Foundational perspectives on causality in large-scale brain networks

Accepted Manuscript Foundational perspectives on causality in large-scale brain networks

Michael Mannino, Steven L. Bressler

PII: DOI: Reference:

S1571-0645(15)00161-X http://dx.doi.org/10.1016/j.plrev.2015.09.002 PLREV 656

To appear in:

Physics of Life Reviews

Received date: Accepted date:

3 September 2015 8 September 2015

Please cite this article in press as: Mannino M, Bressler SL. Foundational perspectives on causality in large-scale brain networks. Phys Life Rev (2015), http://dx.doi.org/10.1016/j.plrev.2015.09.002

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Highlights • An account of causality in large-scale brain networks is presented. • We clarify the concept of brain-network causality philosophically and scientifically. • A distinction is made between deterministic and probabilistic causality.

 Foundational Perspectives on Causality in Large-Scale Brain Networks

Michael Manninoa, Steven L. Bresslera,b* aCenter for Complex Systems and Brain Sciences, Florida Atlantic University, 777 Glades Road, Boca

Raton, FL 33431 bDepartment

of Psychology, Florida Atlantic University 777 Glades Road. Boca Raton, FL 33431 *Corresponding Author

Abstract  ’”‘ˆ—•‹‘ ‘ˆ ”‡…‡– ™‘” ‹ …‘‰‹–‹˜‡ ‡—”‘•…‹‡…‡ Šƒ• „‡‡ …‘…‡”‡† ™‹–Š –Š‡ ‡†‡ƒ˜‘” –‘ —…‘˜‡”…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•Ǥ‘™‡˜‡”ǡ†‡•’‹–‡–Š‡ˆƒ…––Šƒ–ƒ›’ƒ’‡”• ‰‹˜‡ƒ‘†–‘–Š‡‹’‘”–ƒ––Š‡‘”‡–‹…ƒŽ…ŠƒŽŽ‡‰‡•’‘•‡†„›–Š‡…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›ǡ–Š‹•‡š’Ž‘•‹‘‘ˆ ”‡•‡ƒ”…Š Šƒ• ‰‡‡”ƒŽŽ› ‘– „‡‡ ƒ……‘’ƒ‹‡† „› ƒ ”‹‰‘”‘—• …‘…‡’–—ƒŽ ƒƒŽ›•‹• ‘ˆ –Š‡ ƒ–—”‡ ‘ˆ …ƒ—•ƒŽ‹–›‹–Š‡„”ƒ‹ǤŠ‹•”‡˜‹‡™’”‘˜‹†‡•„‘–Šƒdescriptiveƒ†prescriptiveƒ……‘—–‘ˆ–Š‡ƒ–—”‡ ‘ˆ…ƒ—•ƒŽ‹–›ƒ•ˆ‘—†™‹–Š‹ƒ†„‡–™‡‡Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•Ǥ •Š‘”–ǡ‹–•‡‡•–‘…Žƒ”‹ˆ›–Š‡ …‘…‡’– ‘ˆ …ƒ—•ƒŽ‹–› ‹ Žƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹ ‡–™‘”• „‘–Š ’Š‹Ž‘•‘’Š‹…ƒŽŽ› ƒ† •…‹‡–‹ˆ‹…ƒŽŽ›Ǥ Š‹• ‹• ƒ……‘’Ž‹•Š‡† „› „”‹‡ˆŽ› ”‡˜‹‡™‹‰ –Š‡ ”‹…Š ’Š‹Ž‘•‘’Š‹…ƒŽ Š‹•–‘”› ‘ˆ ™‘” ‘ …ƒ—•ƒŽ‹–›ǡ ‡•’‡…‹ƒŽŽ› ˆ‘…—•‹‰ ‘ …‘–”‹„—–‹‘• „› ƒ˜‹† —‡ǡ ƒ—‡Ž ƒ–ǡ ‡”–”ƒ† —••‡ŽŽǡ ƒ† Š”‹•–‘’Š‡” ‹–…Š…‘…Ǥ‡‰‘‘–‘†‹•…—••–Š‡‹’ƒ…––Šƒ–˜ƒ”‹‘—•‹–‡”’”‡–ƒ–‹‘•‘ˆ‘†‡”’Š›•‹…•Šƒ˜‡Šƒ† ‘ ‘—” —†‡”•–ƒ†‹‰ ‘ˆ …ƒ—•ƒŽ‹–›Ǥ Š”‘—‰Š‘—– ƒŽŽ –Š‹•ǡ ƒ …‡–”ƒŽ ˆ‘…—• ‹• –Š‡ †‹•–‹…–‹‘ „‡–™‡‡ –Š‡‘”‹‡• ‘ˆ †‡–‡”‹‹•–‹… …ƒ—•ƒŽ‹–› ȋȌǡ ™Š‡”‡„› …ƒ—•‡• —‹“—‡Ž› †‡–‡”‹‡ –Š‡‹” ‡ˆˆ‡…–•ǡ ƒ† ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›ȋȌǡ™Š‡”‡„›…ƒ—•‡•…Šƒ‰‡–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‘……—””‡…‡‘ˆ–Š‡‹”‡ˆˆ‡…–•Ǥ‡ ƒ”‰—‡ –Šƒ–ǡ ‰‹˜‡ –Š‡ –‘’‘Ž‘‰‹…ƒŽ …‘’Ž‡š‹–› ‘ˆ ‹–• Žƒ”‰‡Ǧ•…ƒŽ‡ …‘‡…–‹˜‹–›ǡ –Š‡ „”ƒ‹ •Š‘—Ž† „‡ …‘•‹†‡”‡† ƒ• ƒ …‘’Ž‡š •›•–‡ ƒ† ‹–• …ƒ—•ƒŽ ‹ˆŽ—‡…‡• –”‡ƒ–‡† ƒ• ’”‘„ƒ„‹Ž‹•–‹… ‹ ƒ–—”‡Ǥ ‡ …‘…Ž—†‡ –Šƒ–  ‹• ™‡ŽŽ •—‹–‡† ˆ‘” ‡š’Žƒ‹‹‰ …ƒ—•ƒŽ‹–› ‹ –Š‡ „”ƒ‹ ˆ‘” –Š”‡‡ ”‡ƒ•‘•ǣ ȋͳȌ „”ƒ‹ …ƒ—•ƒŽ‹–›‹•‘ˆ–‡—–—ƒŽǢȋʹȌ…‘‡…–‹‘ƒŽ…‘˜‡”‰‡…‡†‹…–ƒ–‡•–Šƒ–‘Ž›”ƒ”‡Ž›‹•–Š‡ƒ…–‹˜‹–›‘ˆ‘‡ ‡—”‘ƒŽ ’‘’—Žƒ–‹‘ —‹“—‡Ž› †‡–‡”‹‡† „› ƒ‘–Š‡” ‘‡Ǣ ƒ† ȋ͵Ȍ –Š‡ …ƒ—•ƒŽ ‹ˆŽ—‡…‡• ‡š‡”–‡† „‡–™‡‡‡—”‘ƒŽ’‘’—Žƒ–‹‘•ƒ›‘–Šƒ˜‡‘„•‡”˜ƒ„Ž‡‡ˆˆ‡…–•Ǥ—„‡”‘ˆ†‹ˆˆ‡”‡––‡…Š‹“—‡•ƒ”‡ …—””‡–Ž›ƒ˜ƒ‹Žƒ„Ž‡–‘…Šƒ”ƒ…–‡”‹œ‡…ƒ—•ƒŽ‹ˆŽ—‡…‡‹–Š‡„”ƒ‹Ǥ›’‹…ƒŽŽ›ǡ–Š‡•‡–‡…Š‹“—‡•“—ƒ–‹ˆ› –Š‡•–ƒ–‹•–‹…ƒŽŽ‹‡Ž‹Š‘‘†–Šƒ–ƒ…Šƒ‰‡‹–Š‡ƒ…–‹˜‹–›‘ˆ‘‡‡—”‘ƒŽ’‘’—Žƒ–‹‘ƒˆˆ‡…–•–Š‡ƒ…–‹˜‹–›‹ ƒ‘–Š‡”Ǥ‡ƒ”‰—‡–Šƒ––Š‡•‡‡ƒ•—”‡•ƒ……‡••–Š‡‹Š‡”‡–Ž›’”‘„ƒ„‹Ž‹•–‹…ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡• ‹ –Š‡ „”ƒ‹ǡ ƒ† ƒ”‡ –Š—• „‡––‡” •—‹–‡† ˆ‘” Žƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹ ‡–™‘” ƒƒŽ›•‹• –Šƒ ƒ”‡ Ǧ„ƒ•‡† ‡ƒ•—”‡•Ǥ —” ™‘” ‹• …‘•‹•–‡– ™‹–Š ”‡…‡– ƒ†˜ƒ…‡• ‹ –Š‡ ’Š‹Ž‘•‘’Š‹…ƒŽ •–—†› ‘ˆ ’”‘„ƒ„‹Ž‹•–‹… …ƒ—•ƒŽ‹–›ǡ ™Š‹…Š ‘”‹‰‹ƒ–‡† ˆ”‘ ‹Š‡”‡– …‘…‡’–—ƒŽ ’”‘„Ž‡• ™‹–Š †‡–‡”‹‹•–‹… ”‡‰—Žƒ”‹–› –Š‡‘”‹‡•Ǥ –ƒŽ•‘”‡•‘ƒ–‡•™‹–Š…‘…‡’–•‘ˆ•–‘…Šƒ•–‹…‹–›–Šƒ–™‡”‡‹˜‘Ž˜‡†‹‡•–ƒ„Ž‹•Š‹‰‘†‡” ’Š›•‹…•Ǥ •—ƒ”›ǡ™‡ƒ”‰—‡–Šƒ–’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›‹•ƒ…‘…‡’–—ƒŽŽ›ƒ’’”‘’”‹ƒ–‡ˆ‘—†ƒ–‹‘ ˆ‘”†‡•…”‹„‹‰‡—”ƒŽ…ƒ—•ƒŽ‹–›‹–Š‡„”ƒ‹Ǥ

Keywords: brain; large-scale neurocognitive networks; causality; probability; determinism; brain connectivity



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The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. – ‡”–”ƒ†—••‡ŽŽȋͳͻͳ͵Ȍ

1. Introduction By virtue of what is one thing or event the cause of another thing or event? Š‡“—‡•–‹‘‹•ƒ‘Ž†ƒ†ˆƒ‹Ž‹ƒ”‘‡ǡƒ†Šƒ•„‡‡…ƒ‘—ˆŽƒ‰‡†‹˜ƒ”‹‘—•…Ž‘–Š• –Š”‘—‰Š‘—––Š‡Š‹•–‘”›‘ˆ•…‹‡…‡ǡƒ–Š‡ƒ–‹…•ƒ†’Š‹Ž‘•‘’Š›Ǥ –‹•…Ž‘•‡Ž›”‡Žƒ–‡† –‘˜ƒ”‹‘—•‘–Š‡”’”‘„Ž‡•…‘…‡”‹‰–Š‡ˆ‘—†ƒ–‹‘•‘ˆ…ƒ—•ƒŽ‹–›ǣ™Šƒ–‹•–Š‡ ˆ—†ƒ‡–ƒŽƒ–—”‡‘ˆ…ƒ—•ƒŽ”‡Žƒ–‹‘•ǫ •…ƒ—•ƒŽ‹–›”‡ƒŽǡƒ†a fortioriǡ‘–‘Ž‘‰‹…ƒŽŽ› ‹†‡’‡†‡–‘ˆ–Š‡‹†ǡ‘”‹•‹–‡”‡Ž›ƒ‡’‹•–‡‹…Ž‹‹–ƒ–‹‘ǫ –Š‡…‘–‡š–‘ˆ •–ƒ–‹•–‹…ƒŽƒƒŽ›•‹•ǡƒ”‡…ƒ—•ƒŽ”‡Žƒ–‹‘•‹Š‡”‡–Ž›†‡–‡”‹‹•–‹…‘”’”‘„ƒ„‹Ž‹•–‹…ǫ ‹ƒŽŽ›ǡƒ†’‡”Šƒ’•‘•–‹’‘”–ƒ–Ž›ˆ‘”™Šƒ–ˆ‘ŽŽ‘™•ǣ‹•…ƒ—•ƒŽ‹–›ƒˆˆ‡…–‡†„› …‘’Ž‡š‹–›ǫŠƒ–‹•ǡ‹•‹–‡…‡••ƒ”›–‘‡š’ƒ†‘—”…‘…‡’–‹‘‘ˆ…ƒ—•ƒŽ‹–›–‘…‘˜‡” …ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡Š—ƒ„”ƒ‹ǡ™Š‹…Šƒ›„‡ƒˆˆ‡…–‡†„›‹–•’”‘’‡”–‹‡•ƒ•ƒ …‘’Ž‡šƒ†ƒ’–‹˜‡„‹‘Ž‘‰‹…ƒŽ•›•–‡ǫ”ǡ‘”‡‰‡”ƒ‡–‘–Š‡…—””‡–†‹•…—••‹‘ǡ —•––Š‡…ƒ—•ƒŽ‹ˆŽ—‡…‡•„‡–™‡‡‡—”‘ƒŽ’‘’—Žƒ–‹‘•ͳ‹…‘’Ž‡š„”ƒ‹•›•–‡• „‡†‡•…”‹„‡†‹ƒ‘”‡…‘’”‡Š‡•‹˜‡™ƒ›Ȃ™‹–Šƒ†‹ˆˆ‡”‡–ˆ‘—†ƒ–‹‘ƒŽ …‘…‡’–‹‘Ȃ–Šƒ‹ˆŽ—‡…‡•‹•‹’Ž‡’Š›•‹…ƒŽ•›•–‡•ǫ ‹•–‘”‹…ƒŽƒ•™‡ŽŽƒ•‘†‡”ƒ––‡’–•–‘ˆ‘”—Žƒ–‡ƒ—ƒ„‹‰—‘—• …‘…‡’–—ƒŽ†‡•…”‹’–‹‘‘ˆ…ƒ—•ƒŽ‹–›ƒ”‡”‹…Šƒ†’Ž‡–‹ˆ—ŽǢ‘†‡”’Š‹Ž‘•‘’Š‡”••—…Š ƒ•ƒ˜‹†—‡ǡ ƒ—‡Žƒ–ǡ‡”–”ƒ†—••‡ŽŽǡƒ…›ƒ”–™”‹‰Š–ǡƒ–”‹…—’’‡•ǡ ƒ†Š”‹•–‘’Š‡”‹–…Š…‘…ǡƒ‘‰‘–Š‡”•ǡŠƒ˜‡†‡˜‡Ž‘’‡†„‘–Š‘–‘Ž‘‰‹…ƒŽƒ† ‡’‹•–‡‘Ž‘‰‹…ƒŽƒ……‘—–•‘ˆ…ƒ—•ƒŽ‹–›Ǥ‘”‡‘˜‡”ǡ‘†‡”ƒ–Š‡ƒ–‹…‹ƒ•ǡ •–ƒ–‹•–‹…‹ƒ•ǡƒ†‡…‘‘‹•–•ǡ•—…Šƒ•—•–‹”ƒ†ˆ‘”†‹ŽŽǡ‘”„‡”–‡‹‡”ƒ†Ž‹˜‡

