In philosophy of mind, dualism is a set of beliefs which begin with the claim that the mental and the physical have a fundamentally different nature. It is constrasted with varying kinds of monism, including materialism and phenomenalism. Dualism is one answer to the mind-body problem. Pluralism holds that there are even more kinds of events or things in the world.
Note that other fields have their own meanings for "dualism". See dualism.
Types of ontological dualism
Ontological dualism makes dual commitments about the nature of existence as it relates to mind and matter. Substance dualism asserts that the mind and matter are fundamentally distinct kinds of substances, while property dualism suggests that the ontological distinction lies in what properties mind and matter differ as in emergentism. Yet a weaker type of ontological dualism is predicate dualism which claims the irreducibility of mental predicates to physical predicates.
Cartesian dualism is a kind of substance dualism, a great difficulty with which is the explanation of the interaction between mind and matter, if mind is to be immaterial.
Types of interaction dualism
Regardless of whether ontological dualism is correct, one may wish to inquire how the mental interacts with the material.
Interaction dualism can be distinguished based on if and how mind and matter are thought to causally interact. In dualistic interactionism (also Cartesian dualism, as it was Descartes' position), arguably the most popular and widespread version, mind events can cause physical events and vice versa. Thus when Johnny touches a hot stove and burns his skin (physical events), he experiences pain (a mental event). Conversely, when Jessica decides her dog needs exercise (a mental event), she takes it for a walk (a physical event). This is arguably most people's common sense view of the relationship between mind and matter.
Epiphenomenalism allows causality to flow only in one direction, claiming that physical events have mental effects, but not vice versa. So although the mental cannot be reduced to the physical, mental events are side-effects, or by-products, of physical processes. Usually, the mind is seen as being a by-product of the brain and its neurons. The contrary position, that physical events are somehow by-products of mental events, is relatively unpopular and does not have a standard name.
According to a rather different theory called parallelism, mental events and physical events are perfectly coordinated by God; so that when a mental event such as Sally's decision to walk across the room occurs, then it just so happens that Sally's body heads across the room. But there is no cause-effect relation between mind and body; mental and physical events are just perfectly coordinated by God, either in advance (as per Gottfried Leibniz's idea of pre-established harmony) or at the time (as in the Occasionalism of Nicolas Malebranche).
Arguments for dualism
One argument for dualism, especially dualistic interactionism, is that it is a very common sense view. Some developmental psychologists claim to have shown that dualism is commonsensical for very young children as well. This is obviously not "proof", but it suggests we should at least have a reason for not abandoning dualism.
A second argument is that the mind is (or resides in) the immortal soul. Traditional Christianity actually believed in the binding of the soul and body in one's redemption. Only in more recent branches off of Christanity was the idea that your body will die and then your soul will go to heaven, or hell. If you believe in this idea then you believe in dualism. Another idea in contrast to dualism is if you accept phenomenalism, which holds that everything is, ultimately, mental. But in any event you absolutely cannot hold that the soul is reducible to anything physical. If events in your soul were reducible to events in your brain, then when your brain stopped functioning, your soul would cease to exist. This is not necessarily the case, as some views of the universe admit the possibility that the laws of physics are not static. See the book The Physics of Immortality (ISBN 0385467990).
Note that although this religious account may motivate or reinforce a religious person's belief in dualism, it may well seem altogether unconvincing to dualism's skeptics. To use this argument to convert, say, a card-carrying materialist to dualism, it seems necessary to first establish that people do, in fact, have immortal souls. And yet the card-carrying materialist is one of the last kinds of people who are going to admit to this.
A third argument for dualism goes like this: if dualism is false, we should be able to reduce mind to matter, or vice versa, or to reduce both to a neutral third substance. Notably Buddhist philosophy argues this point, but says everything reduces to "emptyness" or Shunyata rather than a "substance".
A final argument, to be explored in depth, is that the mental and the physical seem to have quite different and perhaps irreconcilable properties.
First, mental events are not publicly observable. When I touch the hot stove, you may see me whip back my hand and say "Ouch!" but you are not feeling my pain. Unless you're Mr. Spock, or God, you can't as it were get inside my mind and take a look at what's going on in there. And of course it's not just because my mind is hidden beneath my skull. If you knew just where to look in my brain, you wouldn't be able to see thoughts and feelings jiggling around in there. That's just not how it works. So unlike physical events, like fireworks displays, mental events are private, not publicly observable.
Second, mental events are often said not to be spatially located. Where is my pain supposed to be? Maybe you could say in my fingertips, because they hurt. But is that where the feeling is? Does it really make sense to say that the feeling is in my aching fingertips? That sounds a little funny, anyway. A better example would be an emotion like happiness. When I say I'm happy, can I locate my happiness in my head, or does it exist all my body, or something? Doesn't that sound odd? It would seem better to say that my happiness isn't the sort of thing that can be located in a particular place.
