  An invariant differential cross section measurement of inclusive $\pi^{0}$
and $\eta$ meson production at mid-rapidity in pp collisions at $\sqrt{s}=8$
TeV was carried out by the ALICE experiment at the LHC. The spectra of
$\pi^{0}$ and $\eta$ mesons were measured in transverse momentum ranges of
$0.3<p_{\rm T}<35$ GeV/$c$ and $0.5<p_{\rm T}<35$ GeV/$c$, respectively.
Next-to-leading order perturbative QCD calculations using fragmentation
functions DSS14 for the $\pi^{0}$ and AESSS for the $\eta$ overestimate the
cross sections of both neutral mesons, although such calculations agree with
the measured $\eta/\pi^{0}$ ratio within uncertainties. The results were also
compared with PYTHIA~8.2 predictions for which the Monash~2013 tune yields the
best agreement with the measured neutral meson spectra. The measurements
confirm a universal behavior of the $\eta/\pi^{0}$ ratio seen for NA27, PHENIX
and ALICE data for pp collisions from $\sqrt{s}=27.5$ GeV to $\sqrt{s}=8$ TeV
within experimental uncertainties. A relation between the $\pi^{0}$ and $\eta$
production cross sections for pp collisions at $\sqrt{s}=8$ TeV is given by
$m_{\rm T}$ scaling for $p_{\rm T}>3.5$ GeV/$c$. However, a deviation from this
empirical scaling rule is observed for transverse momenta below $p_{\rm T}<3.5$
GeV/$c$ in the $\eta/\pi^0$ ratio with a significance of $6.2\sigma$.
