* In: There are more age_classes than grade_classes in the White School. We just replace this by: There are more age_wholes than grade_wholes in the White School, where an age_whole is the individual composed of all pupils in the school who were born during a single calendar year, and a grade_whole is an individual composed of all pupils who receive equally advanced instruction. (Quine and Goodman)
* We believe Quine is using words against their conventional use in order to advance his agenda against classes. He is saying that 'individuals' can be wholes. In one senses individuals are groups in that I am an individual and I am a group/whole of particles. In another sense, b is a group iff b is not an individual. So Quine is just using the word 'whole' which we denote as 'wholeᶜ' in a way that is simply synonymous with class or concept.
It isᵃ contradictory that JFK isᵍ aʳ Kennedy and JFK isᵍ not partᶠ of the Kennedyᵃ family
* Class A is included in Class B may be rephrased as: Everything that is an A is a B. (Quine and Goodman)
* At the time Quine and Goodman had something against classes, so they showed that we could built a consistent language without mentioned classes. However, when one says that two different objects have the relation isᵍ to the same object b, then an object needs to be given a name. So B in Quine and Goodman's sentence is still a class, it's just that the word 'class' does not appear in the sentence.
It isᵃ contradictory that theʳ conceptⁿ mind isʳ inʳ this house
* Locke wrote: [T]his whole mystery of genera and species, which make such a noise in the schools, and are with justice so little regarded out of them, is nothing else but abstract ideas
* What Locke calls 'species' as in 'this is a mammal', we call 'universal'. So he believes that 'mammal' is an abstractᵗ term. There are other things which are abstract and which are not the names of species, such as a particular point. But for now, this sense of the word 'abstract' can be formalized.
It isᵃ contradictory that someᵖ numbersⁱ areᵃ physical
* We can never, to take a crude example, decide by means of our definitions whether any concept has the number Julius Caesar belonging to it, or whether that same familiar conqueror of Gaul is a number or is not. - Frege, Foundations of Arithmetic [198, _56]
It isᵃ consistent that a moment isʳ not greater than a numberⁱ
* Zalta wrote: Categories hardly ever share crucial properties with the objects categorised. The category of redness is not red, the notion of foreignness is not foreign, the notion of length is not long. [Zalta 42]
It isᵃ contradictory that theʳ propertyⁿ redness isᵃ red
* It appears natural to say that the causal role played in the world by each particular is defined as soon as that particular exists. However, if such a causal role is everything that is required to establish whether the particular is or is not similar to another particular, it follows that the existence of the particular (as the particular with such and such qualitative/causal features) is sufficient for establishing facts of similarity or dissimilarity. (Morganti)
* What Morganti is trying to do is to show that properties do not exist, though he does not say that explicitly in the above passage. All he does is replace 'property' with 'causal role'. In the following we show that to replace talk of 'properties' with talk of 'causal roles' does not make properties go away.