Third, more generally, mental events do not seem to have various physical properties which physical events have. For one thing, mental events do not involve anything having mass, or physical motion. We can't weigh a thought. We can't say that a feeling has a velocity of 10 miles an hour. To say such things is to talk nonsense. Now you might say: that's only because mental events are events. You can't say that physical events have mass or velocity either. Point well enough taken; that's true, no event, per se, has mass or velocity. But physical events do involve objects which have mass and velocity. Mental events do not have any components which have mass and velocity. For example, when I think, "I like ice cream," I have a concept of ice cream; and my concept of ice cream has no mass and velocity. Nothing involved in my appreciation for ice cream would appear to have any such physical properties. This is a point to which we will have to return. But on the face of it, this seems pretty obvious.
Fourth, mental events have a certain subjective quality to them, which physical events obviously do not. I mean, for example, what a burned finger feels like, what sky blue looks like, what nice music sounds like, and so on. I'm going to expand on this fourth point at some length. Recently, philosophers have been calling the subjective aspects of mental events qualia, and they also call them raw feels. There is something that it's like to feel pain, to see a familiar shade of blue, and so on; there are qualia involved in these mental events. And the claim is that qualia seem particularly difficult to reduce to anything physical. Just think of what that would involve. You'd be saying: feeling the top of my hand right now, this "raw feel" I'm experiencing right now, is itself nothing more than a physical event.
In fact, there is an article by an American, Thomas Nagel, that came out in the late 1970s called "What Is It Like to Be a Bat?" In this article Nagel argued roughly as follows. You are familiar with the fact that bats use a certain kind of sonar, right? They emit high-pitched shrieks which allow them to fly around in dark caves; they can tell how far away the walls are based on how their shrieks echo around in the cave. Bat sonar allows bats to perceive distance, shape, size, and so on, in a way similar to, but obviously different from the way vision works for us. Now Nagel invited us to ask, "So what is it like to be a bat, flying around in the dark using bat sonar?" Surely bats do have experiences; we just don't know what they are. Suppose we were to take apart a bat brain and figure out how the neural apparatus for bat sonar works. No doubt biologists have actually done so, dissected bat brains and so forth. But in understanding how the bat brain works, do those biologists learn what it is like to be a bat? Well of course not. They're mucking around in the grey matter of bats. In order to know what it's like to be a bat, and to have bat sonar, why, you'd have to be a bat. So argued Nagel.
So what's the point of all this? The point is that if indeed there are "bat qualia," then there are peculiar mental events of a sort that only bats have, and we cannot learn what they are like even if we have a detailed understanding of physical events going on in the bat brain. Or to put it even more simply: there is a strange "bat sonar experience" we'll never have. We won't have it even if we learn what physical events in bat brains are associated with bat sonar. So that's excellent evidence that mental events cannot be reduced to physical events; mental events must be regarded as quite a different sort of thing from physical events. Really, you can make the same point without even bringing up weird cases like bat sonar. Just think of your own unique feelings. Do you think that a psychologist could, simply by digging around in your brain and doing tests on your grey matter, ever learn what that feeling was like?
So there are at least four major differences between the mental and the physical, which make it difficult, to say the least, to understand how one might reduce the mental to the physical. Mental events are not publicly observable; they are not spatially located; they do not involve physical properties such as mass and velocity; and there seems to be an irreducibly subjective aspect to them. That seems to give us considerable reason to think that the mind and the body are two totally different categories of being. So there you have one basic, powerful argument for dualism.
Arguments against dualism
Varieties of dualism in which mind can causually affect matter have come under strenuous attack from different quarters, especially starting in the 20th century. How can something totally immaterial, people ask, affect something totally material? That's the basic problem. We can analyze the problem here into three parts.
First, it is not clear where the interaction would take place. Burning my fingers causes pain, right? Well, apparently there is some chain of events, leading from the burning of skin, to the stimulation of nerve endings, to something happening in the nerves of my body that lead to my brain, to something happening in a particular part of my brain; and then, I feel pain. But the pain is not supposed to be spatially located. So what I want to know is, where does the interaction take place? If you say, "It takes place in the brain," then I will say, "But I thought pains weren't located anywhere." And you, as a dualist, might stick to your guns and say, "That's right, pains aren't located anywhere; but the brain event that immediately leads to the pain is located in the brain." But then we have a very strange causal relation on our hands. The cause is located in a particular place but the effect is not located anywhere. Well, you might say, that might be puzzling but it's not a devastating criticism.
