On the Filioque:
This is a philosophical point, but a fairly basic one. Demonstrating the falsity of the East’s position on the Filioque is, in fact, trivial, because the position taken by the East necessarily denies the Trinity by conflating the Son and the Spirit.
1. The 4th Law of Logic:
Identity of Indiscernibles: ∀x∀y [∀P(Px↔︎Py) → x=y]
Indiscernibility of Identicals: ∀x∀y [x=y → ∀P(Px↔︎Py)]
Ignore the symbols, what is being said is simple: If two things cannot be distinguished (i.e., discerned), then they are identical; similarly, things that are actually identical (i.e., not actually separate things) cannot be discerned.
2. A logical distinction is not an actual distinction.
A concrete example: A man may have more than one name (a logical distinction), but still be the same man (not an actual distinction); on the other hand, two different men will have actual differences (e.g., eye color, hair color) and so are not identical (i.e., are actually distinct).
3. “Procession” and “generation” with regard to the Trinity are merely logical distinctions unless they can be shown to be actually distinct.
This is the crux of it. If the Spirit proceeds and the Son is generated, then we must have some way to distinguish procession and generation if the Spirit and the Son are actually distinct (i.e., not the same Person). In the West (following Scripture), we distinguish procession from generation because the Spirit proceeds from the Father and from the Son (Filioque); in the East, they claim the Spirit proceeds from the Father alone, which makes their conception of procession only logically (i.e., not actually) distinct from the generation of the Son — this is a denial of the Trinity.
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Thus, as already stated, the conclusion must be drawn that the Filioque is necessary in order not to commit the trinitarian heresy of conflating the Persons of the Son and the Spirit. If the Spirit proceeds from the Father alone, then there is no actual distinction between generation (of the Son) and procession (of the Spirit), and, thus, no actual distinction between the Son and the Spirit. The East teaches falsely with regard to the Trinity, and is thus in open heresy.