is not necessary for the effect to occur, but if it occurs, it is sufficient to bring about the fire. For illustration, consider a simpler type of regularity theory according to which causation is just regular succession. Obviously, these events coincided but are not causally related. To forgo this problem, philosophers devised counterfactual theories of causation. The initial idea presented by David K. Lewis b is to equate causal dependence with counterfactual dependence.

The idea seems plausible: had the cause not occurred, there would all else being equal not have been the effect. For example, if the short circuit is the cause of the fire, then the house would have burned down if the short circuit had occurred, and it would not have burned down if the short circuit had not occurred. Lewis saw that this initial account is flawed as it yields intuitively incorrect results in so-called pre-emption scenarios. Imagine two people, Suzy and Billy, throwing stones at a bottle.

Now picture a situation where if Suzy does not throw her rock, Billy will. Suppose Suzy throws her rock, hits, and the bottle shatters. However, the effect would have occurred even if Suzy hat not thrown, because in that case Billy would have thrown his rock and shattered the bottle. Although more sophisticated counterfactual theories are more successful in dealing with pre-emption and other problems, some philosophers choose to take a different approach.

Proponents of transfer or conserved quantity theories like Salmon , , Phil Dowe , and Max Kistler claim that causation is best understood as a transfer of a physical quantity from one event to another. For example, Suzy is causally responsible for shattering the bottle and Billy is not if it was her energy that set the stone in motion to physically interact with the bottle on impact and shatter it. Transferable quantities include energy, momentum, and charge, for example.

These quantities are subject to conservation laws, which means that in any isolated system, the sum total of the remaining and the transferred amount of the quantity will always equal the initial amount. Transfer theories face difficulties in accounting for negative causation. For instance, omitting to water plants may cause them to wither, but there is no transfer of a conserved quantity from anything to the withering.

Other problems derive from examples where the supposed causal relationship is not obviously of a physical nature. Woodward suggests that causation is best characterized by appeal to intervention. Consider the following example: Testing a drug for efficiency consists in finding out whether a group of people who are administered the drug are cured while a group who does not receive the drug remains uncured.

In other words, drug testers intervene by giving the drug to some patients and a placebo to others. If the drug intervention leads to recovery while the placebo intervention does not, the drug is said to be causally relevant for the recovery. Woodward places further constraints on interventions, one of which is that the intervention of administering the drug or the placebo, respectively must be performed in such a way that other potential influences are absent.

For example, if the drug were given to healthy and young patients while only the elderly and frail receive the placebo, the test might falsely attribute causal efficacy to the drug. Intervention, however, is itself a causal notion. Woodward has clarified that his theory is meant to explicate and enlighten our concept of causation, not to reduce causation to other phenomena.

It seems that all theories of causation face difficulties either in the form of recalcitrant exemplary cases or in that they do not capture certain features of causation. One possible conclusion to draw from this is that causation is not one unified phenomenon but at least two and potentially many more.

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For example, Ned Hall argues that our intuitions characterize causation both as production and counterfactual dependence, and that the problems of analyses of causation can be traced back to the attempt of squeezing these into one unified concept. The debates over the nature of dispositions, modality, laws of nature, and causation are still ongoing. Many promising approaches have been proposed in their course and will continue to be explored in the future. For a detailed account of the relation between the debates surrounding dispositions, counterfactuals, laws of nature, and causation in Metaphysics of Science, see Schrenk In everyday contexts we habitually classify objects or group them together.

Some of these groupings seem more natural to us than others. They are also highly projectible: we can inductively infer from the behavior of one object to that of all objects of the same natural kind. If natural kinds exist and contribute to the structuring of the world, then ideally we want the sciences to discover what natural kinds there are. A natural kind enthusiast may claim that physics tells us that electrons and quarks exist, chemistry says that there are chemical elements like gold Au and compounds like water H 2 O , and biology seems to suggest that organisms are ordered hierarchically along the lines of family, genus, and species.

However, there are also conventionalists who believe that so-called natural kinds are not independent of the minds, theories, and ambitions of human beings, or that no way of dividing up the world is inherently better than any other. To illustrate their claims, they remind us that the concept of biological species used to be regarded a prime example for natural kinds, but that, in the meantime, various paradigms based on the morphology, interbreeding capacities, or shared ancestry of organisms have been proposed, each leading to a different system of classifications.

If natural kinds exist in nature, then what are they? What makes a natural kind the kind it is? Different ideas have been proposed and have given rise to a multitude of questions: Do objects which belong to natural kinds share at least some properties? Are natural kinds determined by the roles they play in inductive inferences or laws of nature? Is there a hierarchy of natural kinds, such that some kinds are more fundamental than others? A position that has been particularly influential in the 20 th century is the view that natural kinds have essences.

Intuitively, Putnam claims, XYZ is not water, which leads him to assume that, unlike the superficial properties of being wet, potable, and so on, being H 2 O is a necessary condition for being water. We must, hence, acquire it a posteriori. Linked to but distinct from the question of what natural kinds are is the question of whether natural kinds form an ontological category in their own right, or if they can be reduced to other existents like properties.

Realists regarding natural kinds believe that talk of natural kinds and successful inferences presupposes the existence of natural kinds in nature. Reductionists, on the other hand, may argue that membership in natural kinds is not only determined by a number of shared properties, but also that it consists in nothing over and above having these properties. Unsurprisingly, metaphysicians of science are especially interested in finding out which, if any, natural kinds are postulated or discovered by the various branches of science and whether they really identify as natural kinds by the standards of contemporary metaphysical theories, or whether the theories of natural kinds need to be revised.

The world consists of many different things. Philosophers have always dreamed of rendering it more orderly by systematizing it in just the right way. An important step towards doing so seems to entail an analysis of the relationships and dependencies between things which belong to different strata or levels of reality.

The world apparently comes structured in levels, with things on higher levels somehow depending on the things on lower levels. For example, a factory consists of machines, conveyor belts, and so forth; machines are made of various interacting cogs, levers, and wires which, if left to themselves, cannot fulfill the functions they fulfill within the machine ; the cogs are made out of molecules, the molecules are made of atoms, and the atoms are made of protons, neutrons, electrons, and so on.