”ƒ‰‡”Šƒ˜‡†‡˜‡Ž‘’‡†‡–Š‘†‘Ž‘‰‹‡•ˆ‘”‡ƒ•—”‹‰…ƒ—•ƒŽ‹–›™‹–Š•–ƒ–‹•–‹…ƒŽ–‘‘Ž• ˆ”‘–Š‡’‡”•’‡…–‹˜‡‘ˆ•–‘…Šƒ•–‹…’”‘…‡••‡•Ǥ‡˜‡”–Š‡Ž‡••ǡ–Š‡„ƒ•‹…ƒ–—”‡‘ˆ …ƒ—•ƒŽ‹–›™‹–Š‹‘†‡”…‘…‡’–‹‘•”‡ƒ‹•–‘„‡…Žƒ”‹ˆ‹‡†ǡ‡•’‡…‹ƒŽŽ›ˆ‘”…‘’Ž‡š •›•–‡••—…Šƒ•–Š‡Š—ƒ„”ƒ‹Ǥ –Š‹•”‡˜‹‡™ǡ™‡ƒ††”‡••…Žƒ••‹…ƒŽƒ† …‘–‡’‘”ƒ”›™‘”‹’Š‹Ž‘•‘’Š›ǡ…‘‰‹–‹˜‡‡—”‘•…‹‡…‡ǡƒ†•–ƒ–‹•–‹…•ǡƒ† ’”‘’‘•‡ˆ—–—”‡”‡•‡ƒ”…Šƒ˜‡—‡•‘ˆƒ’’”‘ƒ…Š–‘ƒ…‡–”ƒŽǡ„—–—ƒ•™‡”‡†“—‡•–‹‘ǣ ™Šƒ–‹•–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡Š—ƒ„”ƒ‹ǡ•’‡…‹ˆ‹…ƒŽŽ›‹Žƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹‡–™‘”•ǫ†‘”‡‰‡‡”ƒŽŽ›ǡ™Šƒ–‹•–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹ …‘’Ž‡š•›•–‡•ǫ –‹•Š‹‰ŠŽ›†‘—„–ˆ—Ž–Šƒ–—‡‘”ƒ–…‘•‹†‡”‡†™Šƒ–•‘”–•‘ˆ …ƒ—•ƒŽ‹–›‘……—”‹‘”‰ƒ‹œ‡†…‘’Ž‡š•›•–‡•ǡˆ‘”‡šƒ’Ž‡ǡ…‘—’Ž‡†‡—”‘ƒŽ  ͳŠ‹•’ƒ’‡”†‹•…—••‡•‡—”ƒŽ…ƒ—•ƒŽ‹–›ƒ––Š‡Ž‡˜‡Ž‘ˆ‡—”‘ƒŽ’‘’—Žƒ–‹‘•„‡…ƒ—•‡‹–‹•–Š‡‡—”‘ƒŽ ’‘’—Žƒ–‹‘–Šƒ–‹•–Š‘—‰Š––‘”‡’”‡•‡––Š‡—‹–‘ˆ‹–‡”ƒ…–‹‘‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ǡ™Š‘•‡ ‘’‡”ƒ–‹‘•ƒ”‡’”‘’‘•‡†–‘—†‡”Ž‹‡…‘‰‹–‹‘‹–Š‡„”ƒ‹ȋ•‡‡ȏͷ͸ȐȌǤ‡—”ƒŽ…ƒ—•ƒŽ‹–›ƒ›ƒŽ•‘ƒ’’Ž› –‘–Š‡‹–‡”ƒ…–‹‘•‘ˆ‹†‹˜‹†—ƒŽ‡—”‘•™‹–Š‹ƒ’‘’—Žƒ–‹‘™Š‡”‡˜‡”ƒ•‹‹Žƒ”…‘‡…–‹‘ƒŽ –‘’‘Ž‘‰›’”‡˜ƒ‹Ž•ƒ––Š‡•‹‰Ž‡Ǧ‡—”‘Ž‡˜‡ŽǤ





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’‘’—Žƒ–‹‘•‹–Š‡Š—ƒ„”ƒ‹Ǣ‡˜‡”–Š‡Ž‡••ǡ‹–‹•–‹‡ǡ‘…‡ƒ‰ƒ‹‹–Š‡Š‹•–‘”›‘ˆ •…‹‡…‡ǡˆ‘”–Š‡‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›–‘„‡conceptuallyexpandedǡ–Š‹•–‹‡‹–‘–Š‡ •–—†›‘ˆ„”ƒ‹‡–™‘”•Ǥ ‹˜‡–Š‹•ƒ„‹–‹‘—•…Žƒ‹ǡ–Š‡…‡–”ƒŽ‰‘ƒŽ‘ˆ–Š‹•”‡˜‹‡™‹• –‘‡šƒ‹‡ǡ‹–Š‡…‘–‡š–‘ˆƒ…‘’Ž‡š„‹‘Ž‘‰‹…ƒŽ•›•–‡ǡ™Š‡–Š‡”–Š‡…Žƒ••‹…ƒŽ ‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹•˜ƒŽ‹†Ǥ Š‡…Žƒ••‹…ƒŽ…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›‹•†‹•…—••‡†‹‘”‡†‡–ƒ‹Ž„‡Ž‘™Ǥ‡”‡™‡ ‘–‡–Šƒ–‡˜‡„‡ˆ‘”‡–Š‡ƒ†˜‡–‘ˆ‘†‡”’Š›•‹…•ǡ—‡™ƒ•™‡ŽŽ‘™ˆ‘”Š‹• •‡’–‹…ƒŽ‡Ž‹‹ƒ–‹‘‘ˆ–Š‡…‘…‡’–‘ˆ‡…‡••‹–›ˆ”‘…ƒ—•ƒŽ‹–›ǡ–Šƒ–‹•ǡˆ‘”…Žƒ‹‹‰ –Šƒ––Š‡‘Ž›„ƒ•‹•ˆ‘”ƒ…ƒ—•ƒŽ”‡Žƒ–‹‘„‡–™‡‡–™‘‡˜‡–•‹••‹’Ž›–Š‡‹†ǯ• ’‡”…‡’–‹‘–Šƒ––Š‡‡˜‡–•ƒ”‡”‡’‡ƒ–‡†Ž›ȋ‘”…‘•–ƒ–Ž›Ȍ…‘Œ‘‹‡†Ǥ—‡ …‘˜‡”–‡†–Š‡‘„Œ‡…–‹˜‡”‡‰—Žƒ”‹–›„‡–™‡‡‡˜‡–•‹–‘ƒ•—„Œ‡…–‹˜‡ ȋ”‡’”‡•‡–ƒ–‹‘ƒŽ‹•–Ȍ‡š’‡”‹‡…‡Ǥ ‘”—‡ǡ–Š‡”‡‹•‘…ƒ—•ƒŽ‹–›ƒ’ƒ”–ˆ”‘–Š‡ ’‡”…‡’–‹‘‘ˆ‡˜‡–•–Šƒ–ƒ”‡•–”‹…–Ž›…‘””‡Žƒ–‡†‹–‹‡Ǥƒ–ǡ‹ƒ•–—‹‰ ˆ‘”‡•Šƒ†‘™‹‰‘ˆ‘†‡”’‡”…‡’–—ƒŽ‡—”‘•…‹‡…‡ǡƒ”‰—‡†–Šƒ–…ƒ—•ƒŽ‹–›‹•ƒ •›–Š‡–‹…a priori Œ—†‰‡–Ǥ……‘”†‹‰–‘ƒ–ǡ‡–ƒŽ”‡’”‡•‡–ƒ–‹‘•ǡ‹…Ž—†‹‰ …ƒ—•ƒŽ‹–›ǡƒ”‡‘–•‹’Ž›”‡ˆŽ‡…–‹‘•‘ˆ–Š‡™‘”Ž†ǡ„—–ƒ”‡…ƒ–‡‰‘”‹‡•‘ˆ —†‡”•–ƒ†‹‰—•‡†–‘ƒ…–‹˜‡Ž›‹–‡”’”‡–‡˜‡–•‹–Š‡™‘”Ž†ǤŠ‡‹’Ž‹…ƒ–‹‘‹•–Šƒ– …ƒ—•ƒŽ‹–›‡‡†‘–„‡†‡–‡”‹‡†„›‡š–‡”ƒŽ‡˜‡–•Ǥ ‘‹‰‡˜‡ˆ—”–Š‡”ǡ‡”–”ƒ† —••‡ŽŽƒ”‰—‡†–Šƒ–‘†‡”•…‹‡…‡Šƒ•†‡‘•–”ƒ–‡†–Šƒ–…ƒ—•ƒŽ‹–›‡‡†‘–„‡ ‹–”‹•‹…ƒŽŽ›–‹‡†–‘†‡–‡”‹‹•ǤŠ—•ǡ•‹…‡–Š‡–‹‡‘ˆ—••‡ŽŽǡƒ†‹•–‹…–‹‘‹• ƒ†‡„‡–™‡‡†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›ƒ†’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›Ǥ•™‡•ŠƒŽŽ•‡‡ǡ ‘–‹˜ƒ–‹‘•ˆ‘”’”‘„ƒ„‹Ž‹•–‹…–Š‡‘”‹‡•‘ˆ…ƒ—•ƒŽ‹–›•–‡ˆ”‘†‹ˆˆ‹…—Ž–‹‡•™‹–Š•‘Ǧ …ƒŽŽ‡†”‡‰—Žƒ”‹–›–Š‡‘”‹‡•ǡ™Š‹…Š‘”‹‰‹ƒ–‡‹—‡ǯ•‹†‡ƒ‘ˆ…‘•–ƒ–…‘Œ—…–‹‘•Ǥ Š‹•”‡˜‹‡™…‘•‹†‡”•–Š‡’”‘’‘•‹–‹‘–Šƒ–’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›‹•™‡ŽŽ •—‹–‡†ˆ‘”—†‡”•–ƒ†‹‰…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹ǡ™Š‡”‡„‹Ǧ†‹”‡…–‹‘ƒŽƒ† …‘˜‡”‰‡–’ƒ–Š™ƒ›•’Žƒ›ƒƒŒ‘””‘Ž‡‹’”‘…‡••‹‰Ǥ—…Š…‘’Ž‡š‘”‰ƒ‹œƒ–‹‘ƒŽ ˆ‡ƒ–—”‡•‘ˆ„”ƒ‹…‘‡…–‹˜‹–›‹’Ž›–Šƒ–‹–‡”ƒ…–‹‘‘†‡Ž•„ƒ•‡†‘Ž‹‡ƒ” –”ƒ•‹••‹‘ˆ”‘—‹–ƒ”›•‡†‡”•–‘—‹–ƒ”›”‡…‡‹˜‡”•ƒ”‡–‘‘”‹‰‹†ǤŠ‡ˆ‹”•–ŠƒŽˆ‘ˆ –Š‡”‡˜‹‡™…‘•‹•–•‘ˆƒ†‹•…—••‹‘‘ˆ…Žƒ••‹…ƒŽ‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›ǡ‹‘”†‡”–‘ ’”‘˜‹†‡ƒ„”‹‡ˆ’Š‹Ž‘•‘’Š‹…ƒŽ„ƒ…‰”‘—†ˆ‘”–Š‡‡•—‹‰†‹•…—••‹‘ǤŠ‡…‘…‡’–‘ˆ …ƒ—•ƒŽ‹–›‹•”‡…ƒ•–‹ƒ‡™Ž‹‰Š––‘Š‘’‡ˆ—ŽŽ›‹ŽŽ—‹ƒ–‡–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹–›‹ „”ƒ‹‡–™‘”•ƒ†–Š‡‡–Š‘†•—•‡†–‘—…‘˜‡”‹–ǤŠ‡•‡…‘†ŠƒŽˆ‹•ƒ†‹•…—••‹‘ ‘ˆ–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹–›‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ǡƒ†–Š‡‡ƒ•—”‡‡–‘ˆ …ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡•‡‡–™‘”•Ǥ‡ƒ”‰—‡–Šƒ–…Žƒ••‹…ƒŽ…‘…‡’–‹‘•‘ˆ…ƒ—•ƒŽ‹–› †‘‘–ƒ’’Ž›–‘…ƒ—•ƒŽ‹–›‹–Š‡„”ƒ‹ǡ™Š‹…Š—•–„‡…‘…‡‹˜‡†‹ƒˆ—†ƒ‡–ƒŽŽ› †‹ˆˆ‡”‡–ƒ‡”–Šƒ…ƒ—•ƒŽ‹–›‹‘Ǧ…‘’Ž‡š’Š›•‹…ƒŽ•›•–‡•Ǥ



