phi_270_text_a

	Symbolic notation	`English notation` or `English reading`
Negation	¬ φ	`not` φ
Conjunction	φ ∧ ψ	`both` φ `and` ψ	(φ `and` ψ)
Disjunction	φ ∨ ψ	`either` φ `or` ψ	(φ `or` ψ)
The conditional	φ → ψ ψ ← φ	`if` φ `then` ψ `yes` ψ `if` φ	(φ `implies` ψ) (ψ `if` φ)
Identity	τ = υ	τ `is` υ
Predication	θτ₁…τ_n	θ `fits` τ₁, …, τ_n	A series of terms τ₁, …, τ_n can be read (`series`) τ₁, …, `ən` τ_n (using the expression `ən` to distinguish this use of `and` from its use in conjunction and adding `series` when necessary to avoid ambiguity)
Compound term	γτ₁…τ_n	γ `of` τ₁, …, τ_n γ `applied to` τ₁, …, τ_n
Predicate abstract	[φ]_{x₁…x_n}	`what` φ `says` `of` x₁…x_n
Functor abstract	[τ]_{x₁…x_n}	τ `for` x₁…x_n
Universal quantification	∀x θx	`forall` x θx `everything`, x, `is` `such` `that` θx
Restricted universal	(∀x: ρx) θx	`forall` x `st` ρx θx `everything`, x, `such` `that` ρx `is` `such` `that` θx
Existential quantification	∃x θx	`forsome` x θx `something`, x, `is` `such` `that` θx
Restricted existential	(∃x: ρx) θx	`forsome` x `st` ρx θx `something`, x, `such` `that` ρx `is` `such` `that` θx
Definite description	Ix ρx	`the` x `st` ρx `the` `thing`, x, `such` `that` ρx

Truth-functional compounds
`neither` φ `nor` ψ		¬ (φ ∨ ψ) ¬ φ ∧ ¬ ψ
ψ `only if` φ		¬ ψ ← ¬ φ
ψ `unless` φ		ψ ← ¬ φ
Generalizations
`All` C`s are such that (` … `they` … `)`		(∀x: x `is a` C) … x …
`No` C`s are such that (` … `they` … `)`		(∀x: x `is a` C) ¬ … x …
`Only` C`s are such that (` … `they` … `)`		(∀x: ¬ x `is a` C) ¬ … x …
with:	`among` B`s`	add to the restriction:	x `is a` B
	`except` E`s`		¬ x `is an` E
	`other than` τ		¬ x = τ
Numerical quantifier phrases
`At least 1` C `is such that (` … `it` … `)`		(∃x: x `is a` C) … x …
`At least 2` C`s are such that (` … `they` … `)`		(∃x: x `is a` C) (∃y: y `is a` C ∧ ¬ y = x) ( … x … ∧ … y … )
`Exactly 1` C `is such that (` … `it` … `)`		(∃x: x `is a` C) ( … x … ∧ (∀y: y `is a` C ∧ ¬ y = x) ¬ … y … ) or (∃x: x `is a` C) ( … x … ∧ (∀y: y `is a` C ∧ … y … ) x = y)
Definite descriptions (on Russell’s analysis)
`The` C `is such that (` … `it` … `)`		(∃x: x `is a` C ∧ (∀y: ¬ y = x) ¬ y `is a` C) … x … or (∃x: x `is a` C ∧ (∀y: y `is a` C) x = y) … x …