Ock The question is is can we prove that globally the MWP was warmer than CWP ?
You appear to be claiming that lack of proof means that it must have been warmer during the MWP by invoking the null hypothesis.
It is probable that today is globally warmer than the MWP
(dark blue 1000-1991): P.D. Jones, K.R. Briffa, T.P. Barnett, and S.F.B. Tett (1998). "High-resolution Palaeoclimatic Records for the last Millennium: Interpretation, Integration and Comparison with General Circulation Model Control-run Temperatures". The Holocene 8: 455-471. doi:10.1191/095968398667194956
(blue 1000-1980): M.E. Mann, R.S. Bradley, and M.K. Hughes (1999). "Northern Hemisphere Temperatures During the Past Millennium: Inferences, Uncertainties, and Limitations". Geophysical Research Letters 26 (6): 759-762.
(light blue 1000-1965): Crowley and Lowery (2000). "Northern Hemisphere Temperature Reconstruction". Ambio 29: 51-54. Modified as published in Crowley (2000). "Causes of Climate Change Over the Past 1000 Years". Science 289: 270-277. doi:10.1126/science.289.5477.270
(lightest blue 1402-1960): K.R. Briffa, T.J. Osborn, F.H. Schweingruber, I.C. Harris, P.D. Jones, S.G. Shiyatov, S.G. and E.A. Vaganov (2001). "Low-frequency temperature variations from a northern tree-ring density network". J. Geophys. Res. 106: 2929-2941.
(light turquoise 831-1992): J. Esper, E.R. Cook, and F.H. Schweingruber (2002). "Low-Frequency Signals in Long Tree-Ring Chronologies for Reconstructing Past Temperature Variability". Science 295 (5563): 2250-2253. doi:10.1126/science.1066208.
(green 200-1980): M.E. Mann and P.D. Jones (2003). "Global Surface Temperatures over the Past Two Millennia". Geophysical Research Letters 30 (15): 1820. doi:10.1029/2003GL017814.
(yellow 200-1995): P.D. Jones and M.E. Mann (2004). "Climate Over Past Millennia". Reviews of Geophysics 42: RG2002. doi:10.1029/2003RG000143
(orange 1500-1980): S. Huang (2004). "Merging Information from Different Resources for New Insights into Climate Change in the Past and Future". Geophys. Res Lett. 31: L13205. doi:10.1029/2004GL019781
(red 1-1979): A. Moberg, D.M. Sonechkin, K. Holmgren, N.M. Datsenko and W. Karlén (2005). "Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data". nature 443: 613-617. doi:10.1038/nature03265
(dark red 1600-1990): J.H. Oerlemans (2005). "Extracting a Climate Signal from 169 Glacier Records". Science 308: 675-677. doi:10.1126/science.1107046
(black 1856-2004): Instrumental data was jointly compiled by the w:Climatic Research Unit and the UK Meteorological Office Hadley Centre. Global Annual Average data set TaveGL2v [2] was used.