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2. Concepts of Causality2 Š‡•–ƒ†ƒ”†ǡ‘”…Žƒ••‹…ƒŽǡ†‡ˆ‹‹–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹•‰‹˜‡„›ǣ ȋͳȌ ‘”–‘Dz…ƒ—•‡dz‹–‹•„‘–Šnecessaryƒ†•—ˆˆ‹…‹‡––Šƒ–™Š‡Šƒ’’‡•ǡ  Šƒ’’‡•ǤŠƒ–‹•ǡ‹ˆ…ƒ—•‡•ǡmustˆ‘ŽŽ‘™ȏͳȐǤ Š‹•†‡ˆ‹‹–‹‘‹…Ž—†‡•…‘…‡’–•‘ˆ„‘–Š–Š‡…ƒ—•ƒŽ”‡Žƒ–‹‘ǡ‹Ǥ‡Ǥǡ–Š‡”‡Žƒ–‹‘•Š‹’‘” Ž‹„‡–™‡‡ƒ†ǡƒ†–Š‡…ƒ—•ƒŽ”‡Žƒ–ƒǡ–Š‡‹–‡•–Šƒ–•Šƒ”‡–Š‹•Ž‹ǤŠ‡„ƒ•‹• ˆ‘”–Š‡…ƒ—•ƒŽŽ‹ǡƒ†–Š‡–›’‡‘ˆ–Š‹‰–Šƒ–ƒ”‡…ƒ—•ƒŽ”‡Žƒ–ƒǡ‡Ǥ‰Ǥǡ‘„Œ‡…–•ǡ‡˜‡–•ǡ ‡–…Ǥǡƒ”‡„›‘‡ƒ•ƒ‰”‡‡†—’‘ȏʹǡ͵ǡͶȐǤ‘”‡‘˜‡”ǡ–Š‡™‘”†•Dz—•–dzƒ† Dz‡…‡••ƒ”›dz‹–Š‡ƒ„‘˜‡†‡ˆ‹‹–‹‘ƒ›ǡƒ•‡”–”ƒ†—••‡ŽŽ•–ƒ–‡†ǡ„‡Dz”‡Ž‹…•‘ˆƒ „›‰‘‡ƒ‰‡Ǥdz ‘”‹•–ƒ…‡ǡŠ‘™•Š‘—Ž†‘‡ƒ‡•‡•‡‘ˆ–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹–›‹ ˆ‘ŽŽ‘™‹‰•–ƒ–‡‡–•ǫ ȋʹȌŠ‡„ƒ•‡„ƒŽŽ…ƒ—•‡†–Š‡™‹†‘™–‘•Šƒ––‡”Ǥ ȋ͵Ȍ‘‹‰…ƒ—•‡•Ž—‰…ƒ…‡”Ǥ͵ ȋͶȌŠ‹•’Š›•‹…ƒŽ•–ƒ–‡…ƒ—•‡†–Šƒ–‡–ƒŽ•–ƒ–‡Ǥ ȋͷȌŠ‡’ƒ–‹‡–ǯ•ˆŽ—™ƒ•…ƒ—•‡†„›Š‡”‡š’‘•—”‡–‘•‘‡‘‡‡Ž•‡™‹–Š–Š‡ˆŽ—Ǥ ȋ͸Ȍ‡˜‡”ƒŽˆƒ…–‘”•ǡ™‘”‹‰–‘‰‡–Š‡”ǡ…ƒ—•‡†–Š‡Š—””‹…ƒ‡–‘ˆ‘”Ǥ ȋ͹Ȍ˜‡”›–Š‹‰–Šƒ–Šƒ•ƒ„‡‰‹‹‰‘ˆ‹–•‡š‹•–‡…‡—•–Šƒ˜‡ƒ…ƒ—•‡‘ˆ‹–• ‡š‹•–‡…‡ǤͶ •–Š‡…ƒ—•ƒŽ‹–›‹ȋʹȌ‹†‡–‹…ƒŽ–‘–Šƒ–‹ȋ͵Ȍ‘”ȋ͹Ȍǫ †‡‡†ǡ†‘ƒŽŽ•‹š‘ˆ–Š‡•‡ •–ƒ–‡‡–•”‡ˆ‡”–‘…ƒ—•ƒŽ‹–›‹–Š‡•ƒ‡™ƒ›ǫ‘–Š‡›mean–Š‡•ƒ‡–Š‹‰ǫ ˆ‘–ǡ …ƒ–Š‡›„‡ˆ‘”ƒŽŽ›†‹•–‹‰—‹•Š‡†ǫ —”–Š‡”‘”‡ǡ†‘‡•ȋͳȌ•‡”˜‡ƒ•–Š‡„ƒ•‹•ˆ‘”ȋ͵Ȍǫ Žƒ••‹…ƒŽŽ›ǡ…ƒ—•ƒŽ‹–›Šƒ•„‡‡™‡††‡†–‘†‡–‡”‹‹•Ǥ‘™‡˜‡”ǡ–Š‡ ƒˆ‘”‡‡–‹‘‡†’”‘’‘•‹–‹‘•ǡ‹ƒ††‹–‹‘–‘ƒ›‘ˆ–Š‡‡’‹”‹…ƒŽ”‡•—Ž–•ˆ”‘ ‘†‡”’Š›•‹…•ǡƒ†ǡƒ•™‡†‡‘•–”ƒ–‡‹–Š‹•”‡˜‹‡™ǡ‡–Š‘†•–Šƒ–“—ƒ–‹ˆ› …ƒ—•ƒŽ‹ˆŽ—‡…‡‹…‘’Ž‡š„‹‘Ž‘‰‹…ƒŽ•›•–‡•Ž‹‡–Š‡Š—ƒ„”ƒ‹ǡ†‡‘•–”ƒ–‡ –Šƒ–†‡–‡”‹‹•‹•‹ƒ†‡“—ƒ–‡–‘†‡•…”‹„‡…ƒ—•ƒŽ‹–›‹ƒ›•‹–—ƒ–‹‘•ǤŠ—•ǡ–Š‡ …Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹…†‡•…”‹’–‹‘ƒ›„‡‹ƒ’’”‘’”‹ƒ–‡ƒ•ƒ‰‡‡”ƒŽˆ‘”—Žƒ–‹‘‘ˆ …ƒ—•ƒŽ‹–›ǡƒ†•‘ǡ™‡™‹ŽŽ‡šƒ‹‡‘–‹˜ƒ–‹‘•ˆ‘”†‹•…ƒ”†‹‰–Š‡…Žƒ••‹…ƒŽ †‡–‡”‹‹•–‹……‘…‡’–‹‘‘ˆ…ƒ—•ƒŽ‹–›Ǥ ‹”•–ǡŠ‘™‡˜‡”ǡ‹–™‹ŽŽ„‡—•‡ˆ—Ž–‘„”‹‡ˆŽ› ‡šƒ‹‡–Š‡”‹•–‘–‡Ž‹ƒ…‘…‡’–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǡƒ†–Š‡…‘…‡–”ƒ–‡‘–Š”‡‡ ‘”‡”‡…‡–Š‹•–‘”‹…ƒŽƒ––‡’–•–‘—…‘˜‡”–Š‡ƒ–—”‡‘ˆ…ƒ—•ƒŽ‹–›ǣ–Š‘•‡‘ˆ—‡ǡ ƒ–ǡƒ†—••‡ŽŽǤ  ʹŠ‡–‡”•Ǯ…ƒ—•ƒŽ‹–›ǯƒ†Ǯ…ƒ—•ƒ–‹‘ǯƒ”‡‰‡‡”ƒŽŽ›…‘•‹†‡”‡†–‘„‡‡“—‹˜ƒŽ‡–Ǥ‡—•‡Ǯ…ƒ—•ƒŽ‹–›ǯ

Š‡”‡ǡƒŽ–Š‘—‰ŠǮ…ƒ—•ƒ–‹‘ǯ‹•‘ˆ–‡—•‡†–‘”‡’”‡•‡–ƒ…ƒ—•ƒŽ”‡Žƒ–‹‘‹–Š‡’Š‹Ž‘•‘’Š‹…ƒŽŽ‹–‡”ƒ–—”‡Ǥ ͵—•–‹”ƒ†ˆ‘”†‹ŽŽ™ƒ•–Š‡ˆ‹”•––‘‡ƒ•—”‡ƒ…‘””‡Žƒ–‹‘„‡–™‡‡•‘‹‰ƒ†Ž—‰…ƒ…‡”ȏͷǡ͸ȐǤ ͶŠ‹•…‘‡•ˆ”‘–Š‡ƒŽƒ‘•‘Ž‘‰‹…ƒŽ”‰—‡–ˆ‘” ‘†ǯ•‡š‹•–‡…‡ǡƒƒ”‰—‡–„ƒ•‡†‘ …ƒ—•ƒŽ‹–›Ǥ



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2.1 The Ontology and Epistemology of Causality: Aristotle, Hume, Kant, and Russell ƒ—•ƒŽ‹–›‹”‹•–‘–‡Ž‹ƒ’Š‹Ž‘•‘’Š›‹•—…Š„”‘ƒ†‡”‹•…‘’‡–Šƒƒ”‡ ‘†‡”…‘…‡’–‹‘•ǡ„—–”‹•–‘–Ž‡„‡Ž‹‡˜‡†–Šƒ–…ƒ—•ƒŽ‹–›‹•ƒ‘„Œ‡…–‹˜‡ǡ †‡–‡”‹‹•–‹…ˆ‡ƒ–—”‡‘ˆ–Š‡™‘”Ž†ȏ͹ǡͺȐǤŽ–Š‘—‰Š•‘‡‡Ž‡‡–•‘ˆ”‹•–‘–Ž‡ǯ• ’Š‹Ž‘•‘’Š›ƒ”‡•–‹ŽŽƒ……‡’–‡†–‘†ƒ›ǡ–Š‡ƒ…‹‡–”‹•–‘–‡Ž‹ƒ†‡ˆ‹‹–‹‘‘ˆ…ƒ—•ƒŽ‹–› Šƒ•„‡‡”‡‡˜ƒŽ—ƒ–‡†ǡ’ƒ”–‹…—Žƒ”Ž›ƒˆ–‡”—‡ƒ†ƒ–Žƒ–‡”‡•’‘—•‡†‘”‡ ’Š‹Ž‘•‘’Š‹…ƒŽŽ›•‘’Š‹•–‹…ƒ–‡†…‘…‡’–‹‘•ǡƒ†–Š—•™‡„‡Ž‹‡˜‡–Šƒ–”‹•–‘–Ž‡ǯ• ƒ……‘—–‘ˆ…ƒ—•ƒŽ‹–›‹••‘‡™Šƒ–”‡‘˜‡†™Š‡…‘•‹†‡”‡†‹–Š‡…‘–‡š–‘ˆ ˆ‘—†ƒ–‹‘ƒŽ…‘…‡’–•‘ˆ…ƒ—•ƒŽ‹–›‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•Ǥ —‡ǯ•ƒ……‘—–‘ˆ…ƒ—•ƒŽ‹–›•–‡‡†ǡŽ‹‡ƒŽŽŠ‹•’Š‹Ž‘•‘’Š‹…ƒŽ …‘–”‹„—–‹‘•ǡˆ”‘Š‹•„‡Ž‹‡ˆ–Šƒ–Š—ƒ‘™Ž‡†‰‡†‡”‹˜‡•ˆ”‘•—„Œ‡…–‹˜‡ ’‡”…‡’–—ƒŽ‡š’‡”‹‡…‡ǤŽ–Š‘—‰ŠŠ‡ˆƒ‘—•Ž›”‡ˆ‡””‡†–‘…ƒ—•ƒŽ‹–›ƒ•Dz–Š‡…‡‡–‘ˆ –Š‡—‹˜‡”•‡dzǡŠ‡™ƒ••‡’–‹…ƒŽ‘ˆ…Žƒ••‹…ƒŽ‘Ǧ•—„Œ‡…–‹˜‡‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›Ǥ—‡ †‡ˆ‹‡†ƒ…ƒ—•‡–‘„‡Dzƒ‘„Œ‡…–ǡˆ‘ŽŽ‘™‡†„›ƒ‘–Š‡”ǡƒ†™Š‡”‡ƒŽŽ–Š‡‘„Œ‡…–• •‹‹Žƒ”–‘–Š‡ˆ‹”•–ƒ”‡ˆ‘ŽŽ‘™‡†„›‘„Œ‡…–••‹‹Žƒ”–‘–Š‡•‡…‘†dzȋ…‹–‡†‹ȏͻȐȌǤŠ—•ǡ —‡ǯ•‹•ƒ•‡’–‹…ƒŽƒ……‘—–…‘‘Ž›”‡ˆ‡””‡†–‘ƒ•ƒregularity theory of causalityͷȏͳͲǡͳͳǡͳʹȐǤ –‹•ƒ”‡‰—Žƒ”‹–›–Š‡‘”›„‡…ƒ—•‡–Š‡…‡–”ƒŽˆ‡ƒ–—”‡‘ˆ—‡ǯ• ƒ……‘—–…‘…‡”•™Šƒ–Š‡…ƒŽŽ‡†constant conjunctionsǡ–Šƒ–‹•ǡˆ‘”‡˜‡––‘…ƒ—•‡ ‡˜‡–ǡ‹•‘„•‡”˜‡†–‘ƒŽ™ƒ›•ȋ”‡‰—Žƒ”Ž›Ȍˆ‘ŽŽ‘™ǤŽƒ••‹…ƒŽ‡šƒ’Ž‡•‘ˆ ”‡‰—Žƒ”‹–›ƒ„‘—†ǣ„‘‹Ž‹‰™ƒ–‡”‹•‘„•‡”˜‡†–‘ƒŽ™ƒ›•ˆ‘ŽŽ‘™ˆ”‘ƒ’’Ž‹…ƒ–‹‘‘ˆƒ •’‡…‹ˆ‹…ƒ‘—–‘ˆŠ‡ƒ–Ǣ–Š‡‘–‹‘‘ˆ‘‡„‹ŽŽ‹ƒ”†„ƒŽŽ‹•‘„•‡”˜‡†–‘ƒŽ™ƒ›•ˆ‘ŽŽ‘™ ˆ”‘„‡‹‰•–”—…„›ƒ‘–Š‡”Ǥƒ—•ƒŽ‹–›‹—‡ǯ•’Š‹Ž‘•‘’Š›‹•”‡†—…‡†–‘ …‘””‡Žƒ–‹‘ǣ‘……—””‡…‡‘ˆ–Š‡ˆ‹”•–‡˜‡–ȋȌ‹•…‘””‡Žƒ–‡†™‹–Š‘……—””‡…‡‘ˆ–Š‡ •‡…‘†‡˜‡–ȋȌǤ—‡–Š‘—‰Š––Šƒ–ƒŽŽ„‡Ž‹‡ˆ•‹”‡‰—Žƒ”…‘‡…–‹‘‡‡†–‘„‡ ‡š’Žƒ‹‡†Ǣƒ†Š‹•‡š’Žƒƒ–‹‘…ƒ‡†‹”‡…–Ž›ˆ”‘–Š‡‡š’‡”‹‡…‡‘ˆŠ—ƒ„‡‹‰•Ǥ ‘”—‡ǡ™‡‡š’‡”‹‡…‡ǡ‘––Š‡…ƒ—•ƒŽ”‡Žƒ–‹‘‹–•‡Žˆǡ„—–”ƒ–Š‡”…‘•–ƒ– …‘Œ—…–‹‘•‘ˆ‡˜‡–•ˆ”‘–Š‡‘‡–™‡ƒ”‡„‘”ǡƒ†–Š‡”‡‰—Žƒ”‹–›‘ˆ–Š‡•‡ ‡š’‡”‹‡…‡•…”‡ƒ–‡•ƒ•‡•‡‘ˆ”‡‰—Žƒ”‹–›‹’‡”…‡’–‹‘Ǥ……‘”†‹‰–‘—‡ǡ–Š‡ •‡•‡‘ˆ”‡‰—Žƒ”‹–›‘ˆ…ƒ—•ƒŽ‹–›…‘‡•ˆ”‘•—„Œ‡…–‹˜‡‡š’‡”‹‡…‡ǡƒ†‹•‘–ƒ ’”‘’‡”–›‘ˆ–Š‡‘„Œ‡…–‹˜‡‡š–‡”ƒŽ™‘”Ž†Ǥ •Š‘”–ǡ…ƒ—•ƒŽ”‡Žƒ–‹‘•ƒ”‡•—„Œ‡…–‹˜‡ ’Š‡‘‡ƒ–Šƒ–ƒ”‡’”‘Œ‡…–‡†‘–‘–Š‡™‘”Ž†ȏͻǡͳ͵ǡͳͶȐǤŠ—•ǡƒŽ–Š‘—‰Š—‡ ”‡Œ‡…–‡†…ƒ—•ƒŽ‡…‡••‹–›ǡƒ‘„Œ‡…–‹˜‡’”‘’‡”–›ǡŠ‡‡„”ƒ…‡†…ƒ—•ƒŽ”‡‰—Žƒ”‹–›ǡƒ •—„Œ‡…–‹˜‡ƒ––”‹„—–‡Ǥ˜‡–Š‘—‰Š—‡ǯ•˜‹‡™‹•–Šƒ–…ƒ—•ƒŽ‹–›†‡’‡†•‘ •—„Œ‡…–‹˜‡‡š’‡”‹‡…‡ǡƒ†–Š—•‹‰Š–ƒŽŽ‘™ˆ‘”’”‘„ƒ„‹Ž‹•–‹…‡ˆˆ‡…–•ǡŠ‹•‡’Šƒ•‹•‘ –Š‡”‡‰—Žƒ”‹–›‘ˆ…ƒ—•‡ƒ‡•Š‹•…ƒ—•ƒŽ‹–›–Š‡‘”›†‡–‡”‹‹•–‹…Ǥ  ͷƒ”‹‘—•‹–‡”’”‡–ƒ–‹‘•‘ˆ–Š‡—‡ƒ‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›‡š‹•–ǡƒ†–Š‡”‡•‡‡•–‘„‡‘

