Hodge: In what sense is Christ present in the Lord's Supper

It [the body and blood of Christ] is present to the mind, not to our bodies. It is perceived and received by faith and not otherwise. He is not present to unbelievers. By presence is meant not local nearness, but intellectual cognition and apprehension, believing appropriation, and spiritual operation. The body and blood are present to us when they fill our thoughts, are apprehended by faith as broken and shed for our salvation, and exert upon us their proper effect. (Charles Hodge, Systematic Theology, 3:642)