Scripture and the Magisterium attest that the Church is a visible body

From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

If we would define and describe this true Church of Jesus Christ—which is the One, Holy, Catholic, Apostolic and Roman Church12—we shall find nothing more noble, more sublime, or more divine than the expression “the Mystical Body of Christ”—an expression which springs from and is, as it were, the fair flowering of the repeated teaching of the Sacred Scriptures and the Holy Fathers.

That the Church is a body is frequently asserted in the Sacred Scriptures. “Christ,” says the Apostle, “is the Head of the Body of the Church.”13 If the Church is a body, it must be an unbroken unity, according to those words of Paul: “Though many we are one body in Christ.”14 But it is not enough that the Body of the Church should be an unbroken unity; it must also be something definite and perceptible to the senses as Our predecessor of happy memory, Leo XIII, in his Encyclical Satis Cognitum asserts: “the Church is visible because she is a body.”15 Hence they err in a matter of divine truth, who imagine the Church to be invisible, intangible, a something merely “pneumatological” as they say, by which many Christian communities, though they differ from each other in their profession of faith, are untied by an invisible bond.

12 Cf. [First] Vat. Council, Const. de fide cath., c. 1.
13 Col., I, 18.
14 Rom., XII, 5.
15 Cf. Acta Sanctæ Sedis, XXVIII, p. 710.

Mystici Corporis Christi 13-14