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One possible question in the debate between consequentialism and deontological ethics is whether deontology might in fact be a type of consequentialism. Under deontology, actions are supposed to be right or wrong in and of themselves, regardless of consequences; however, it can be argued that even deontological theories have an end (teleos) or 'final cause' at which they aim, and can thus be considered a type of consequentialism.
An example of this would be in Natural Law presented by St. Thomas Aquinas, which is supposed to be deontological. The primary precepts of Natural Law suggest the end to which a supposed deontological action is rooted, such as the need to worship God. This underpins each and every action taken within Natural Law, which undermines its deontological status - as everything is for the 'greater glory of God' or 'self preservation and the preservation of the innocent' etc.
Other examples can be found in Kant's Categorical Imperative, whereby the fulfilment of one's duty is considered to be good intrinsically and universally. Arguably, this cannot be so, as an action is deemed "good" by virtue of the imperative, and so is good by virtue of its "consequence" of satisfying the imperative.
A counter-argument is that, under any type of consequentialism, the aim is to maximise good effects and minimise bad ones. But in some cases, deontology simply does not allow this. For example, a deontological theory of ethics might say that murder is wrong. If this was seen as a type of consequentialism, the aim would be to minimise the number of murders committed, even if one had to commit some murders to do this. But deontological ethics explicitly forbids this - one cannot commit a murder to prevent five murders by someone else.
In response to this, it can be argued that, in non-consequentialist theories, there is not (and never can be) a satisfactory explanation as to why an action is deemed good or bad intrinsically; any explanation (e.g. "murder is wrong because life is sacred") would permit a return to consequentialism, and to simply maximising the good and minimising the bad, even if one must "break the rules" to do so.
This argument ultimately turns on whether one is allowed to take subjective facts about who carries out an act into consideration - that is, whether it is worse to choose a situation where you yourself commit one murder than a situation where someone else commits five. Deontologists can (and do) argue that they are not consequentialists, precisely because they care not only about what happens, but also about who is responsible for it happening.
The idea that deontological ethical theories are a subset of consequentialist theories is not at all widely accepted.
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