…‘•‡•—•‘™Š‹…Š‘‡ǡ‹ˆƒ›ǡƒ”‡…‘””‡…–Ǣˆ‘”–Š‡’—”’‘•‡•‘ˆ–Š‹•’ƒ’‡”ǡ™‡–ƒ‡–Š‡‘•–‰‡‡”ƒŽ ‹–‡”’”‡–ƒ–‹‘Ǥ



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—„‡”‘ˆ’”‘„Ž‡•‡š‹•–ˆ‘”—‡ǯ•–Š‡‘”›ǡƒ†ˆ‘””‡‰—Žƒ”‹–›–Š‡‘”‹‡•‹ ‰‡‡”ƒŽȏͳͲǡͳͳǡͳͷǡͳ͸ȐǤ•ƒ‡šƒ’Ž‡ǡspurious regularitiesƒ›‰‹˜‡”‹•‡–‘ˆƒŽ•‡ …‘…Ž—•‹‘•ǣ‹ˆƒ•‹‰Ž‡…ƒ—•‡‹•”‡‰—Žƒ”Ž›ˆ‘ŽŽ‘™‡†„›–™‘‡ˆˆ‡…–•ƒ–†‹ˆˆ‡”‡––‹‡•ǡ —‡ǯ•‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›™‘—Ž†Ž‡ƒ†‘‡–‘…‘…Ž—†‡–Šƒ––Š‡‡ƒ”Ž‹‡”‡ˆˆ‡…–‹• …ƒ—•ƒŽ–‘–Š‡Žƒ–‡”‘‡ǡ‡˜‡–Š‘—‰Š–Š‡›ƒ”‡‘–†‹”‡…–Ž›”‡Žƒ–‡†ǤŠ‹•‹•ƒ ‹’‘”–ƒ–’‘‹–ǡƒ†‘‡‘ˆ–Š‡’”‹ƒ”›‘–‹˜ƒ–‹‘•ˆ‘”ƒ’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ …ƒ—•ƒŽ‹–›–Šƒ–™‡•ŠƒŽŽ”‡–—”–‘Žƒ–‡”‹‘—”†‹•…—••‹‘‘ˆ ”ƒ‰‡”…ƒ—•ƒŽ‹–›Ǥ Ž–Š‘—‰Š’”‘„Ž‡••—…Šƒ••’—”‹‘—•”‡‰—Žƒ”‹–›Šƒ˜‡‰‹˜‡’Š‹Ž‘•‘’Š‡”•ƒ† •…‹‡–‹•–•”‡ƒ•‘–‘ƒ„ƒ†‘”‡‰—Žƒ”‹–›–Š‡‘”‹‡•‘ˆ…ƒ—•ƒŽ‹–›ǡ‹–™ƒ•ƒ–™Š‘ ˆƒ‘—•Ž›–”‹‡†–‘”‡•…—‡–Š‡‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›ƒ•‡š‹•–‹‰‹–Š‡‡š–‡”ƒŽ™‘”Ž† ˆ”‘—‡ǯ••‡’–‹…‹•Ǥƒ–‹•™‡ŽŽ‘™ˆ‘”’”‘˜‹†‹‰™Šƒ––—”‡†‘—––‘„‡ ˆ‘—†ƒ–‹‘ƒŽƒ†…‘…‡’–—ƒŽŒ—•–‹ˆ‹…ƒ–‹‘ˆ‘”ƒ›‘ˆ–Š‡”‡•—Ž–•‘ˆ–Š‡‘†‡” •…‹‡…‡‘ˆ˜‹•—ƒŽ’‡”…‡’–‹‘Ǥ‡•–ƒ–‡†–Šƒ–ǡDz’–‘‘™‹–Šƒ•„‡‡ƒ••—‡†–Šƒ–ƒŽŽ ‘—”…‘‰‹–‹‘—•–…‘ˆ‘”–‘–Š‡‘„Œ‡…–•Ǣ„—–ǥŽ‡–—•‘…‡–”›™Š‡–Š‡”™‡†‘‘– ‰‡–ˆƒ”–Š‡”™‹–Š–Š‡’”‘„Ž‡•‘ˆ‡–ƒ’Š›•‹…•„›ƒ••—‹‰–Šƒ––Š‡‘„Œ‡…–•—•– …‘ˆ‘”–‘‘—”…‘‰‹–‹‘dzȏͳʹȐǤ†•‘ƒ–„‡Ž‹‡˜‡†–Šƒ–’‡”…‡’–‹‘‹•‘–•‹’Ž›ƒ ’ƒ••‹˜‡’‡”…‡’–—ƒŽ’”‘…‡••ǡ„—–”ƒ–Š‡”ƒƒ…–‹˜‡‹–‡”’”‡–ƒ–‹‘‘ˆ•‡•‘”›‹’—–Ǥ‹‡ —‡ǡƒ–„‡Ž‹‡˜‡†–Šƒ–‘–ƒŽŽ‘™Ž‡†‰‡•–‡•ˆ”‘‡š’‡”‹‡…‡ǡ„—–ǡ—Ž‹‡ —‡ǡŠ‡„‡Ž‹‡˜‡†–Šƒ–•‘‡‘™Ž‡†‰‡†‡”‹˜‡•ˆ”‘™Šƒ–Š‡…ƒŽŽ‡†concepts or categories of the understanding, ‘ˆ™Š‹…Š…ƒ—•ƒŽ‹–›‹•ƒ’”‹‡‡šƒ’Ž‡Ǥ ‘”ƒ–ǡ –Š‡•‡…ƒ–‡‰‘”‹‡•ƒ”‡a priori‡Ž‡‡–•‘ˆ–Š‡Š—ƒ‹†ǡ–Šƒ–‹•ǡ‹ƒ–‡…‘‰‹–‹˜‡ ˆ‡ƒ–—”‡•–Šƒ–‡†‘™Š—ƒ•™‹–Š…‡”–ƒ‹’‡”…‡’–—ƒŽ…ƒ’ƒ…‹–‹‡•ǤŠ‡•‡…ƒ–‡‰‘”‹‡• ƒŽŽ‘™—•–‘‡š’‡”‹‡…‡™Šƒ––Š‡™‘”Ž†‹•”‡ƒŽŽ›Ž‹‡ǡƒ†a priori‘™Ž‡†‰‡‡š‹•–• ƒŽ‘‰•‹†‡‡’‹”‹…ƒŽ‘™Ž‡†‰‡ ȏͳ͵ȐǤƒ–…‘…Ž—†‡†–Šƒ––Š‡’”‹…‹’Ž‡‘ˆ…ƒ—•ƒŽ‹–›‹• ƒa priori–”—–Šǡ„—–‹•‘‡–Š‡Ž‡••†‡–‡”‹‡†ȋ„›„‘–Ša prioriƒ†‡’‹”‹…ƒŽ ‘™Ž‡†‰‡ȌǤƒ–ǯ•‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›™ƒ•–Š‡†‘‹ƒ–˜‹‡™’‘‹–‹‡•–‡” ’Š‹Ž‘•‘’Š›—–‹Ž—••‡ŽŽ’”‘˜‹†‡†ƒ‘†‡”—†‡”•–ƒ†‹‰–Šƒ–‹…Ž—†‡†ƒ…”‹–‹“—‡ ‘ˆ–Š‡†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›–‘™Š‹…Š„‘–Š—‡ƒ†ƒ–™‡”‡†‡†‹…ƒ–‡†Ǥ —••‡ŽŽǯ•ƒ……‘—–‹•ƒ”‡Œ‡…–‹‘‘ˆ–Š‡…Žƒ••‹…ƒŽǮŽƒ™‘ˆ…ƒ—•ƒŽ‹–›ǯǤŠ‹•‹• ‹’‘”–ƒ–ǡ‘–‘Ž›ˆ‘”‰”‘—†‹‰‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›‹‘†‡”’Š›•‹…•ǡ„—–ƒŽ•‘ ˆ‘”‘–‹˜ƒ–‹‰ƒ…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›–Šƒ–‹•—•‡ˆ—Žˆ‘”—†‡”•–ƒ†‹‰…ƒ—•ƒŽ‹–›‹ „”ƒ‹‡–™‘”•Ǥ Š‹•‡••ƒ›ǡOn the Notion of Causeǡ—••‡ŽŽ™ƒ•ƒŠ‡ƒ†‘ˆŠ‹•–‹‡ ™Š‡Š‡”‡ƒ•‘ƒ„Ž›…Žƒ‹‡†–Šƒ–•…‹‡–‹ˆ‹…‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›•Š‘—Ž†‘–„‡Ž‹‡† –‘†‡–‡”‹‹•ȏͳͺȐǤ—••‡ŽŽƒ••‡”–‡†ǡ„ƒ•‡†‘…‘…‡’–—ƒŽƒƒŽ›•‹•ǡƒ†’‘••‹„Ž›‘ –Š‡”‡•—Ž–•‘ˆ‘†‡”’Š›•‹…•͸ǡ–Šƒ–‘–‡˜‡”›‡˜‡–mustŠƒ˜‡ƒ†‹”‡…–…ƒ—•‡Ǥ ƒ—•ƒŽ‹–›ǡˆ‘”—••‡ŽŽǡ‹•–‘„‡Dz—†‡”•–‘‘†‹–‡”•‘ˆˆ—…–‹‘ƒŽ”‡Žƒ–‹‘•dzȏͳͺȐǤ‡ …Žƒ‹‡†–Šƒ–•…‹‡–‹ˆ‹…Žƒ™•†‘‘–”‡˜‡ƒŽ–Š‡…ƒ—•ƒŽ‡ˆˆ‡…–•‘ˆ‘‡‡˜‡–‘ƒ ˆ‘ŽŽ‘™‹‰‘‡ǡ„—–”ƒ–Š‡”•–ƒ–‡ˆ—…–‹‘ƒŽ”‡Žƒ–‹‘•„‡–™‡‡–Š‡‡˜‡–•Ǥ—••‡ŽŽ …‘…Ž—†‡†„›”‡…‘‡†‹‰–Šƒ––Š‡‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹–•‡Žˆ„‡”‡‘˜‡†ˆ”‘ •…‹‡–‹ˆ‹…†‹•…‘—”•‡Ǥ 

͸ –‹•ƒ”‰—ƒ„Ž‡™Š‡–Š‡”—••‡ŽŽŠƒ†…‘•‹†‡”‡†™Šƒ–‹’Ž‹…ƒ–‹‘•Dz‘†‡”dz’Š›•‹…•ǡƒ‡Ž›–Šƒ–‘ˆ

”‡Žƒ–‹˜‹–›ƒ†“—ƒ–—‡…Šƒ‹…•ǡ™‘—Ž†Šƒ˜‡‘…ƒ—•ƒŽ‹–›™Š‡Š‹•ͳͻͳ͵’ƒ’‡”™ƒ•™”‹––‡Ǥ‘–Š ‘ˆ–Š‘•‡–Š‡‘”‹‡•™‡”‡˜‡”›‡™ǡƒ†–Š‡‹”‹’Ž‹…ƒ–‹‘•ˆ‘”…ƒ—•ƒŽ‹–›™‡”‡‘–™‡ŽŽ‘™Ǥ 



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 Š‡‘†‡”‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›Šƒ•—†‡”‰‘‡ǡ‹Ž‹‰Š–‘ˆ‡’‹”‹…ƒŽ”‡•—Ž–• ˆ”‘ƒ—„‡”‘ˆ•…‹‡–‹ˆ‹…†‹•…‹’Ž‹‡•ǡ’ƒ”–‹…—Žƒ”Ž›’Š›•‹…•ǡ„‹‘Ž‘‰›ǡ‡…‘‘‹…•ƒ† •–ƒ–‹•–‹…•ǡƒ†”ƒ•–‹……‘…‡’–—ƒŽ•Š‹ˆ–ǡ™‹–ŠƒƒŒ‘”…‘…‡’–—ƒŽ…‘–”‹„—–‹‘„›—••‡ŽŽǤ Ž–Š‘—‰Š—••‡ŽŽ†‹†‘–‡š’Ž‹…‹–Ž›…‘•‹†‡”…ƒ—•ƒŽ‹–›‹„‹‘Ž‘‰‹…ƒŽŽ›…‘’Ž‡š •›•–‡••—…Šƒ•–Š‡Š—ƒ„”ƒ‹ǡŠ‹•ƒ”‰—‡–•ˆ‘”‡•Šƒ†‘™–Šƒ–ƒ’’Ž‹…ƒ–‹‘ǤŠ—•ǡ —••‡ŽŽǯ•…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›’”‡•ƒ‰‡†Žƒ–‡”†‡˜‡Ž‘’‡–•‹—†‡”•–ƒ†‹‰ …ƒ—•ƒŽ‹–›‹…‘’Ž‡š•›•–‡•ƒ†„”ƒ‹‡–™‘”•Ǥ  2.2 Causality in Classical and Modern Physics –‹•†‘—„–ˆ—Ž–Šƒ–—••‡ŽŽ…‘—Ž†Šƒ˜‡ˆ‘”‡•‡‡™Šƒ–‹’ƒ…–‘†‡”•…‹‡…‡ǡ ‡•’‡…‹ƒŽŽ›’Š›•‹…•ǡ„‹‘Ž‘‰›ǡ‡…‘‘‹…•ƒ†•–ƒ–‹•–‹…•™‘—Ž†Šƒ˜‡‘–Š‡…‘…‡’–‘ˆ …ƒ—•ƒŽ‹–›Ǣ‡˜‡”–Š‡Ž‡••ǡ‹–‹•…Ž‡ƒ”–Šƒ–Š‡Šƒ†ƒ‹†‡ƒ–Šƒ–ƒ…Šƒ‰‡™ƒ•…‘‹‰Ǥ ™‡–‹‡–Šȋƒ†–™‡–›Ǧˆ‹”•–Ȍ…‡–—”›•…‹‡–‹ˆ‹……‘…‡’–•Šƒ˜‡„‘–Š…ŠƒŽŽ‡‰‡†ƒ† …Žƒ”‹ˆ‹‡†ˆ‘—†ƒ–‹‘ƒŽ…‘…‡’–•‘ˆ…ƒ—•ƒŽ‹–›‹’Š›•‹…•ƒ†‘–Š‡”•…‹‡…‡•Ǥ‘…‡’–• ‹‘†‡”’Š›•‹…•–Šƒ–‹˜‘Ž˜‡…ƒ—•ƒŽ‹–›‹…Ž—†‡–Š‡”‡Žƒ–‹˜‹–›‘ˆ•‹—Ž–ƒ‡‹–›ǡ–‹‡ †‹Žƒ–‹‘ǡ–Š‡•’ƒ…‡Ǧ–‹‡‹–‡”˜ƒŽǡ‘Ž‘…ƒŽ‹–›ǡ“—ƒ–—‡–ƒ‰Ž‡‡–ǡƒ†„ƒ…™ƒ”† …ƒ—•ƒŽ‹–›ȋ‡Ǥ‰Ǥǡ–Š‡†‡Žƒ›‡†…Š‘‹…‡“—ƒ–—‡”ƒ•‡”‡š’‡”‹‡–ȌȏͳͻǡʹͲǡʹͳȐǤ ‹‘Ž‘‰‹…ƒŽ…‘…‡’–•‹…Ž—†‡„‹‘Ž‘‰‹…ƒŽ’Žƒ—•‹„‹Ž‹–›ǡ‡˜‘Ž—–‹‘ƒ”›‡…Šƒ‹••ǡ ‡’‹‰‡‡–‹…•ǡ‰‡‡–‹…”‡‰—Žƒ–‘”›‡–™‘”•ǡƒ†ƒ”–‹ˆ‹…‹ƒŽƒ†„‹‘Ž‘‰‹…ƒŽ‡—”ƒŽ ‡–™‘”•Ǥ‡‡š–’”‘˜‹†‡ƒ„”‹‡ˆ…‘…‡’–—ƒŽƒƒŽ›•‹•‘ˆ–Š‡”‘Ž‡‘ˆ…ƒ—•ƒŽ‹–›‹ ‘†‡”’Š›•‹…•Ǥ ‡…Šƒ‹…•‹•ƒ…‡–”ƒŽ–‘’‹…‹…Žƒ••‹…ƒŽ’Š›•‹…•ǡƒ†‹’Ž‹…‹–‹–Š‡…Žƒ••‹…ƒŽ …‘…‡’–‘ˆ‡…Šƒ‹…•‹•–Š‡…‘…‡’–‘ˆ†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›ǤŽƒ••‹…ƒŽ’Š›•‹…•‹• „ƒ•‡†‘…‘…‡’–••—…Šƒ•‘Ǧ“—ƒ–—‘”…Žƒ••‹…ƒŽŽ‘‰‹…ǡ‡™–‘‹ƒ‡…Šƒ‹…•ǡ †‡–‡”‹‹•ǡ‘„Œ‡…–‹˜‹–›ǡƒ†…‡”–ƒ‹–›Ǥ›–Š‡‡†‘ˆ–Š‡‹‡–‡‡–Š…‡–—”›ǡ–Š‡ …Žƒ••‹…ƒŽ‡™–‘‹ƒŽ‡‰ƒ…›Šƒ†„‡…‘‡‡„‘†‹‡†‹•‡˜‡”ƒŽˆ—†ƒ‡–ƒŽ ‡’‹•–‡‘Ž‘‰‹…ƒŽƒ†‡–ƒ’Š›•‹…ƒŽƒ••—’–‹‘•ƒ„‘—––Š‡ƒ–‡”‹ƒŽ™‘”Ž†ȏʹʹȐǤ ‹˜‡ ƒ••—’–‹‘•™‡”‡ǣ





