The limits and basis of logical tolerance: Carnap’s combination of Russell and Wittgenstein

<p><i>Notes</i>: All data series were filtered by 40-yr Butterworth low-pass filter prior to statistical analysis. Differencing:</p>△<p>no difference,</p>α<p>1^stdifference. Significance (2-tailed):</p>∧<p>p<0.1,</p><p>*p<0.05,</p><p>**p<0.01,</p><p>***p<0.001.</p

Climate Change and Macro-Economic Cycles in Pre-Industrial Europe

<div><p>Climate change has been proven to be the ultimate cause of social crisis in pre-industrial Europe at a large scale. However, detailed analyses on climate change and macro-economic cycles in the pre-industrial era remain lacking, especially within different temporal scales. Therefore, fine-grained, paleo-climate, and economic data were employed with statistical methods to quantitatively assess the relations between climate change and agrarian economy in Europe during AD 1500 to 1800. In the study, the Butterworth filter was adopted to filter the data series into a long-term trend (low-frequency) and short-term fluctuations (high-frequency). Granger Causality Analysis was conducted to scrutinize the associations between climate change and macro-economic cycle at different frequency bands. Based on quantitative results, climate change can only show significant effects on the macro-economic cycle within the long-term. In terms of the short-term effects, society can relieve the influences from climate variations by social adaptation methods and self-adjustment mechanism. On a large spatial scale, temperature holds higher importance for the European agrarian economy than precipitation. By examining the supply-demand mechanism in the grain market, population during the study period acted as the producer in the long term, whereas as the consumer in the short term. These findings merely reflect the general interactions between climate change and macro-economic cycles at the large spatial region with a long-term study period. The findings neither illustrate individual incidents that can temporarily distort the agrarian economy nor explain some specific cases. In the study, the scale thinking in the analysis is raised as an essential methodological issue for the first time to interpret the associations between climatic impact and macro-economy in the past agrarian society within different temporal scales.</p></div

Regression results on temperature change and macro-economy by 15 year low-pass filtered data.

<p>Significance:</p><p>*p < 0.05, and</p><p>**p < 0.01.</p><p>Regression results on temperature change and macro-economy by 15 year low-pass filtered data.</p

Visualization of the Causal Linkages in the Conceptual Model of Raw, Low-Pass Filtered, and High-Pass Filtered Data.

<p>Note: Column I represents raw data; Column II represents low-pass filtered data; and Column III represents high-pass filtered data. Row (a) represents Temperature; (b) Precipitation; (c) Grain Yield; (d) Grain Price; (e) CPI; (f) Real Wage; and (g) Population. Variables with obvious long-term trends, such as grain price, CPI, real wage, and population size, were linearly detrended. All data have been standardized.</p

Correlation Analysis Results of Causal Linkages in Figure 1.

<p><i>Notes</i>: Significance (2-tailed):</p><p>*p<0.05,</p><p>**p<0.01.</p

Correlation results on climate change and macro-economy.

<p>Significance:</p><p>*p < 0.05, and</p><p>**p < 0.01.</p><p>Correlation results on climate change and macro-economy.</p

The continuous wavelet power spectrum (left panels) and average wavelet power spectrum (right panels, solid lines) in 1- to 100-year band of (A, B) temperature in AD 1500–AD 1800; (C, D) grain yield ratio in AD 1500–AD 1800; (E, F) grain price in AD 1500–AD 1800; (G, H) CPI in AD 1500–AD 1800; (I, J) real wage in AD 1500–AD 1800; (K, L) population in AD 1500–AD 1800, and (M, N) precipitation in AD 1500–AD 1800 in Europe.

<p>The color code for coherence values transitions from dark blue (low values) to dark red (high values). The black line delimits the region that is not influenced by edge effects.</p

GCA Results for Each of the Causal Linkages by Raw Data.

<p><i>Notes</i>:</p><p>†For 0 AIC lag of population, we exclude link (8) from GCA due to data limitation. Differencing:</p>△<p>no difference,</p>#<p>2nd difference. Significance (2-tailed):</p>∧<p>p<0.1,</p><p>*p<0.05,</p><p>**p<0.01,</p><p>***p<0.001.</p

Location and geographic configuration of our study area (modified from [32–34]).

<p>Our study area is delineated into two regions (Regions A and B) according to the present-day 400 mm isohyet. The hydro-climate in Regions A and B is dominated by the Westerlies and ASM, respectively. Arrows represent ASM (including East ASM and Indian Summer Monsoon), Westerlies, and Winter Monsoon. The checkered belt is the region between the 200–400 mm isohyets, which is the approximate present-day northern fringe of ASM.</p

Wavelet coherency between the IRPV index and ocean-atmospheric modes.

<p>(<b>A</b>) AO [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131693#pone.0131693.ref028" target="_blank">28</a>] and the IRPV. (<b>B</b>) AMO [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131693#pone.0131693.ref060" target="_blank">60</a>] and the IRPV. (<b>C</b>) NAO [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131693#pone.0131693.ref061" target="_blank">61</a>] and the IRPV. (<b>D</b>) PDO [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131693#pone.0131693.ref062" target="_blank">62</a>] and the IRPV. (<b>E</b>) ENSO [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131693#pone.0131693.ref063" target="_blank">63</a>] and the IRPV. For the upper-left graphs of <b>A</b>–<b>E</b>, the color code for coherence values varies from dark blue (low values) to dark red (high values). The black curve indicates the cone of influence that delimits the region not influenced by edge effects and the dashed line show the α = 10% significance levels computed based on 1,000 Markov bootstrapped series. For the lower-left graphs of <b>A</b>–<b>E</b>, the dotted lines represent phase difference; the red line represents the phase of the ocean-atmospheric mode considered; and the blue lines represent the phase of IRPV. For the lower-right graph of <b>A</b>–<b>E</b>, the distribution of the phase difference of the two considered time-series is shown.</p