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Here is an example of a weak thesis statement: Pollution is a problem in the world today.
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Then we can try out (in the next section) a weaker thesis: that death and posthumous events cannot affect us in a way that is bad for us.
Other arguments are narrower in scope and aim to establish a weaker thesis: that certain kinds of haecceitistic differences are spurious.
This is not a weaker thesis concerning variation on the level of inflection, where the underlying structure of the "Why?"-question is causal.
A strong Similarity Thesis might contend that some dreams are experientially indistinguishable from waking, even subsequent to waking-up; a weaker thesis might contend merely that dreams seem similar to waking while having them, but not upon waking.
Thus someone who asserts a weak supervenience thesis but denies the corresponding strong supervenience thesis must provide an explanation of why the weak supervenience thesis is true that does not entail that the relevant strong supervenience thesis is true as well.
We are content to note that some such answer is required from anyone who holds a weak supervenience thesis without the corresponding strong supervenience thesis.
For a different defense of the weak thesis, see Thomasson 2009.
The progenitor of the modern version of the thesis is Baxter (1988a, 1988b, 2001) but it is most often discussed under the formulation of it given by Lewis (1991), who first considers the strong thesis before rejecting it in favour of the weak thesis.
Another question that arises is whether the global supervenience thesis should be a weak global supervenience thesis, an intermediate global supervenience thesis, or a strong global supervenience thesis (see Section 4.3.2).
For example, all versions of necessitism must reject unqualified "essentialist" theses such as the view that a person is necessarily a person; at most, one can perhaps maintain the weaker thesis that a person is necessarily if concrete, a person.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com