The best opposite of "mutually exclusive" I can think of is "necessarily accompanying", but it sounds awkward.
Most answers I looked up give words like "concordant" and "accompanying", but these words have more passive definitions that mean things are "compatible", "harmonious" or "in agreement".
I want a word with a harder definition that means things must exist together or not at all.
In philosophy the expression would be mutually necessary:
Definition: A necessary condition for some state of affairs S is a condition that must be satisfied [in order to obtain] S.
Example of mutually necessary conditions:
Jack and Jill will go up the hill only if they both go up the hill.
- Jack will not go up the hill without Jill.
- Jill will not go up the hill without Jack.
so
- Jack going up the hill is necessary for Jill to go up the hill.
- Jill going up the hill is necessary for Jack to go up the hill
Jack going up the hill and Jill going up the hill are mutually necessary.
In a broader context:
Interdependent implies a certain level of mutual necessity:
ADJECTIVE
(Of two or more people or things) dependent on each other:
OED
Codependent relationships exhibit an intensity of interdependence that increases the sense of necessity:
Derivative of codependency:
NOUN
[MASS NOUN]
Excessive emotional or psychological reliance on a partner, typically one with an illness or addiction who requires support:
Symbiotic relationships do not all exibit necessary, but the mutual benefit is a specialized expression of interdependence:
derivative of symbiosis
NOUN
[MASS NOUN] Biology
1.0 Interaction between two different organisms living in close physical association, typically to the advantage of both.
There is a brand of symbiosis referred to as obligate symbiosis, which does imply the must of the OP:
In animals, a common mutualistic symbiosis occurs between many herbivores and microorganisms of their digestive tracts. Ungulates (hoofed animals) and some other animals eat plant material that is high in cellulose , even though they lack enzymes capable of breaking down cellulose molecules. They obtain energy from cellulose with the help of symbiotic bacteria and protozoa living within their digestive tracts. These microbes produce enzymes called cellulase that break down cellulose into smaller molecules that the host animal can then utilize. Similarly, wood-consuming termites depend upon symbiotic protozoans living within their intestines to digest cellulose. These are obligate symbioses. The termites cannot survive without their intestinal inhabitants, and the microorganisms cannot live without the host. In each of these symbioses, the host animal benefits from the food provided by the microorganism and the microorganism benefits from the suitable environment and nourishment provided by the host.
Read more: http://www.biologyreference.com/Se-T/Symbiosis.html#ixzz3R4tP9zIU
Emphasis mine
Synergetic, a derivative of synergy approaches the meaning you are looking for:
NOUN
[MASS NOUN]
The interaction or cooperation of two or more organizations, substances, or other agents to produce a combined effect greater than the sum of their separate effects:
It is a twist but there is exclusively mutual.
Urbandictionary has a definition even:
when two events can occur only in conjunction with one another, i.e. neither one can occur without the other
I suggest "mutually implicated" as in the following sentence:
If power and knowledge are mutually implicated, then specific orders of knowledge entail specific kinds of contexts as relevant.
Also, Google shows ~26k results for the expression.
If you're thinking of properties, use 'overlapping' (in that there are some items with both properties.
If you mean that all items must have both properties, then they are, as someone else mentioned, 'necessary and sufficient', or 'equivalent' or 'identical'.
Based upon the comments provided, I'd use go hand in hand in the verb phrase, rather than look for a modifier.
Indeterminism and free will go hand in hand.
I would say it is "necessarily coexisting"
Consider using the phrase "inherently inclusive".
While codependent is nice, it has a technical meaning in psychology that you don't seem to be wanting (unless you intend to personify Free Will and Indeterminism).
I would use inseparable to mean that one cannot exist apart from the other. One of the dictionary definitions is
seemingly always together
which matches your usage well. Unlike codependent, it works well for any nouns, including objects and ideas.
I think concomitant is a pretty good fit here.
It is difficult to find an antonym for a construct of multiple ideas, but in this case the question describes the wanted result quite clearly.
Something that has to exist in order for something else to exist is prerequisite.
If A is prerequisite to B and B is prerequisite to A, we can say that the relation, just like in the original, is mutual. So I'd propose mutually prerequisite as an option.
I also looked for this and in the end paraphrased it in the following sentence:
"A and B are neither mutually exclusive, nor does one strictly imply the other."
I preferred this over using non-common expressions, which people may not understand or misinterpret.