ͳȌ ŽŽ…Šƒ‰‡‹‘–‹‘Šƒ•ƒ…ƒ—•‡Ǥ ˆƒ„‘†›‡šŠ‹„‹–•ƒ…Šƒ‰‡‹‘–‹‘ǡ‹– ‹•’‘••‹„Ž‡–‘†‡–‡”‹‡™Šƒ–…ƒ—•‡†–Š‡…Šƒ‰‡Ǥ ʹȌ ˆ–Š‡•–ƒ–‡‘ˆƒ•›•–‡‹•‘™ƒ–‘‡–‹‡Ȃ•ƒ›–Š‡’”‡•‡–Ȃ‹–…ƒ„‡ †‡–‡”‹‡† ƒ– ƒ› ‘–Š‡” –‹‡ ‹ –Š‡ ˆ—–—”‡ ‘” ’ƒ•–Ǥ Š—•ǡ ƒ• ƒ …‘•‡“—‡…‡‘ˆƒ‡ƒ”Ž‹‡”…ƒ—•‡ǡ•—„•‡“—‡–•›•–‡•–ƒ–‡•ƒ”‡…‡”–ƒ‹Ǥ ͵Ȍ Š‡ ’”‘’‡”–‹‡• ‘ˆ Ž‹‰Š– ƒ”‡ …‘’Ž‡–‡Ž› †‡•…”‹„‡† „› ƒš™‡ŽŽǯ• ‡Ž‡…–”‘ƒ‰‡–‹… –Š‡‘”› ƒ† …‘ˆ‹”‡† „› ‡š’‡”‹‡–Ǥ ™‘ ‡“—‹˜ƒŽ‡– ’Š›•‹…ƒŽ ‘†‡Ž• ”‡’”‡•‡– ‡‡”‰›ǡ ‘‡ „ƒ•‡† ‘ ’ƒ”–‹…Ž‡•ǡ –Š‡ ‘–Š‡” ‘ ™ƒ˜‡•Ǥ–‡˜‡”›–‹‡ǡ‡‡”‰›‡š‹•–•ƒ•‡‹–Š‡”’ƒ”–‹…Ž‡‘”™ƒ˜‡Ǥ ͶȌ – ‹• ’‘••‹„Ž‡ ‹ ’”‹…‹’Ž‡ –‘ ‡ƒ•—”‡ –‘ ƒ› †‡‰”‡‡ ‘ˆ ƒ……—”ƒ…› –Š‡ ’”‘’‡”–‹‡•ǡ•—…Šƒ•–‡’‡”ƒ–—”‡‘”•’‡‡†ǡ‘ˆƒ•›•–‡Ǥ ͷȌ ƒ—•ƒŽ‹–›‹•†‡–‡”‹‹•–‹…ƒŽŽ›…‡”–ƒ‹Ǥ

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Š‡ˆ‹”•–ƒ••—’–‹‘ƒ„‘˜‡†‡”‹˜‡•ˆ”‘–Š‡‡–ƒ’Š›•‹…ƒŽ†‘…–”‹‡‘ˆ ‡…Šƒ‹•ǡ™Š‹…ŠŠ‘Ž†•–Šƒ––Š‡—‹˜‡”•‡‘’‡”ƒ–‡•ƒ•ƒ…‘’Ž‹…ƒ–‡†ƒ…Š‹‡ǤŠ‡ …Ž‘…Šƒ•„‡‡–Š‡‘•–…‘‘‡–ƒ’Š‘”—•‡†–‘’‘”–”ƒ›‡…Šƒ‹••ǡƒ†–Š‡ ‡…Šƒ‹•–‹……Ž‘…™‘”‡–ƒ’Š‘”’‡”‡ƒ–‡†…Žƒ••‹…ƒŽ’Š›•‹…•ˆ‘”…‡–—”‹‡•ǤŠ‡ ‘’‡”ƒ–‹‘‘ˆ–Š‡…Ž‘…•›•–‡…‘—Ž†„‡‡š’Žƒ‹‡†‹–‘–ƒŽ‹–›„›•‹’Ž›‡š’Žƒ‹‹‰‹–• ’ƒ”–•ƒ†Š‘™–Š‡›‘˜‡†™‹–Š‹–Š‡•›•–‡Ǥ‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›™ƒ•ƒ•…”‹„‡† –‘–Š‡•›•–‡„‡…ƒ—•‡‡˜‡”›‘–‹‘„›‘‡’ƒ”–‘ˆ–Š‡•›•–‡™ƒ•…‘•‹†‡”‡†–‘ †‡–‡”‹‡‘–Š‡”‘–‹‘•„›‘–Š‡”’ƒ”–•Ǥ —”–Š‡”‘”‡ǡŒ—•–ƒ•–Š‡…Ž‘…™ƒ•ƒ ‡…Šƒ‹…ƒŽ•›•–‡–Šƒ–…‘—Ž†„‡—†‡”•–‘‘†‹–‡”•‘ˆ‹–•’ƒ”–•ƒ†–Š‡‹”‘–‹‘•ǡ •‘–‘‘–Š‡—‹˜‡”•‡™ƒ•…‘•‹†‡”‡†–‘„‡ƒ‡…Šƒ‹…ƒŽ•›•–‡–Šƒ–…‘—Ž†„‡ ‡š’Žƒ‹‡†‹–‡”•‘ˆ‹–•’ƒ”–•ǡƒ‡Ž›ƒ–‡”‹ƒŽ‘„Œ‡…–•ǡƒ†–Š‡‹”‘–‹‘•Ǥ ‘”‡‘˜‡”ǡ–Š‡‡–ƒ’Š›•‹…ƒŽ†‘…–”‹‡‘ˆ‡…Šƒ‹•’”‡•—’’‘•‡†”‡‰—Žƒ”‹–›ǡƒ† –Š—•†‡–‡”‹‹•ǣ–Š‡”‡‰—Žƒ”‹–›‡šŠ‹„‹–‡†„›–Š‡—‹˜‡”•‡…‘—Ž†„‡—†‡”•–‘‘†‹ –‡”•‘ˆ†‡–‡”‹‹•–‹…Žƒ™•‘ˆƒ–—”‡ǤŠ‹•†‘…–”‹‡‘–‘Ž›ƒ’’Ž‹‡†–‘–Š‡—‹˜‡”•‡ ƒ•ƒ™Š‘Ž‡ǡ„—–ƒŽ•‘–‘ƒŽŽ’Š‡‘‡ƒ™‹–Š‹–Š‡—‹˜‡”•‡Ǥ Š‡•‡…‘†ƒ••—’–‹‘ƒ„‘˜‡‹•„‡•–‡š‡’Ž‹ˆ‹‡†„›–Š‡‡šƒ’Ž‡‘ˆ ƒ’Žƒ…‡ǯ•‡‘ǡ™Š‹…Šƒ’Žƒ…‡—•‡†–‘†‡‘•–”ƒ–‡…ƒ—•ƒŽ†‡–‡”‹‹•Ǥ ͳͺͳͶǡ Š‡•–ƒ–‡†ǡ ‡ ƒ› ”‡‰ƒ”† –Š‡ ’”‡•‡– •–ƒ–‡ ‘ˆ –Š‡ —‹˜‡”•‡ ƒ• –Š‡ ‡ˆˆ‡…– ‘ˆ ‹–• ’ƒ•–ƒ†–Š‡…ƒ—•‡‘ˆ‹–•ˆ—–—”‡Ǥ‹–‡ŽŽ‡…–™Š‹…Šƒ–ƒ…‡”–ƒ‹‘‡– ™‘—Ž†‘™ƒŽŽˆ‘”…‡•–Šƒ–•‡–ƒ–—”‡‹‘–‹‘ǡƒ†ƒŽŽ’‘•‹–‹‘•‘ˆƒŽŽ ‹–‡• ‘ˆ ™Š‹…Š ƒ–—”‡ ‹• …‘’‘•‡†ǡ ‹ˆ –Š‹• ‹–‡ŽŽ‡…– ™‡”‡ ƒŽ•‘ ˜ƒ•– ‡‘—‰Š–‘•—„‹––Š‡•‡†ƒ–ƒ–‘ƒƒŽ›•‹•ǡ‹–™‘—Ž†‡„”ƒ…‡‹ƒ•‹‰Ž‡ ˆ‘”—Žƒ –Š‡ ‘˜‡‡–• ‘ˆ –Š‡ ‰”‡ƒ–‡•– „‘†‹‡• ‘ˆ –Š‡ —‹˜‡”•‡ ƒ† –Š‘•‡ ‘ˆ –Š‡ –‹‹‡•– ƒ–‘Ǣ ˆ‘” •—…Š ƒ ‹–‡ŽŽ‡…– ‘–Š‹‰ ™‘—Ž† „‡ —…‡”–ƒ‹ƒ†–Š‡ˆ—–—”‡Œ—•–Ž‹‡–Š‡’ƒ•–™‘—Ž†„‡’”‡•‡–„‡ˆ‘”‡‹–• ‡›‡•ȏʹ͵ȐǤ Š‹•“—‘–‡‡’Šƒ•‹œ‡•–Š‡ƒ””‹ƒ‰‡‘ˆ…ƒ—•ƒŽ‹–›™‹–Š†‡–‡”‹‹•Ǥ‘™‡˜‡”ǡƒ› •—„•‡“—‡–†‡˜‡Ž‘’‡–•‹’Š›•‹…•ǡ‹…Ž—†‹‰‘Ž‹‡ƒ”†›ƒ‹…•ǡ…Šƒ‘•–Š‡‘”›ǡ ƒ†“—ƒ–—’Š›•‹…•ȋȌǡŠƒ˜‡•‹‰ƒŽ‡†ƒ†‹˜‘”…‡ǤŠ‡ƒ†˜‡–‘ˆ“—ƒ–—’Š›•‹…•ǡ ƒ•Ž‹˜‡ ”ƒ‰‡”ȏʹͶȐ‘–‡•‹Š‹•‡••ƒ›Testing for Causalityȋ•‡‡†‹•…—••‹‘„‡Ž‘™Ȍ Šƒ†ƒ‰”‡ƒ–‹’ƒ…–‘’Š‹Ž‘•‘’Š‹…ƒŽ…‘•‹†‡”ƒ–‹‘•‘ˆ…ƒ—•ƒŽ‹–›ƒ††‡–‡”‹‹•Ǥ ‡˜‡”ƒŽƒ•’‡…–•‘ˆƒ”‡’ƒ”–‹…—Žƒ”Ž›‹’‘”–ƒ–‹–Š‹•…‘–‡š–ǡ‹…Ž—†‹‰ ‡‹•‡„‡”‰ǯ•—…‡”–ƒ‹–›’”‹…‹’Ž‡ǡ‘”ǯ•”—Ž‡ǡ–Š‡‡ƒ•—”‡‡–’”‘„Ž‡ǡƒ†‡˜‡ ‘”‡‘†‡”ǡ‡’‹”‹…ƒŽ”‡•—Ž–•ˆ”‘‡š’‡”‹‡–•‹˜‘Ž˜‹‰‡ŽŽǯ•–Š‡‘”‡ǡ “—ƒ–—‡–ƒ‰Ž‡‡–ǡ„ƒ…™ƒ”†…ƒ—•ƒ–‹‘ƒ†–Š‡†‡Žƒ›‡†“—ƒ–—…Š‘‹…‡‡”ƒ•‡” ‡š’‡”‹‡–ȏͳͻǡʹͲǡʹͷǦ͵ͳȐǤ‡„”‹‡ˆŽ›†‹•…—•••‘‡‘ˆ–Š‡•‡‡šƒ’Ž‡•–‘Š‹‰ŠŽ‹‰Š– –Š‡„”‡ƒ†‘™‘ˆ†‡–‡”‹‹•ƒ††‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›Ǥ‘‡–Š‡Ž‡••ǡŽ‡†• ‹–•‡Žˆ–‘ƒ—Ž–‹–—†‡‘ˆ‹–‡”’”‡–ƒ–‹‘•ǡƒ†•‘‡Šƒ˜‡„‡‡‹–‡”’”‡–‡†‹ƒ …‘’Ž‡–‡Ž›†‡–‡”‹‹•–‹…ˆ”ƒ‡™‘”ȏʹ͸ȐǤ‹•–‡‹ǡ‹’ƒ”–‹…—Žƒ”ǡŠ‡Ž†–Š‹•˜‹‡™ǡ ’”‘’‘•‹‰–Šƒ––Š‡–Š‡‘”›‘ˆ™ƒ•‹…‘’Ž‡–‡ƒ†…‡”–ƒ‹Š‹††‡˜ƒ”‹ƒ„Ž‡•™‡”‡ •–‹ŽŽ–‘„‡ˆ‘—†ȏ͵ͲȐǤ‘™‡˜‡”ǡ‘•–…‘‘Ž›ƒ……‡’–‡†‹–‡”’”‡–ƒ–‹‘•ǡ•—…Šƒ• –Š‡‘’‡Šƒ‰‡ –‡”’”‡–ƒ–‹‘ǡ™Š‹…Š‹•–‡‹ˆƒ‘—•Ž›‘’’‘•‡†ǡŠƒ˜‡ƒ•–”‹…–



