What's the difference between negative rights and positive rights? Can negative rights co-exist? Can positive rights co-exist? Can negative rights co-exist with positive rights?
According to Prof. Aeon Skoble
A positive right requires others to provide you with either a good or service.
A negative right only requires others to abstain from interfering with your actions.
They can co-exist in this way : If we believe in negative rights, we can have positive rights as long as it is grounded in a consensual arrangement.
A positive right is a right to something, a claim. This may be a social (right to education) or political (right to vote) right. A negative right is a right against interference, a defense. An example is the first amendment's prohibition to restrict free speech.
In general, and regardless if negative or positive, rights can conflict with each other and should be seen as a system that has to be brought into balance or even into an optimum. Moreover, a negative right can usually be expressed as a positive right (right to free expression as prohibition to restrict free speech), but not vice versa.
The general idea is that negative rights are protections of your life, liberty, and property from harm by others. All others have to do is not act upon you or your property to ensure your negative rights. Positive rights are rights to some good thing that others are obligated to give you. For example, property rights are negative rights, you have the right to do what you want with your property and others are restricted from stealing your property or destroying it. Other rights generally seen as negative include the right to not be hurt by others, and the right to say or write whatever you want. Here's one definition from a Santa Clara University article:
Negative rights, such as the right to privacy, the right not to be killed, or the right to do what one wants with one's property, are rights that protect some form of human freedom or liberty, . These rights are called negative rights because such rights are a claim by one person that imposes a "negative" duty on all others—the duty not to interfere with a person's activities in a certain area. The right to privacy, for example, imposes on us the duty not to intrude into the private activities of a person.
Meanwhile, the article describes positive rights:
Where negative rights are "negative" in the sense that they claim for each person a zone of non-interference from others, positive rights are "positive" in the sense that they claim for each person the positive assistance of others in fulfilling basic constituents of human well-being like health and education.
An example of a positive right is the right to have healthcare. By this right, others, or more likely the government, have an obligation to provide you with some sort of basic health care. Other positive rights include the right to internet access, the right to basic nutrition, or the right to publicly funded education. Many people who love the idea of negative rights get upset about positive rights. They think protection of one's life and property is all well and good, but are skeptical that such essentials of civilized society as negative rights should be classified in the same category as the idea that government should provide an ever expanding number of "necessities" to its citizenry. For example this libertarian leaning article describes positive rights in a rather negative light
“Positive rights” trump freedom. According to this doctrine, human beings by nature owe, as a matter of enforceable obligation, part or even all of their lives to other persons. Generosity and charity thus cannot be left to individual conscience. If people have such positive rights, no one can be justified in refusing service to others; one may be conscripted to serve regardless of one’s own choices and goals.
There are critiques of this negative/positive dichotomy. One goes like this:
As a philosophical or ethical idea, the negative/positive distinction makes sense. Things get fuzzy when we take a step back and look how negative rights are actually guaranteed by government. The most basic negative right is the right to your life. This is your freedom from other people killing you. However, government has to enforce this right. They have to hire police officers to arrest those who would harm you and jailers or executioners to protect you from people who ignore the threat those officers pose. Salaries, equipment, law enforcement facilities, let alone the entire judicial system are all expensive and almost every state in history has found them indispensable for guaranteeing this negative right. Suddenly what looked like a simple right to one's life actually requires a whole bunch of other people's property to fund. If providing for one's right to life is expensive and requires funding from an external source, how is it fundamentally different from providing for someone the right to internet access? They're both nice things that take a bunch of tax dollars to provide. Maybe then, there's no fundamental difference between positive an negative rights.
Positive rights are based on coercion, negative rights are based on the freedom from coercion.
An example of negative rights is freedom of speech, you have the freedom to speak and express your opinion free from coercion or violence.
An example of a positive right is of an entitlement paid to you by the government to guarantee you a certain living standard. however coercion must be used on your behalf to collect the resources in order to pay this entitlement.
Positive rights cannot co-exist with negative rights without some degree of compromise of the negative rights.
IMO there are no such things as positive rights and they are based on the left's fundamental confusion of the difference between power and freedom. Freedom is for everyone, even the poorest person is free to live like a king, they just don't have the power to do so. Positive rights are nothing more than the political redistribution of power and as such are obviously incompatible with freedom.
Negative rights = Natural Rights Positive rights require the violation of one group's Natural Rights in order to accomplish. Therefore, they cannot co-exist
Easy example: Marxists say everyone has a universal right to healthcare. In order to provide 1 individual with "free" healthcare, the government has to violate someone else's property rights in order to provide it. The idea that government can give anyone anything is a fallacy. Government has to steal from one group before it can give it to another group. It doesn't have anything of it's own to give.
At their most basic, negative rights are described as 'do not do bad things to me', while positive rights are described as 'please do good things for me'. That simplicity breaks down once we notice the ambiguity of the word 'rights' in these comparisons . . .
Elephant in the Room: Rights-as-Ideals vs. Rights-as-Implemented
Of the many ways in which people differ in their views on rights, perhaps one of the most influential one is about whether or not Natural Rights (Rights-as-Ideals) are a real thing, or whether all rights are merely things we decide to make up and only their implementations matter. This is very much related to the difference between moral realist views and moral nihilist views.
If one doesn't believe in natural rights, one needs to only consider implementation of whatever rights one deems desirable. If one does believe in natural rights, sooner or later one still will have to answer the question, 'So if this is the Right Way For Things to Be, then what do we actually do to achieve the right state of affairs?' and hopefully put one's effort where one's mouth is.
So You Wanna Implement Rights
Here we get to the issue that protecting even negative rights doesn't happen all by itself. If one has a right to property, one is still unlikely to be able to protect one's property against a sufficiently bigger group of robbers. So protecting such rights still requires collective effort, and collective actions often benefit significantly from specialisation, which in turn raises the question of financing such protective work. There are incentives to, after reaching some scale of a community, treat the implementation of the protection of such a negative right as a positive right ('you are granted community protection').
Communities tend to have dim views of inefficiencies of patchwork jurisdictions, and of the losses to freebooters, so financing of such positive rights tends to stop being opt-in, and becomes mandatory for anyone who directly or indirectly benefits by being in a given community's turf. This of course may interfere with certain negative rights (depending on one's views of what negative rights exist and are currently applicable).
The above is just one, and rather simplified, example. Hopefully it does demonstrate how negative and positive rights interact 'in the wild' and become intertwined in societies, and how different views on which (if any) rights are real as a thing in itself can influence the interaction.