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Source: p 268 Middle, Introducing Philosophy for Canadians: A Text with Integrated Readings (2011 1 ed).

  Second, the theory doesn't satisfactorily explain what true beliefs correspond to. With what kind of thing or entity are they supposed to 'agree' or 'correspond'? To many philosophers, the answer has seemed obvious: true beliefs correspond to 'the facts'. But what, exactly, are facts? Here we need to be careful. Sometimes when we speak of 'facts', We are simply using that word as a synonym for truths, meaning 'true propositions or beliefs'. However. a defender of the correspondence theory had better not be using the word fact in this sense; for then all she would be saying is that true beliefs correspond to true beliefs— and that certainly isn't very helpful. Perhaps what is meant by fact is something like an actual state of affairs in the world, such as the cat being on the mat in the kitchen. This suggestion sounds more promising; but it, too, faces problems. For what are we to say about beliefs such as 'There is no cat on the mat', or 'There is no milk in the refrigerator', or 'I do not have a brother'? If beliefs of this sort can be true — and they obviously can — doesn't this mean that there must be lots of shadowy 'negative' facts out there in the world, as well as positive ones? [...]

In the last sentence above, the use of the adjective 'shadowy' implies inferiority of negative facts compared to positive facts: is this true? Why? Does not their relative merit vary with the context? E.g., the negative fact that you have no disease (as told by your doctor), is good news to a patient.

  • I believe that author's use of shadowy is to highlight that negative facts are often more difficult to identify that positive facts, not that they are somehow inferior. – Nick Jun 29 '16 at 5:12
  • See Facts for a review of the issue related to the philosophical concept of facts. In this context, "negative" is not a valuation; if we assume that a true proposition stay for a fact, then we have to conclude that a false proposition stay for a "negative" fact... – Mauro ALLEGRANZA Jun 29 '16 at 9:54
  • What is the difference between a "positive" fact and a "negative" fact? My impression is that "positivity" and "negativity" are qualities of our language, not of the "facts" themselves. "The cat is not on the mat" just means that "the cat is out of the mat" or "the cat is elsewhere"; the only "fact" is the exact location of the cat. Whether we use negative or positive words to describe that fact doesn't change it. – Luís Henrique Jun 29 '16 at 13:21
  • @LuísHenrique 'Negative' has a traditional use as 'involving a negation' going back to Greek (where Latin-style double-negation does not exist, and multiple negative elements lead to an intensified single negative.) It is the root of weird translations like 'One cannot prove a negative.' (Which, to an Ango ear is just a silly statement.) – user9166 Jun 29 '16 at 16:21
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"The cat is on the mat" is only true for only one conceptually distinct "state of the world". "The cat is not on the window sill" is true for a large number of conceptually distinct states of the world: the cat could be on the mat, or the cat could be on the table, or the cat could be in the sink... Thus the "negative" fact is, in this sense, less specific; kind of, say, insubstantial.

One aspect of this is that a multiplicity of negative facts flow from (are entailed from) one "positive" fact. If the cat is on the mat, then the cat is not on the window sill, and the cat is not on the counter and the cat is not on the table... (unless of course, we're talking about Schroedinger's cat). Although this is the logical case, most people, most of the time, don't think about any of these implied facts -- thus they are not "clearly seen", i.e. shadowy.

A final note on "conceptually distinct": this is setup by the context and actual description of the fact. If you look at the details, "the cat is on the mat" can be satisfied by a large number of "states of the world": the cat could be sitting on the mat, or lying down down... But just from the conventions of normal English usage, by indicating that the relevant status is "on the mat" the speaker has implied that these details don't matter for the conversation at hand; hence the inclusion of "conceptually distinct".

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Take a look at Meinongianism, which is basically an extensive experiment in what it would take to put negative facts on par with positive ones logically.

"There are no unicorns" means for every thing, it is not a unicorn. On the other hand 'there is a horse' means what it says, and the 'there' even has an antecedent, because the horse would, in fact, have to be somewhere, even if we don't know exactly where. The former is shadowy because we don't necessarily know what all the things are, and we have to admit right off that we cannot investigate each of them, so it might be meaningless in the long run. The latter is clear.

Every principally negative fact is, in effect, a universal quantification, a much higher-order logical artifact than a simple proposition. Whereas most (though not all) positive facts can be captured by simple propositions.

To put these two things together as the basis of your logic makes room for a broad range of category errors and other problems. We would prefer to stick to 'positive facts' (and in particular only those logical facts statable propositionally), and place or build quantification on top of propositional logic.

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