(Problems with the above paragraph: 1) some dualisms maintain that the mind resides in a particular place, say, in the pineal(?) gland. In this case the arguments about the mental being "nowhere" look less strange. 2) it seems a little blurred -- is the problem locating the mind or the mental events or both? 3) it should at least be emphasized that things don't necessarily have to be in the same place to interact, as we see with the "attraction at a distance" in gravity.)
So look at a second problem about the interaction. Namely, how does the interaction take place? Maybe you think, "Well, that's a matter for science -- scientists will eventually discover the connection between mental and physical events." But philosophers have something to say about the matter, because the very idea of a mechanism, which explains the connection between the mental and the physical, would be very strange, at best. Why do I say it would be strange? Compare it to a mechanism that we do understand. Take a very simple causal relation, such as when the cue ball strikes the eight ball and causes it to go into the pocket. Here we can say that the cue ball has a certain amount of momentum as its mass moves across the pool table with some velocity, and then that momentum is transferred to the eight ball, which then heads toward the pocket. Now compare that to the situation in the brain, where we want to say a decision causes some neurons to fire and thus cause my body to move across the room. The decision, "I will cross the room now," is a mental event; and as such it does not have physical properties such as force. If it has no force, then how on earth could it cause any neuron to fire? Is it magic? Honestly, how could something without any physical properties have any physical effects at all?
Here you might reply, as some philosophers have indeed replied, as follows. You might say: "Well sure, there is a mystery about how the interaction between mental and physical events can occur; but the fact that there is a mystery doesn't mean that there is no interaction. Because plainly there is an interaction and plainly the interaction is between two totally different sorts of events." Now I expect that some of you may want to say this. But the problem with it is that it does not seem to answer the full power of the objection.
So let me explain the objection more precisely. Let's take as our example my decision to walk across the room. We say: my decision, a mental event, immediately causes a group of neurons in my brain to fire, a physical event, which ultimately results in my walking across the room. The problem is that if we have something totally nonphysical causing a bunch of neurons to fire, then there is no physical event which causes the firing. That means that some physical energy seems to have appeared out of thin air. Even if we say that my decision has some sort of mental energy, and that the decision causes the firing, we still haven't explained where the physical energy, for the firing, came from. It just seems to have popped into existence from nowhere.
A fundamental principle of physics is involved, the conservation of energy. According to this principle, "In all physical processes, the total amount of energy in the universe remains constant." Or in a form you may have heard before: in any change anything undergoes, energy is neither created nor destroyed. This is a basic principle you probably learned about in high school physics. So the point is that nerve firings, which are allegedly caused by a totally nonphysical decision, would appear to violate the Principle of the Conservation of Energy.
Now, dualistic interactionists have tried to answer these objections, and other such objections, but most philosophers these days are not impressed by their answers. It has come to the point where, in fact, there aren't very many interactionists around, and there haven't been many for decades. When I say this, I don't mean to imply that dualistic interactionism is false. All I mean to imply is that many philosophers today think it is false, and perhaps also that, if you want to hold onto interactionism yourself, you should try to come up with some effective replies to these objections.
(Another very interesting route to take for the aspiring substance dualist might be to question the causal closure of the physical domain. Briefly: there seem to be events on the quantum level which lack a physical cause; if they lack a physical cause, then either they have a nonphysical cause or they are uncaused; in either of these cases, the physical domain is not causally closed. But it remains true that there are very serious objections to substance dualism which must be met.)
John R. Searle, Professor of Philosophy at the University of California, Berkeley, has pioneered an approach to mind-body issues that is dualistic in some respects, monist in others. He calls it "biological naturalism."
Searle's views sound like dualistic interactionism. He believes that consciousness "is a real part of the real world and it cannot be eliminated in favor of, or reduced to, something else" whether that something-else is a neurological state of the brain or a software program. He contends, for example, that the software known as Deep Blue knows nothing about chess. He also believes that consciousness is both a cause of events in the body and a response to events in the body.
On the other hand, Searle doesn't treat consciousness as a ghost in the machine. He treats it, rather, as an emergent property of the brain as a whole. (See holism). The causal interaction of mind and brain can be described in naturalistic terms, thus: events at the micro-level (perhaps at that of individual neurons) cause consciousness. Changes at the macro-level (the whole brain) constitute consciousness. Micro-changes cause and then are impacted by holistic changes, in much the same way that individual football players cause a team (as a whole) to win games, then the individuals gain confidence from the knowledge that they are part of a winning team.
 (http://artsci.wustl.edu/~philos/MindDict/dualism.html) Dictionary of philosophy of mind entry  (http://plato.stanford.edu/entries/dualism/) Stanford encyclopedia of philosophy