Step 1: List the rules for aromaticity. A species is aromatic when it is cyclic, planar, has continuous conjugation around the ring, and contains $(4n+2)\pi$ electrons (Huckel's rule). A conjugated ring with $4n\pi$ electrons is antiaromatic, hence not aromatic. Step 2: Test pyridine (option 1). Pyridine is a planar six membered ring with $6\pi$ electrons, fitting $4n+2$ with $n=1$, so it is aromatic. Step 3: Test the cyclopentadienyl cation (option 2). This five membered conjugated ring carries only $4\pi$ electrons, which is a $4n$ count with $n=1$, so it is antiaromatic and not aromatic. Step 4: Test anthracene (option 3). Anthracene is a fused ring system with continuous conjugation that satisfies Huckel's rule, so it is aromatic. Step 5: Test furan (option 4). In furan one lone pair on oxygen joins the conjugation, giving $6\pi$ electrons in a planar ring, so it is aromatic. Step 6: Pick the non-aromatic one. Only the cyclopentadienyl cation fails the rule, which is option (2). \[ \boxed{\text{Cyclopentadienyl cation}} \]