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‹†‡–‡”‹‹•„—‹Ž–‹Ǥ –‡”‡•–‹‰Ž›ǡ–Š‡…Š”Ú†‹‰‡”‡“—ƒ–‹‘‹•…‘’Ž‡–‡Ž› †‡–‡”‹‹•–‹…ǡƒ–Ž‡ƒ•–‹’”‘˜‹†‹‰–Š‡‡˜‘Ž—–‹‘‘ˆ–Š‡™ƒ˜‡ˆ—…–‹‘‘ˆƒ’ƒ”–‹…Ž‡ ȏʹͳȐǤ‘™‡˜‡”ǡ‹–‹•Š‡”‡ƒŽ•‘–Šƒ–†‡–‡”‹‹•„”‡ƒ•†‘™ǡ‰‹˜‡‘”ǯ•”—Ž‡ǡ‘” •–ƒ–‹•–‹…ƒŽ‹–‡”’”‡–ƒ–‹‘ǡ™Š‹…Š•ƒ›•–Šƒ––Š‡™ƒ˜‡ˆ—…–‹‘‘Ž›‰‹˜‡•–Š‡ ’”‘„ƒ„‹Ž‹–›‘ˆˆ‹†‹‰ƒ’ƒ”–‹…Ž‡ƒ–ƒ’ƒ”–‹…—Žƒ”Ž‘…ƒ–‹‘ƒ–ƒ’ƒ”–‹…—Žƒ”–‹‡ǡƒ†–Š‡ ’”‘„ƒ„‹Ž‹–›‹•‰‹˜‡ƒ–Š‡ƒ–‹…ƒŽŽ›„›–Š‡™ƒ˜‡ˆ—…–‹‘ȋƒ•ƒˆ—…–‹‘‘ˆ•’ƒ…‡ƒ† –‹‡Ȍ•“—ƒ”‡†ȏʹͳȐǤŠ‹•‹•’”‡…‹•‡Ž›™Š‡”‡‹†‡–‡”‹‹•‡–‡”•ǣ‘Ž›’”‘˜‹†‡• ‹ˆ‘”ƒ–‹‘ǡ˜‹ƒ–Š‡…Š”Ú†‹‰‡”‡“—ƒ–‹‘ǡƒ„‘—––Š‡™ƒ˜‡ˆ—…–‹‘ǡƒ††‘‡•‘– ƒŽŽ‘™†‡ˆ‹‹–‡’”‡†‹…–‹‘‘ˆƒ’ƒ”–‹…Ž‡ǯ•Ž‘…ƒ–‹‘Ǥ…ƒ‘Ž›‘ˆˆ‡”•–ƒ–‹•–‹…ƒŽ ‹ˆ‘”ƒ–‹‘ƒ„‘—–’‘••‹„Ž‡”‡•—Ž–•‘ˆ‡š’‡”‹‡–•Ǥ‘™‡˜‡”ǡ–Š‡‘”‹‰‹‘ˆ–Š‹• ‹†‡–‡”‹ƒ…›Šƒ•„‡‡“—‡•–‹‘‡†ǣ‹•‹–ƒ’”‘„Ž‡™‹–Š–Š‡–Š‡‘”›ǡ‹Š‡”‡–‹ ƒ–—”‡ǡ‘”•‘‡–Š‹‰‡Ž•‡ǫ Š‹•‹–‡”’”‡–ƒ–‹‘‘ˆ–Š‡—…‡”–ƒ‹–›’”‹…‹’Ž‡ǡ‘Š ȏʹ͸Ȑ•–ƒ–‡•–Šƒ–ǡ ǥ–Š‡ ‹†‡–‡”‹‹• ‹• ‹Š‡”‡– ‹ –Š‡ ˜‡”› •–”—…–—”‡ ‘ˆ ƒ––‡” ƒ† –Šƒ– –Š‡ ‘‡–— ƒ† ’‘•‹–‹‘ …ƒ‘– ‡˜‡ ‡š‹•– ™‹–Š •‹—Ž–ƒ‡‘—•Ž› ƒ† ’‡”ˆ‡…–Ž› †‡ˆ‹‡† ˜ƒŽ—‡•Ǥ Š‡ –‡” Dz—…‡”–ƒ‹–› ’”‹…‹’Ž‡dz‹•–Š‡”‡ˆ‘”‡ǡ•‘‡™Šƒ–‘ˆƒ‹•‘‡”Ǥ„‡––‡”–‡”™‘—Ž† „‡Dz–Š‡’”‹…‹’Ž‡‘ˆŽ‹‹–‡††‡–‡”‹‹•‹–Š‡•–”—…–—”‡‘ˆƒ––‡”dzǤ  —†ƒ‡–ƒŽ–‘–Š‡“—‡•–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹’Š›•‹…•Šƒ•„‡‡–Š‡ ’Š‡‘‡‘‘ˆ“—ƒ–—‡–ƒ‰Ž‡‡–ǣ–Š‡“—‡•–‹‘Šƒ•–—”‡†‘™Š‡–Š‡”‘”‘– …ƒ—•ƒŽ‹–›‹•ƒŽ™ƒ›•Ž‘…ƒŽǤ—ƒ–—‡–ƒ‰Ž‡‡–‹•–Š‡’Š‡‘‡‘™Š‡”‡„›’ƒ‹”• ‘ˆ’ƒ”–‹…Ž‡•–Šƒ–Šƒ˜‡’”‡˜‹‘—•Ž›‹–‡”ƒ…–‡†ǡ„—–ƒ”‡‘™•‡’ƒ”ƒ–‡†‹•’ƒ…‡ǡ‡šŠ‹„‹– …‘””‡Žƒ–‡†“—ƒ–—’”‘’‡”–‹‡•ƒ†—•–„‡†‡•…”‹„‡†ƒ†–”‡ƒ–‡†ƒ•ƒ™Š‘Ž‡Ǥ ‘”‡‘˜‡”ǡƒ›‡ƒ•—”‡‡–‘‘‡’ƒ”–‹…Ž‡Šƒ•ƒ‹•–ƒ–ƒ‡‘—•‡ˆˆ‡…–ǡ‘”…ƒ—•ƒŽ ‹ˆŽ—‡…‡ǡ‘–Š‡‘–Š‡”’ƒ”–‹…Ž‡Ǥ—ƒ–—‡–ƒ‰Ž‡‡–Šƒ•„‡‡‹–‡”’”‡–‡†ƒ• ˜‹‘Žƒ–‹‰…ƒ—•ƒŽ‹–›„›˜‹‘Žƒ–‹‘‘ˆ–Š‡’”‹…‹’Ž‡‘ˆŽ‘…ƒŽ‹–›ǡ™Š‹…Š•–ƒ–‡•–Šƒ–ƒ› ‡˜‡–‘”…Šƒ‰‡‘ˆƒ›…‘’‘‡–‹ƒ’Š›•‹…ƒŽ•›•–‡—•–Šƒ˜‡ƒ’Š›•‹…ƒŽ…ƒ—•‡ –Šƒ–…ƒ„‡Ž‘…ƒŽ‹œ‡†–‘‹–•‹‡†‹ƒ–‡•’ƒ–‹‘–‡’‘”ƒŽ‡‹‰Š„‘”Š‘‘†Ǥ ‘–Š‡”™‘”†•ǡ ‘’Š›•‹…ƒŽ‹ˆŽ—‡…‡…ƒ’”‘’ƒ‰ƒ–‡ˆƒ•–‡”–ŠƒŽ‹‰Š–ǤŠ—•ǡ‹‘†‡” ‹–‡”’”‡–ƒ–‹‘•‘ˆ“—ƒ–—‡…Šƒ‹…•ǡ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›ƒ›„‡•—’’‘”–‡†„› –Š‡‘Ž‘…ƒŽ‹–›‘ˆ“—ƒ–—‡–ƒ‰Ž‡‡–ǡ™Š‹…Š’‘••‹„Ž›˜‹‘Žƒ–‡•†‡–‡”‹‹•–‹… …‘…‡’–•‘ˆ…ƒ—•ƒŽ‹–›Ǥ‘™‡˜‡”ǡ•‹…‡‡–ƒ‰Ž‡†•–ƒ–‡•Šƒ˜‡…‘””‡Žƒ–‡†‘—–…‘‡•ǡ ƒ‘–Š‡”’‘••‹„Ž‡‹–‡”’”‡–ƒ–‹‘‹•–Šƒ––Š‡›•—’’‘”–†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹ˆŽ—‡…‡• –Šƒ–ƒ”‡‹ˆ‘”ƒ–‹‘ƒŽ‹ƒ–—”‡ȏʹͳȐǤŠ‹•‹••—‡‹••–‹ŽŽ—†‡”‹–‡•‡†‡„ƒ–‡ǡƒ†‹– ƒ›–—”‘—––Šƒ–…ƒ—•ƒŽ‹–›…ƒ„‡„‘–Š‘Ž‘…ƒŽƒ††‡–‡”‹‹•–‹…ǤŠƒ–‹•–”—‡‹• –Šƒ––Š‡…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›‹“—ƒ–—’Š›•‹…•ǡ™Š‹…Š†‡•…”‹„‡•‡˜‡–•–Šƒ–†‘‘– Šƒ˜‡…Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹……ƒ—•‡•ǡŠƒ•„‡‡‡š’ƒ†‡†–‘‹…Ž—†‡’”‘„ƒ„‹Ž‹–‹‡•Ǥ ‡ƒ”‰—‡„‡Ž‘™–Šƒ––Š‡•‡…‘•‹†‡”ƒ–‹‘•ˆ”‘‘†‡”’Š›•‹…•Š‡Ž’–‘ ‘–‹˜ƒ–‡ǡƒ•—••‡ŽŽ’‘••‹„Ž›ˆ‘”‡•Šƒ†‘™‡†ǡƒprobabilistic notion of causalityǤ ƒ—•ƒŽ‹–›‹“—ƒ–—’Š›•‹…•Šƒ•„‡‡‡š’ƒ†‡†–‘‹…Ž—†‡—’”‡†‹…–ƒ„Ž‡ ’”‘„ƒ„‹Ž‹–‹‡•ǡƒ†ǡ“—ƒ–—‡…Šƒ‹…•†‡•…”‹„‡•‡˜‡–•–Šƒ–†‘‘–Šƒ˜‡…Žƒ••‹…ƒŽ †‡–‡”‹‹•–‹……ƒ—•‡•Ǥ 

