Consider the property of being 5ft long. Clearly this property is more like the property of being 6ft long then it is like the property of being a good conductor of electricity. Which implies that somehow the two properties are similar to each other. But similarity implies shared properties; in general to say that two things are similar is to say that they have properties in common, and this would commit us to the a very questionable position, namely that properties have properties.
We might try to do away with this problem by re-casting the property of being a specific length as being a relation between an object and a length value, meaning that saying that x is 5ft long is really to say that L(x, 5) and that to say that y is 6ft long is to say that L(y, 6). And thus we can say that they are similar because the same relation is involved. But to do this might be to commit us to the position that numbers are in some way real, or of the same order as physical objects, so that there can be relations between them, a position more questionable than assuming that properties have properties. And this problem can’t be eliminated by trying to re-cast the relation as between the object and some other object of reference length, like the meter stick, because numbers are still required in order to say how many multiples of that reference object the length is. And, furthermore, even if that difficulty could be overcome we would still need a way to define what makes a relation between two objects the same relation as one that holds between two different objects.
But, even if the above problems weren’t showstoppers, and we could resolve at least some of these problematic cases by redefining them in terms of a relation to a value, it wouldn’t resolve every case of similarity. For example, the properties of being a particular color or a particular shape seem to make up a family of properties, meaning that the property of being a particular color is more like the property of being some other color than it is like the property of being 5ft long, and the same can be said about the property of being some particular shape. And these properties cannot be re-cast as relations between an object and a value, at least not obviously so.
To define what makes two properties similar we must return for a moment to the definition of what a property is (here). A property just is a particular causal disposition, meaning a pattern of having the same causal effects in the same circumstances. And what it means to have the same causal effects was defined in terms of an ideal observer which was sensitive to those effects, meaning that it was put into a characteristic state by those effects, and that it had the ability to compare the states it was put into and to determine if they were the same or different.
Now consider what allows this ideal observer to be put into its various states by the causal effects it is sensitive to. Clearly it must have some mechanism which is affected, and which then puts the observer in a particular state as a result of being affected. Now it is possible that this mechanism could be constructed in a Boolean fashion, meaning that it is either triggered, and puts the observer in some state, or it isn’t. But it could also be an analogue mechanism, which puts the observer in a variety of different states depending on the strength of the effects. Of course even an ideal observer may or may not judge these numerous different states to be similar, if not the same, but that is irrelevant to the matter at hand. Instead consider the nature of the mechanism that is sensitive to the effects. If some one mechanism is sensitive to a number of different causal effects, and could theoretically put an attached observer into a different state for each, then let us say that those effects are similar with respect to that mechanism. We can then say that two effects are more or less similar depending on how many possible mechanisms can detect both effects. For example, different amounts of charge are fairly similar because there are many possible mechanisms that can detect all those amounts (for example, by measuring the pull on some other charged particle). On the other hand charge and the wavelength of light are less similar because even though there are mechanisms that are sensitive to both they are composed of two mechanisms, one for charge and one for light, and thus there are more possible mechanisms that detect amounts of charge then there are that can detect both the amounts of charge and light (all the mechanisms that detect charge by itself + those that detect both charge and light compared to the number that detect both).*
Of course this definition is constructed with the fundamental physical properties in mind, but it can be easily extended to the macroscopic properties (the ordinary everyday properties) either indirectly by defining their similarity in terms of how similar the fundamental properties that are responsible for them are, or directly by considering the possible mechanisms that are sensitive to them. The exact details are unimportant. What is important is that we can give an account of the relationship between certain properties without giving those properties a complex structure. Which allows us to keep defining properties simply as causal dispositions, instead of forcing us to consider them as independently existing entities.
* An interesting consequence of this definition is that a property and its negation (say being red and not being red) are maximally similar, because any mechanism that can detect red can always detect not being red, simply by failing to detect red. I think this is a strength of the definition.