Necessary & Sufficient conditions: A Medical Example March 22, 2014Posted by larry in Logic, Medicine, Science.
A sufficient condition A for B is one where A being the case is sufficient for bringing about B.
A necessary condition B for A is one where if B is not the case, then A won’t be either.
Logically it looks like this. A is sufficient for B: if A, then B.
B is necessary for A: if not-B, then not-A.
Ex. of a necessary condition: oxygen (B) is necessary for being able to breathe (A). Therefore, if not-B, then not-A.
It is easier to come up with necessary conditions than it is sufficient conditions. For instance, what is sufficient for being able to breathe?
A set of necessary and sufficient conditions for A is often considered to be equivalent to, or for, A.
A slightly more realistic and complicated way of expressing this set of relationships is this. A is sufficient for D and B is necessary for D. This translates to (if A, then D) and (if D, then B). The contrapositive of each yields (if not-D, then not A) and (if not-B, then not-D). It is relatively clear, I think, that A and B each have a distinct relationship to D (I am ignoring the issue of transitivity illustrated in the example.). The potential complexity of this relationship is borne out is the following medical example from research into the dementias.
Here is a quote from a medical investigation of causes of Alzheimer’s and other dementias (from Daily Kos).
“Researchers have found that a protein active during fetal brain development, called REST, switches back on later in life to protect aging neurons from various stresses, including the toxic effects of abnormal proteins. But in those with Alzheimer’s and mild cognitive impairment, the protein — RE1-Silencing Transcription factor — is absent from key brain regions.”
“Our work raises the possibility that the abnormal protein aggregates associated with Alzheimer’s and other neurodegenerative diseases may not be sufficient to cause dementia; you may also need a failure of the brain’s stress response system,” said Bruce Yankner, Harvard Medical School professor of genetics and leader of the study, in a release.”
While the situation is more complicated than the simple example I gave initially, the logic is the same.
From the quote, we have: protein aggregate A; failure brain stress response system B; absence of RE1 (=R); dementia D.
Second paragraph of the above quote may be saying that A & B is sufficient for D.
But from the first paragraph, we also have absence of R (RE1) as a necessary condition for D. I.e., if D, then not-R (absence of RE1).
So, A&B is sufficient for D, hence (if A&B, then D). But, not-R is necessary for D. Or, equivalently, (if R, then not-D). I.e., R is sufficient for not-D.
Similarly as in the simple example: A, B, and R are related in a complex way to D, a relationship that is not entirely spelled out in the quote.
We are, therefore, left with an important question: what is status of A & B with respect to R? Is R a component of either A or B? The quote doesn’t link all these factors together. While this may be obvious from the quote, the logical situation underlying this hiatus may not be clear. Hopefully, it now is and also clearer what additional relationships need to be explored in order to lead to better understanding of the dementias, particularly Alzheimer’s, and thereby better control of their onset and progression if not complete defeat.