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‡‘™„”‹‡ˆŽ›…‘•‹†‡”™Š‡–Š‡”–Š‡–Š‡‘”‹‡•‘ˆ•’‡…‹ƒŽƒ†‰‡‡”ƒŽ ”‡Žƒ–‹˜‹–›ƒŽ•‘…Šƒ‰‡‘—”—†‡”•–ƒ†‹‰‘ˆ…ƒ—•ƒŽ‹–›Ǥ ”ƒ‰‡”ȏʹͶȐ•’‡…‹ˆ‹‡•ƒ• ƒš‹‘ƒ–‹…–Šƒ–ǡDzŠ‡’ƒ•–ƒ†’”‡•‡–ƒ›…ƒ—•‡–Š‡ˆ—–—”‡ǡ„—––Š‡ˆ—–—”‡…ƒ‘– …ƒ—•‡–Š‡’ƒ•–Ǥdz‡Š‘Ž†–Šƒ– ”ƒ‰‡”ǯ•–‹‡Ǧƒ•›‡–”›ƒš‹‘‹•‹†‡‡†’”‡•‡”˜‡† ‹‘†‡”’Š›•‹…•ǡƒ†‹•‘–ƒŽ–‡”‡†„›‡‹–Š‡”•’‡…‹ƒŽ‘”‰‡‡”ƒŽ”‡Žƒ–‹˜‹–›Ǥ  ”‡Žƒ–‹˜‹–›ǡ–Š‡‘–‹‘‘ˆ–‹‡ƒ†•’ƒ…‡ƒ”‡†‡’‡†‡–‘–Š‡‘„•‡”˜‡”ƒ†–Š‡‹” ‹‡”–‹ƒŽ”‡ˆ‡”‡…‡ˆ”ƒ‡Ǥ‡…ƒ—•‡‘ˆ‹•–‡‹ǯ•–™‘’‘•–—Žƒ–‡•–Šƒ––Š‡Žƒ™•‘ˆ ’Š›•‹…•—•–„‡–Š‡•ƒ‡‹ƒŽŽ‹‡”–‹ƒŽ”‡ˆ‡”‡…‡•ˆ”ƒ‡•ǡƒ†–Šƒ––Š‡•’‡‡†‘ˆŽ‹‰Š– ‹•…‘•–ƒ–ǡ’‡”…‡’–‹‘‘ˆ–Š‡•‹—Ž–ƒ‡‹–›‘ˆ‡˜‡–•„›‘„•‡”˜‡”•‹–™‘†‹ˆˆ‡”‡– ‹‡”–‹ƒŽ”‡ˆ‡”‡…‡ˆ”ƒ‡•‹•‘–ƒ„•‘Ž—–‡ǣ™Š‡–Š‡”–™‘‘„•‡”˜‡”•’‡”…‡‹˜‡–™‘ ‡˜‡–•–‘„‡•‹—Ž–ƒ‡‘—•‘”‘–†‡’‡†•‘Š‘™–Š‡‘„•‡”˜‡”•ƒ”‡‘˜‹‰”‡Žƒ–‹˜‡ –‘‘‡ƒ‘–Š‡”ǤŠ—•ǡƒŽ–Š‘—‰Š–Š‡’”‹…‹’Ž‡‘ˆ–‹‡ƒ•›‡–”›‘ˆ…ƒ—•ƒŽ‹–›‹• ‡š’ƒ†‡†„›–Š‡–Š‡‘”‹‡•‘ˆ”‡Žƒ–‹˜‹–›–‘‹…Ž—†‡ƒŽŽ‹‡”–‹ƒŽ”‡ˆ‡”‡…‡ˆ”ƒ‡•‘˜‹‰ ”‡Žƒ–‹˜‡–‘‘‡ƒ‘–Š‡”ǡ‹–‹•„ƒ•‹…ƒŽŽ›—…Šƒ‰‡†‹‹–•ƒ–—”‡Ǥ —”–Š‡”‘”‡ǡ•‹…‡‘ •‹‰ƒŽ…ƒ–”ƒ˜‡Žˆƒ•–‡”–Šƒ–Š‡•’‡‡†‘ˆŽ‹‰Š–‹”‡Žƒ–‹˜‹–›–Š‡‘”›ǡ…ƒ—•ƒŽ‹–›ǡ‡‹–Š‡” †‡–‡”‹‹•–‹…‘”’”‘„ƒ„‹Ž‹•–‹…ǡ‹•‘–˜‹‘Žƒ–‡†ȏ͵ͳǦ͵͵ȐǤŠ—•ǡƒŽ–Š‘—‰Š”‡Žƒ–‹˜‹–› ‡š’ƒ†•–Š‡…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›ǡ‹–†‘‡•‘–ƒŽ–‡”‹–Ǥ—ƒ–—’Š›•‹…•ǡ„›…‘–”ƒ•–ǡ Šƒ•‘”‡†‹”‡…–‹’Ž‹…ƒ–‹‘•ˆ‘”–Š‡…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›Ǥ Š‡†‹•…—••‹‘‹–Š‹••‡…–‹‘Šƒ•Š‹‰ŠŽ‹‰Š–‡†–Š‡ˆƒ…––Šƒ––Š‡…‘…‡’–‘ˆ …ƒ—•ƒŽ‹–›Šƒ•—†‡”‰‘‡†”ƒ•–‹…”‡˜‹•‹‘ǡ•’‡…‹ˆ‹…ƒŽŽ›„›ƒ„ƒ†‘‡–‘ˆ †‡–‡”‹‹•ǡ‹–Š‡Š‹•–‘”›‘ˆ’Š›•‹…•Ǥ ™Šƒ–ˆ‘ŽŽ‘™•ǡ™‡™‹ŽŽ…‘•‹†‡”–Š‡‘†‡” —†‡”•–ƒ†‹‰‘ˆ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›ǡƒ†‹–•‹’Ž‹…ƒ–‹‘•ˆ‘”–Š‡…‘…‡’–‹‘‘ˆ …ƒ—•ƒŽ‹ˆŽ—‡…‡‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•Ǥ  3. The Distinction Between Deterministic and Probabilistic Causality Š‹••‡…–‹‘†‡ƒŽ•™‹–Š–Š‡…‘…‡’–‘ˆ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›ǡ™Š‹…Šǡ™‡ ƒ”‰—‡ǡ‹•–Š‡„‡•–‹–‡”’”‡–ƒ–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹–Š‡…‘–‡š–‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹ ‡–™‘”•Ǥ‡„‡‰‹™‹–Š–Š‡†‹•–‹…–‹‘„‡–™‡‡†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›ȋȌƒ† ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›ȋȌǤ –Š‡…Žƒ••‹…ƒŽ—‡ƒ•‡•‡‘ˆ†‹•…—••‡†ƒ„‘˜‡ǡ –™‘‡˜‡–•‹…ƒ—•ƒŽ”‡Žƒ–‹‘•Š‹’ƒ”‡‡…‡••ƒ”‹Ž›…‘‡…–‡†ǡ™‹–Š–Š‡…ƒ—•‡ †‡–‡”‹‹‰–Š‡‡ˆˆ‡…–ǤǮ…ƒ—•‡•ǯ‡ƒ•ǡceteris paribusǡ–Šƒ–‹ˆŠƒ’’‡•ǡ ƒŽ™ƒ›•ˆ‘ŽŽ‘™•Ǥ ǡŠ‘™‡˜‡”ǡƒ‡˜‡–†‘‡•‘–‡…‡••ƒ”‹Ž›†‡–‡”‹‡ƒ‘–Š‡” ‡˜‡–ǡ„—–”ƒ–Š‡”…Šƒ‰‡•–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‘……—””‡…‡‘ˆ–Š‡‘–Š‡”‡˜‡–Ǥ‘–‡–Šƒ–ǡ ‹ˆƒ‡˜‡–lowers–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡‘–Š‡”ǡ–Š‡‹–‹•‘–…‘•‹†‡”‡†ƒ…ƒ—•‡ǣˆ‘” ‡šƒ’Ž‡ǡ‹ˆƒ’‡”•‘‡ƒ–•‹…‡…”‡ƒǡ–Š‡…Šƒ…‡‘ˆŽ‘•‹‰™‡‹‰Š–‹•Ž‘™‡”‡†ǡƒ†–Š‡ ƒ…–‘ˆ‡ƒ–‹‰‹…‡…”‡ƒ†‘‡•‘–…ƒ—•‡–Š‡Ž‘••‘ˆ™‡‹‰Š–Ǥ‡–Š—•…‘…Ž—†‡–Šƒ–‘‡ ‡˜‡–…ƒ—•‡•ƒ•‡…‘†Œ—•–‹…ƒ•‡–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ–Š‡•‡…‘†‰‹˜‡–Šƒ––Š‡ˆ‹”•– ‘……—”•‹•‰”‡ƒ–‡”–Šƒ–Šƒ–‘ˆ–Š‡•‡…‘†‰‹˜‡–Šƒ––Š‡ˆ‹”•–†‘‡•‘–‘……—”ȏͳͳǡͳ͸ǡ ͵ͶȐǤ ‘‰–Š‡”‡ƒ•‘•‰‹˜‡„›‹–…Š…‘…ȏͳͳǡͳ͸Ȑˆ‘”ƒ„ƒ†‘‹‰”‡‰—Žƒ”‹–› –Š‡‘”‹‡•ǡ™Š‹…Šƒ”‡„ƒ•‡†‘†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›ǡ‹•–Š‡‡š‹•–‡…‡‘ˆ‹’‡”ˆ‡…– ”‡‰—Žƒ”‹–‹‡•ƒ†•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•Ǥ ’‡”ˆ‡…–”‡‰—Žƒ”‹–‹‡•ƒ”‹•‡ˆ”‘–Š‡ˆƒ…––Šƒ– 

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‡ˆˆ‡…–•†‘‘–‹˜ƒ”‹ƒ„Ž›ˆ‘ŽŽ‘™–Š‡‹”•—’’‘•‡†…ƒ—•‡Ǥ‡šƒ’Ž‡‘ˆƒ‹’‡”ˆ‡…– ”‡‰—Žƒ”‹–›‹•–Š‡…ƒ—•ƒŽ•–”—…–—”‡™Š‡”‡„›‡š’‘•—”‡–‘–Š‡ˆŽ—…ƒ—•‡•‹–•…‘–”ƒ…–‹‘ǡ ‡˜‡–Š‘—‰Š•‘‡’‡‘’Ž‡™Š‘ƒ”‡‡š’‘•‡†–‘–Š‡ˆŽ—†‘‘–…‘–”ƒ…–‹–Ǥ†‡”ǡˆŽ— ‡š’‘•—”‡”ƒ‹•‡•–Š‡’”‘„ƒ„‹Ž‹–›‘ˆƒ’‡”•‘…‘–”ƒ…–‹‰–Š‡ˆŽ—Ǥ”‘„ƒ„‹Ž‹•–‹…–Š‡‘”‹‡• ‘ˆ…ƒ—•ƒŽ‹–›”‡…‘‰‹œ‡–Šƒ––Š‡”‡ƒ”‡‘……ƒ•‹‘•™Š‡‡ˆˆ‡…–•‘……—”™‹–Š‘—– ‘……—””‡…‡‘ˆ–Š‡’—–ƒ–‹˜‡…ƒ—•‡ǡƒ†™Š‡ƒ’—–ƒ–‹˜‡…ƒ—•‡‘……—”•™‹–Š‘—–‡Ž‹…‹–‹‰ ‡ˆˆ‡…–•Ǥ ’‡”ˆ‡…–”‡‰—Žƒ”‹–‹‡•‰‡‡”ƒŽŽ›ƒ”‹•‡ˆ‘”‘‡‘ˆ–™‘”‡ƒ•‘•ǣŠ‡–‡”‘‰‡‡‹–› ‘ˆ…ƒ—•ƒŽ‹–›ƒ†–Š‡ˆƒ‹Ž—”‡‘ˆ’Š›•‹…ƒŽ†‡–‡”‹‹•Ǥ ‹”•–ǡ–Š‡ˆƒ…––Šƒ–…ƒ—•ƒŽ ”‡Žƒ–‹‘•†‡’‡†‘ƒ›†‹ˆˆ‡”‡–…‘–‡š–•ƒ†…‹”…—•–ƒ…‡•‡ƒ•–Šƒ–‡ˆˆ‡…–• ƒ”‡”ƒ”‡Ž›•‡‡–‘‹˜ƒ”‹ƒ„Ž›ˆ‘ŽŽ‘™…ƒ—•‡•Ǥ‡…‘†ǡ•‹…‡ƒ›’”‘…‡••‡•ƒ†‡˜‡–• ‹–Š‡’Š›•‹…ƒŽ™‘”Ž†ƒ”‡•–‘…Šƒ•–‹…ƒ†‘†‡–‡”‹‹•–‹…ǡ‹–‹•‘ˆ–‡†‹ˆˆ‹…—Ž–‘” ‹’‘••‹„Ž‡–‘ƒ••‹‰–Š‡Žƒ„‡Ž•Dz…ƒ—•‡dzƒ†Dz‡ˆˆ‡…–dzǤ šƒ’Ž‡•‘ˆ•’—”‹‘—•”‡‰—Žƒ”‹–›ƒ”‡…ƒ—•ƒŽ•–”—…–—”‡•™Š‡”‡—Ž–‹’Ž‡‡ˆˆ‡…–• ˆ‘ŽŽ‘™ˆ”‘ƒ•‹‰Ž‡…ƒ—•‡ǤŠ‡‡ˆˆ‡…–•ƒ›‘……—”…‘…—””‡–Ž›‘”™‹–Š–‹‡†‡Žƒ›Ǥ ‡–‡‘”‘Ž‘‰‹…ƒŽ‡šƒ’Ž‡‰‹˜‡„›‹–…Š…‘…‹•–Šƒ–‘ˆƒ†”‘’‹„ƒ”‘‡–”‹…’”‡••—”‡ …ƒ—•‹‰ƒ†”‘’‹–Š‡Š‡‹‰Š–‘ˆƒ…‘Ž—‘ˆ‡”…—”›ƒ†ǡ•Š‘”–Ž›–Š‡”‡ƒˆ–‡”ǡƒ•–‘” ȋ ‹‰—”‡ͳȌǤ†‡–‡”‹‹•–‹…‹–‡”’”‡–ƒ–‹‘‘ˆ…ƒ—•ƒŽ‹–›™‘—Ž†‹•–ƒ‡Ž›‹ˆ‡”–Šƒ– –Š‡†”‘’‹‡”…—”›…ƒ—•‡•–Š‡•–‘”Ǥ•†‹•…—••‡†„‡Ž‘™ǡƒ…‘†‹–‹‘ƒ›„‡ ‹…Ž—†‡†‹–Š‡†‡ˆ‹‹–‹‘‘ˆ•‘–Šƒ–‹–ƒ†‡“—ƒ–‡Ž›ƒ††”‡••‡••’—”‹‘—•”‡‰—Žƒ”‹–‹‡•Ǥ Ž‘‰–”ƒ†‹–‹‘‡š‹•–•‹’Š‹Ž‘•‘’Š›‘ˆƒƒŽ›œ‹‰…ƒ—•ƒŽ‹–›‹–‡”•‘ˆ ’”‘„ƒ„‹Ž‹–›”ƒ‹•‹‰Ǥ ”‘–Š‡’‡”•’‡…–‹˜‡‘ˆǡ…ƒ—•‡•‹ˆ ”ƒ‹•‡•–Š‡’”‘„ƒ„‹Ž‹–› ‘ˆBȏȋȁȌεȏȋȌȐǤŠƒ–‹•ǡDz…ƒ—•‡•dz‡ƒ•Dz–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‰‹˜‡‹• ‰”‡ƒ–‡”–Šƒ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‘……—””‹‰ƒŽ‘‡dzǤŽ–‡”ƒ–‹˜‡Ž›ǡDz…ƒ—•‡•dzƒ›„‡ †‡ˆ‹‡†ƒ•Dz–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‰‹˜‡‹•‰”‡ƒ–‡”–Šƒ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‰‹˜‡–Šƒ– †‘‡•‘–‘……—”dzǡ‘”ȋȁȌεȋȁ̱ȌǤŠ‹•ˆ‘”—Žƒ–‹‘ǡƒ•‹–•–ƒ†•ǡ…ƒ”‡•‘Ž˜‡ ‹’‡”ˆ‡…–”‡‰—Žƒ”‹–‹‡•ǣƒ›”ƒ‹•‡–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‡˜‡‹ˆ‘……—””‡…‡•‘ˆ†‘ ‘–ƒŽ™ƒ›•ˆ‘ŽŽ‘™‘……—””‡…‡•‘ˆǤ‘™‡˜‡”ǡ•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•”‡ƒ‹ƒ ’”‘„Ž‡„‡…ƒ—•‡‘……ƒ•‹‘•ƒ›ƒ”‹•‡™Š‡”‡ƒ’’‡ƒ”•–‘…ƒ—•‡„—–‘……—””‡…‡• ‘ˆ„‘–Šƒ†ƒ”‡ƒ…–—ƒŽŽ›…ƒ—•‡†„›ƒ–Š‹”†ˆƒ…–‘”ǡǤ ‘”‡šƒ’Ž‡ǡ‹‹–…Š…‘…ǯ• ‡–‡‘”‘Ž‘‰‹…ƒŽ‡šƒ’Ž‡ǡ™‹–Šƒ•–Š‡†”‘’‹‡”…—”›ƒ†ƒ•–Š‡•–‘”ǡ–Š‡ ȋȁȌεȋȁ̱Ȍ‹•–”—‡ǡ‡˜‡–Š‘—‰Š–Š‡†”‘’‹„ƒ”‘‡–”‹…’”‡••—”‡ȋˆƒ…–‘”Ȍ‹• –Š‡ƒ…–—ƒŽ…ƒ—•ƒŽˆƒ…–‘”Ǥ Š‡’”‘„Ž‡‘ˆ•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•Šƒ•ƒ’‘••‹„Ž‡’”‘„ƒ„‹Ž‹–›Ǧ”ƒ‹•‹‰ •‘Ž—–‹‘–Šƒ–‘”‹‰‹ƒ–‡•‹–Š‡™”‹–‹‰•‘ˆƒ•‡‹…Š‡„ƒ…Šǡ™Š‘†‡•…”‹„‡†ƒ ’”‘„ƒ„‹Ž‹•–‹…”‡Žƒ–‹‘•Š‹’…ƒŽŽ‡†Dz•…”‡‡‹‰‘ˆˆdzȏͳ͸ȐǤŠ‡‹…Ž—†‡†ƒ•ƒ…‘†‹–‹‘ ‹–Š‡ˆ‘”—Žƒ–‹‘ǡ–Š‹•”‡Žƒ–‹‘•Š‹’ƒŽŽ‘™•–‘ƒ††”‡•••’—”‹‘—•”‡‰—Žƒ”‹–‹‡•Ǥ ‡‹…Š‡„ƒ…Š•ƒ‹†–Šƒ–ˆƒ…–‘”•…”‡‡•‘ˆˆˆ”‘‹ˆ–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‰‹˜‡„‘–Š ƒ†‹•‡“—ƒŽ–‘–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ‰‹˜‡ƒŽ‘‡ǡ‹Ǥ‡ǤǡȋȁȋƬȌȌαȋȁȌǤ ˆ ƒ†ƒ”‡Dz•’—”‹‘—•Ž›…‘””‡Žƒ–‡†dzǡ–Š‡‹•–Š‡…‘‘…ƒ—•‡–Šƒ–†‘‡•–Š‡ •…”‡‡‹‰‘ˆˆǤ ˆ•…”‡‡‹‰Ǧ‘ˆˆ…ƒ—•‡•ƒ”‡‡š…Ž—†‡†ǡ–Š‡•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•ƒ”‡ ƒ˜‘‹†‡†Ǥ‹–…Š…‘…‡š’Žƒ‹•–Š‹•„›ˆ‘”ƒŽ‹œ‹‰‡‹…Š‡„ƒ…Šǯ•–Š‡‘”›ǣ‹ˆ–ƒ†–ƍ ƒ”‡‡˜‡–•–Šƒ–‘……—”ƒ––‹‡•–ƒ†–ǯǡ™‹–Š–ǯˆ‘ŽŽ‘™‹‰–ǡ–Š‡–…ƒ—•‡•–ƍ‹ˆƒ†‘Ž› ‹ˆ–™‘…‘†‹–‹‘•ƒ”‡‡–ǣ



