The word "spirit" seems to have many meanings in the English language. For instance, when Jesus says "it is the spirit that giveth life, the flesh profiteth nothing," he seems to be saying that this physical world of mortals is worthless. Alternatively, I've always believed that Jesus meant that we shouldn't take religion too literally, as though he were saying "listen to the spirit of my words", or "live according to the spirit of the law." Perhaps this interpretation is the common interpretation; I don't know.
The meaning of "spiritual", however, can been focused much more, especially when it is used as the opposite of words like "material". People speak of a "spiritual" reality that exists beyond the physical, material world. This usage is best defined as "whatever is beyond the grasp of science." For instance, if a phenomenon regarded as spiritual (or synonymously "supernatural") was to be explained mathematically or mechanically by science, it would no longer be regarded as spiritual.
Thus religion stakes its claim in the areas that cannot be methodically expirimented upon. Regardless of what science may discover, this dynamic will always leave room for imagination, superstition, and religion, because there will always be something that might be out there in the gaps, our old friend the spirit world.
In this sense, science and religion are two sides of the same coin, the coin of day and night, the coin of the visible and the invisible.
The Bahá'’ Faith presents itself as being in harmony with science, and presents the principle of "harmony of science and religion" as though it were a new idea or objective. The truth of the matter is that religions have been seeking harmony with science since long before Bahá'u'lláh's time:
Attempts to reconcile religion and science have been on the religious agenda for centuries - at least for those who did not insist on Biblical and Qu'ranic literalism with no room for allegory or metaphor. The crowning achievements of Roman Catholic theology are the Summa Theologica and the Summa Contra Gentiles ("Against the Gentiles") of St. Thomas Aquinas. ... In the [former], Aquinas set himself the task of reconciling 631 questions between Christian and classical sources. ... Similar attempts at reconciliation permeate Talmudic and post-Talmudic Jewish literature and medieval Islamic philosophy.
- Carl Sagan, The Demon-Haunted World, pp. 274-275
Although `Abdu'l-Bahá states that religion without science is superstition, he doesn't hesitate to speak against prevailing science, for instance the case of his alleged lost link of Darwinism:
[the philosophers of the West] find that [man's] anatomy has undergone successive changes, finally assuming human form, and that these intermediate forms or changes are like links connected. Between man and the ape, however, there is one link missing, and to the present time scientists have not been able to discover it ...
The lost link of Darwinian theory is itself a proof that man is not an animal. How is it possible to have all the links present and that important link absent? Its absence is an indication that man has never been an animal. It will never be found.
- `Abdu'l-Bahá, The Promulgation of Universal Peace
Frankly, I have no idea what the lost link is that he's referring to. I suppose he read about a "missing link" in some popular magazine of the time, or perhaps he was told of such an issue by a trusted source. In any case, an opportunity at rebuttle is due to Darwin:
[I]gnorance more frequently begets confidence than does knowledge: it is those who know little, and not those who know much, who so positively assert that this or that problem will never be solved by science.
- Charles Darwin, The Descent of Man (Introduction)
Unfortunately, Bahá'’s are not at liberty to presume that `Abdu'l-Bahá was simply misinformed or mistaken on occasion. Bahá'’s are held to regard his worldly knowledge as infallible. The doctrine of 'Abdu'l-Bahá's infallibility stands upon (1) his unshakable self-confidence in making claims to worldly knowledge, (2) his claim to religious infallibility (meaning that he is infallibly guided as a leader and as an examplar), and (3) the following infallible clarification made by his grandson and heir, Shoghi:
Historians cannot be sure Socrates did not visit the Holy Land. But believing as we do that `Abdu'l-Bahá had an intuitive knowledge quite different from our own, we accept His authority on this matter....
- Shoghi Effendi, Arohanui (1946)
'Abdu'l-Bahá's seemingly unshakable confidence regarding matters of science, history, and the future, in the final reckoning presses the harmony of the Bahá'’ Faith and Science to a breaking point. Though his self-confidence may have impressed the naive and gullible congregations of seekers, the long-term effect of his claims will prove detrimental to his reputation and the validity of his teachings. Even his wisdom, to say nothing of infallibility, as a moral teacher must be called into question.