There might be a little more evidence for these effects than you are crediting.
Sometimes it's true that when something happens to one entity, the same thing happens to others that are closely related. Get one person sick, and his whole tribe may become sick. Make a person sad, and his lover will (after they have been together for a while) become sad too. Maybe enough examples of this kind of thing led to over-generalizing.
It is noteworthy that your examples involve human beings and their responses directly. Very noteworthy.
This idea will be explored further in the next post.
Homeopathic medicine is a good example of both the law of contagion and the law of similarity. For example, mixing snake skin into water, and then diluting it 99.9999% (or even completely removing the substance) is supposed to function as an antidote for most kinds of poisons. I think of it as "magical entanglement".
That's a great example. It's rather similar to the way some branches of Christianity treat "holy water" - if you add 'normal' water to 'holy' water, it becomes more holy water.
As long as the water is neutral, or at least not as unholy or profane as the holy water was blessed or sacred, the blessing transfers without being conserved.
Oddly, this property is actually implemented in the game known as NetHack. If you have one flask of holy / unholy water, you can turn any number of flasks of normal water to sacred / profane by dipping them into the blessed / cursed flask.
I suspect that magical thinking is a consequence of the way the brain stores and retrieves information, and how those mechanisms participate in perception. My layman's understanding is that the brain's internal "data structures" for sensory data, memories, and concepts are organized very associatively. Then, consider that people normally don't bother to distinguish the world-in-their-minds from the world-out-there. When I see two things come into contact in the real world, a connection between their representations forms in my brain as well. This enables a whole class of mental events that feature that connection. Again, since people ordinarily aren't conscious of the important distinction between the good-ol' map and territory, those ideas bleed into their hypotheses about the world-out-there.
Shame you didn't fold the next installment into this one - it could have made an already good post much better. Still, you have my upvote.
People complain when the things I write are "too long". So I try to go for brevity and conceptual specificity: one group of related ideas, one post.
I'll consider that for the future, though.
the Law of Contagion holds that two things which have interacted, or were once part of a single entity, retain their connection and can exert influence over each other; the Law of Similarity holds that things which are similar or treated the same establish a connection and can affect each other.
Are there any relationships between two physical objects that are neither interactions nor similarities? If not, these two laws boil down two "things which are related can influence each other", which is a true statement. It is as reasonable to generalize this rule as it is to generalize any rule, until you have a more specific rule (e.g. "things which are capable of sending and receiving known types of waves to each other across the span separating them can influence each other") that does not generalize the same way.
Are there any relationships between two physical objects that are neither interactions nor similarities?
Simple proximity (my pillow and the blinds on my window are not similar and don't interact, but they're about six inches apart at the moment). Co-use (my serving fork and my jar of minced garlic have no apparent similarities and may never directly interact, but they are both involved when I make certain foods). Having both come into contact with the same thing (I have touched both my shoes and my computer, which are dissimilar and haven't interacted).
I'm guessing, then, that proximity, co-use, and common contact do not generally establish magical connections between things, unlike direct interaction and similarity.
Not according to the laws described in the post, no. Of course there are probably magical systems that invoke some or all of those relationships.
An additional common theme is the natural balance (which is tied up with but not identical to the naturalistic fallacy.)
Human cultures vary wildly and dicursively, so it is worth noting which things all known human societies have in common. Several generations ago, anthropologists noted that cultures' beliefs about a suite of concepts crudely describable as 'magic' had certain principles in common.
Humans seem to naturally generate a series of concepts known as "Sympathetic Magic", a host of theories and practices which have certain principles in common, two of which are of overriding importance. These principles can be expressed as follows: the Law of Contagion holds that two things which have interacted, or were once part of a single entity, retain their connection and can exert influence over each other; the Law of Similarity holds that things which are similar or treated the same establish a connection and can affect each other.
These principles are grossly, obviously, in contradiction with everyday experience. Thusly many cultures restrict the phenomena to which the laws supposedly apply to non-standard, special cases, most especially to individuals who it is asserted have unusual powers or ritual actions that are not commonly replicated in normal life. Examples range from African sorcerers could supposedly bring death to their enemies by stabbing their footprints, the Imperial City of ancient China which was designed to function as a stylized representation of the whole of the country and induce peace as long as the Emperor sat in his throne facing south, and all manner of witchcraft superstitions in which a discarded body part or tiny doll could be used to work magic at a distance.
Yet the laws themselves do not seem to be doubted, and the phenomena which they supposedly describe were historically (and often presently) widely believed despite a complete lack of actual evidence. There are even technical specialties which are not overtly "magical" where the laws were retained. An excellent example of this is herbalism, where a concept named "The Doctrine of Signatures" suggested that the form of a plant hinted or indicated what it was useful for.
Thus the Greeks thought orchids treated impotence and infertility because they vaguely resemble testicles, the Chinese believed ginseng was a potent panacea because its forked root looked somewhat like the human form, and medieval monks thought lungwort's similarity to ulcerated lung tissue meant it was effective against respiratory ailments. In many cases such beliefs persisted for centuries and across civilizations, despite there being absolutely no rational reason to view the beliefs as true.
Sympathetic magic is just a special case of a wider set of phenomena called magical thinking. It is important that you familiarize yourself with that collection of ideas before the next post.