Hopefully we can translate the structure of the proof into knitting, line by line.

"Suppose Γ is a satisfiable set of R-preserved sentences and $\delta$ is R-fragile."
Γ is the rows of some scarf that have already been knitted, while $\delta$ tells us about some arbitrary set of any rows at all.

"Let M be a model which satisfies Γ"
Let M be any scarf with the rows Γ already knitted.

"Either $\delta$ is true in M or it isn’t."
Either the rows described by $\delta$ will be added to M, or they won't.

"If it isn’t, then M is a counterexample showing that Γ⊭ $\delta$"
If the rows $\delta$ are not added to M, the the rows Γ could not have led us to conclude that they would be added.

"But if $\delta$ is true in M, then since $\delta$ is R-fragile there is some M' such that R(M,M') and $\delta$ is not true in M'."
But if the rows $\delta$ are added to the scarf, then since they might not have been added (they are fragile), there is some other scarf M' such that the rows $\delta$ were not added.

"Since each member of Γ was particular, each member of Γ is also true in M'."
Since the rows Γ have already been knitted, they are the same in both scarves. M' also has the rows Γ

"Hence M' is our counterexample, and Γ⊭ $\delta$."
In which case, the other scarf M' has the rows Γ but not the rows $\delta$, and so again, the rows Γ could not have led us to conclude that the rows described by $\delta$ would be added.


Clear as mud? There was a bit of trouble with the parsing, such that I had to use mathjax for the delta but not the Gamma. Odd. Let me know if it doesn't parse well.

The next section shows the structural similarity between Prior's objection and Pp ⊨ FPp

That some sentence was true in past implies that in the future it that sentence will be true in the past. Prima facie, a derivation about the future from a premise about the past. But FPp is on Russell's account neither past nor future, and so Pp ⊨ FPp does not derive a sentence about the future from a sentence about the past.

The logic sets out the incoherence of the intuition.

There'd be a naive objection along the lines that all Russell had done is avoid the issue by re-defining "future"; that the sentence "In the future, p will be in the past" is about the future - it's right there in the syntax.

Trouble is, this is just to give an alternate formal definition of "future" and "past", as if a sentence were "future" when the outermost tense operator is F. Russell's semantic definition gives us a general case that applies also to the Prior dichotomy, while also giving logical support to the intuition that what was true int he past need not be true in the future.

the syntactic version does not generalise, and does not explain why certain inferences do not work. And it is no surprise ot find that the surface syntax can mislead us as to the logical character of a sentence.