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ͳȌ ȋ–ƍȁ–Ȍεȋ–ƍȁ̱–Ȍ ʹȌ ‘‘–Š‡”‡˜‡––Ǝǡ‘……—””‹‰ƒ––‹‡ǡ–ǯǯǡ™Š‹…Š‹•‡‹–Š‡”‡ƒ”Ž‹‡”–Šƒ‘”ƒ––Š‡ •ƒ‡–‹‡ƒ•–ǡ•…”‡‡•–ƍ ‘ˆˆˆ”‘–Ǥ Š‡ˆ‹”•–…‘†‹–‹‘‹••‹’Ž›ƒ•–ƒ–‡‡–‘ˆƒ•†‡•…”‹„‡†ƒ„‘˜‡Ǥ  …‘„‹ƒ–‹‘™‹–Š–Š‡•‡…‘†…‘†‹–‹‘ǡ–Š‡’‘••‹„‹Ž‹–›‘ˆ•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•‹• ”‡‘˜‡†ǤŠ—•ǡŠƒ•–Š‡ƒ†˜ƒ–ƒ‰‡‘ˆŠƒ†Ž‹‰‹••—‡•–Šƒ–…ƒ‘–Ǥ Šƒ–“—ƒ–‹ˆ‹…ƒ–‹‘‡–Š‘†•—•‡†–‘‡ƒ•—”‡…ƒ—•ƒŽ”‡Žƒ–‹‘•ƒ”‡„ƒ•‡†‘ ƒ–Š‡ƒ–‹…ƒŽƒƒŽ›•‹•‘ˆ’Š›•‹…ƒŽ•›•–‡•‹’Ž‹‡•–Šƒ––Š‡•‡”‡Žƒ–‹‘•ƒ”‡‘„Œ‡…–‹˜‡ ˆ‡ƒ–—”‡•‘ˆ–Š‡™‘”Ž†ǤŠ—•ǡ‹ˆ–Š‡…ƒ—•ƒŽ”‡Žƒ–‹‘•ƒ”‡‘„Œ‡…–‹˜‡ǡ–Š‡ƒ’’”‘’”‹ƒ–‡ †‡•…”‹’–‹‘‘ˆ’”‘„ƒ„‹Ž‹–›‹—•–ƒŽ•‘„‡‹–‡”’”‡–‡†ƒ•„‡‹‰‘„Œ‡…–‹˜‡Ǥ „Œ‡…–‹˜‡‹–‡”’”‡–ƒ–‹‘•‘ˆ’Š›•‹…ƒŽ’”‘„ƒ„‹Ž‹–›Šƒ˜‡‰‡‡”ƒŽŽ›ˆƒŽŽ‡‹–‘–™‘ …ƒ’•ǣˆ”‡“—‡…›˜‹‡™•ƒ†’”‘’‡•‹–›˜‹‡™•Ǥˆ–Š‡–™‘ǡ–Š‡‘•–Ž‹‡Ž›…ƒ†‹†ƒ–‡ ˆ‘”™‘—Ž†•‡‡–‘„‡–Š‡’”‘’‡•‹–›˜‹‡™Ǥ –Š‹•˜‹‡™ǡ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–› ”‡ˆŽ‡…–•–Š‡—†‡”Ž›‹‰’Š›•‹…ƒŽ’”‘’‡•‹–›‘ˆƒ‰‹˜‡‘—–…‘‡ȏ͵ͷȐǤŠ‡ƒ–—”‡‘ˆ ’”‘’‡•‹–›ƒ›„‡—…Ž‡ƒ”ǣˆ‘”‡šƒ’Ž‡ǡ‹–ƒ›‘”ƒ›‘–„‡ƒ’”‘’‡”–›‘ˆ–Š‡ ‡˜‡–‘”‘„Œ‡…–‡šŠ‹„‹–‹‰–Š‡’”‘„ƒ„‹Ž‹–›Ǥ‘‡–Š‡Ž‡••ǡ’”‘’‡•‹–‹‡•Dz•‡‡–‘„‡ ‡ƒ•—”‡•‘ˆǮ…ƒ•—ƒŽ–‡†‡…‹‡•ǯǥdzȏͳ͸ȐǤ ˆƒ…–ǡ–Š‡”‡Šƒ˜‡„‡‡ƒ––‡’–•–‘ ˆ‘”—Žƒ–‡ƒDz’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ…ƒŽ…—Ž—•dz„ƒ•‡†‘‘„Œ‡…–‹˜‡ǡ’Š›•‹…ƒŽ’”‘’‡•‹–‹‡• ȏ͵͸ȐǤŠ‡’”‘’‡•‹–›‹–‡”’”‡–ƒ–‹‘‘ˆ’”‘„ƒ„‹Ž‹–›ƒ’’‡ƒ”•–‘…‘””‡•’‘†™‡ŽŽ™‹–Š –Š‡’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒ–‹‘Ǥ 4. Causality in Complex Systems ƒ…›ƒ”–™”‹‰Š–ǡƒ’”‘‹‡–’Š‹Ž‘•‘’Š‡”‘ˆ•…‹‡…‡ƒ†‡…‘‘‹…•ǡŠƒ• •—‰‰‡•–‡†ƒ’‡”–‹‡–˜‹‡™‘ˆ…ƒ—•ƒŽ‹–›–Šƒ–™‡…‘•‹†‡”–‘„‡”‡Ž‡˜ƒ––‘–Š‡–‘’‹… ‘ˆ…ƒ—•ƒŽ‹–›‹…‘’Ž‡š•›•–‡•ǣ Š‡ –‡” Ǯ…ƒ—•‡ǯ ‹• Š‹‰ŠŽ› —•’‡…‹ˆ‹…Ǥ – …‘‹–• —• –‘ ‘–Š‹‰ƒ„‘—––Š‡‹†‘ˆ…ƒ—•ƒŽ‹–›‹˜‘Ž˜‡†‘”ƒ„‘—–Š‘™–Š‡ …ƒ—•‡•‘’‡”ƒ–‡Ǥ‡…‘‰‹œ‹‰–Š‹••Š‘—Ž†ƒ‡—•‘”‡…ƒ—–‹‘—• ƒ„‘—– ‹˜‡•–‹‰ ‹ –Š‡ “—‡•– ˆ‘” —‹˜‡”•ƒŽ ‡–Š‘†• ˆ‘” …ƒ—•ƒŽ ‹ˆ‡”‡…‡ȏ͵͹ȐǤ  ƒ”–™”‹‰Š–…Žƒ‹•–Šƒ–ƒ˜ƒ”‹‡–›‘ˆ†‹ˆˆ‡”‡–Dz‡–Š‘†•‘ˆ…ƒ—•ƒŽ‹ˆ‡”‡…‡dz …ƒ„‡—•‡†–‘‡ƒ•—”‡…ƒ—•ƒŽ‹–›‹˜ƒ”‹‘—••…‹‡–‹ˆ‹……‘–‡š–•ȏ͵ͺȐǤŽ–Š‘—‰Š‡ƒ…Š‘ˆ –Š‡•‡‡–Š‘†•†‹•’Žƒ›•—‹“—‡•‡–•‘ˆ•–”‡‰–Š•ƒ†™‡ƒ‡••‡•ǡ†‡’‡†‹‰‘–Š‡ …‘–‡š–ǡ™‡ƒ”‰—‡–Šƒ–ƒ’’Ž‹…ƒ–‹‘•–‘Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•”‡“—‹”‡ƒ ’”‘„ƒ„‹Ž‹•–‹…‹–‡”’”‡–ƒ–‹‘‘ˆ…ƒ—•ƒŽ‹–›Ǥ –•Š‘—Ž†„‡‘–‡†–Šƒ––Š‡•‡…ƒ—•ƒŽ‹–› ‡–Š‘†•ƒ”‡„ƒ•‡†‘general accounts‘ˆ…ƒ—•ƒŽ‹–›ǡƒ†•–ƒ†‹Œ—š–ƒ’‘•‹–‹‘–‘ singular accountsǡ™Š‹…Š‘Ž›†‡•…”‹„‡’ƒ”–‹…—Žƒ”‘„Œ‡…–•‘”‡˜‡–•–Šƒ–‡š‹•–‹‘‡ …ƒ—•ƒŽ”‡Žƒ–‹‘ǡ‡Ǥ‰ǤǡǮŠ‡„”‹……ƒ—•‡†–Š‡™‹†‘™–‘•Šƒ––‡”ǯǤ ‡‡”ƒŽƒ……‘—–•ǡ„› …‘–”ƒ•–ǡ†‡•…”‹„‡Dz…ƒ—•ƒŽ”‡Žƒ–‹‘•ƒ‘‰ƒ’’”‘’”‹ƒ–‡Ž›‰‡‡”ƒŽ”‡Žƒ–ƒ•—…Šƒ• ‡˜‡–Ǧ–›’‡•‘”’”‘’‡”–‹‡•dzȏͳ͸ȐǤ‡ˆ—”–Š‡”‘–‡ǡ‹ƒ–‹…‹’ƒ–‹‘‘ˆ–Š‡†‹•…—••‹‘ „‡Ž‘™ǡ–Šƒ–ƒ……‘—–•‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ƒ›„‡ ‰‡‡”ƒŽƒ†•–‹ŽŽ„‡’”‘„ƒ„‹Ž‹•–‹…Ǥ 

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‡ˆ‘…—•Š‡”‡‘…‘’Ž‡š•›•–‡•ƒ•„‡‹‰…‘’‘•‡†‘ˆƒ›‹–‡”ƒ…–‹‰ ’ƒ”–•ǡƒ†ƒ‹–ƒ‹–Šƒ–…ƒ—•ƒŽ‹–›‹…‘’Ž‡š•›•–‡•†‹ˆˆ‡”•ˆ”‘–Šƒ–‹‘Ǧ …‘’Ž‡š•›•–‡•ȏͶͳǡͶʹȐǤ‡ˆ—”–Š‡”’‘•–—Žƒ–‡–Šƒ–…‘’Ž‡š•›•–‡•ƒ”‡™‡ŽŽ •‡”˜‡†„›ƒ’”‘„ƒ„‹Ž‹•–‹…ƒ……‘—–‘ˆ…ƒ—•ƒŽ”‡Žƒ–‹‘„‡–™‡‡–Š‡’ƒ”–•Ǥ ’”‘„ƒ„‹Ž‹•–‹…ƒ……‘—–‘ˆ…ƒ—•ƒŽ‹–›‹•„‡––‡”•—‹–‡†–Šƒƒ†‡–‡”‹‹•–‹…‘‡ˆ‘” ‡š’Žƒ‹‹‰…ƒ—•ƒŽ‹–›‹…‘’Ž‡š•›•–‡•„‡…ƒ—•‡ǣȋͳȌ–™‘‹–‡”ƒ…–‹‰…‘’‘‡–• ƒ›„‡…ƒ—•ƒŽ–‘‡ƒ…Š‘–Š‡”ǢȋʹȌ–Š‡…ƒ—•ƒŽ‹ˆŽ—‡…‡ˆ”‘‘‡‹–‡”ƒ…–‹‰ …‘’‘‡––‘ƒ‘–Š‡”ƒ›‘Ž›„‡‘‡‘ˆƒ›…ƒ—•ƒŽƒ‰‡–•Ǣƒ†ȋ͵Ȍ…ƒ—•ƒŽ ‹ˆŽ—‡…‡•†‘‘–ƒŽ™ƒ›•”‡•—Ž–‹‘„•‡”˜ƒ„Ž‡‡ˆˆ‡…–•ȏͶ͵ǦͶ͸ȐǤ –Š‡‡š–•‡…–‹‘ǡ™‡ …‘•‹†‡”–Š‡•–”—…–—”ƒŽƒ†ˆ—…–‹‘ƒŽ…‘’Ž‡š‹–›‘ˆ–Š‡„”ƒ‹ǡƒ†•—‰‰‡•––Šƒ–ƒ ’”‘„ƒ„‹Ž‹•–‹…ƒ……‘—–‘ˆ…ƒ—•ƒŽ‹–›‹•„‡––‡”•—‹–‡†–Šƒƒ†‡–‡”‹‹•–‹…‘‡ˆ‘” ‡š’Žƒ‹‹‰‡—”ƒŽ…ƒ—•ƒŽ‹–›‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•Ǥ  5. Causality in the Brain Š‡„”ƒ‹‹••–”—…–—”ƒŽŽ›‘”‰ƒ‹œ‡†‹–‘†‹•–‹…–•›•–‡•Šƒ˜‹‰•’‡…‹ƒŽ‹œ‡† ‹’—–•ǡ‘—–’—–•ǡƒ†‹–‡”ƒŽ–‘’‘Ž‘‰›ǤŠ‡ˆ—…–‹‘•‘ˆ–Š‡•‡•›•–‡•ƒ”‡—‹“—‡ǡ ƒ†•—’’‘”–—‹“—‡ˆ‘”•‘ˆ…‘‰‹–‹‘ȏͶ͹ǦͷͳȐǤ ‘”‡šƒ’Ž‡ǡ˜‹•—ƒŽ…‘‰‹–‹‘”‡Ž‹‡• ‘–Š‡˜‹•—ƒŽ…‘”–‡šǡƒ„”ƒ‹•›•–‡Šƒ˜‹‰•’‡…‹ƒŽ‹œ‡†‹’—–’ƒ–Š™ƒ›•‘”‹‰‹ƒ–‹‰‹ –Š‡”‡–‹ƒǡ—Ž–‹’Ž‡‘—–’—–’”‘…‡••‹‰•–”‡ƒ•–Šƒ–ˆ‘ŽŽ‘™†‹•–‹…–’ƒ–Š™ƒ›•ǡƒ†ƒ …‘’Ž‡š‹–‡”ƒŽ–‘’‘Ž‘‰‹…ƒŽ‘”‰ƒ‹œƒ–‹‘‘ˆ‹–‡”…‘‡…–‡†ƒ”‡ƒ•Ǥ‘‡–Š‡Ž‡••ǡ ˜‹•—ƒŽˆ—…–‹‘…ƒ„‡ˆ‘”…‡†‹–‘‘–Š‡”…‘”–‹…ƒŽƒ”‡ƒ•„›”‡Ǧ”‘—–‹‰”‡–‹ƒŽ ’”‘Œ‡…–‹‘•ȏͷʹȐǤ Š‡ƒƒ–‘‹…ƒŽ’ƒ–Š™ƒ›„‡–™‡‡ƒ’ƒ‹”‘ˆ‹–‡”…‘‡…–‡†‡—”‘ƒŽ ’‘’—Žƒ–‹‘•‹†‹ˆˆ‡”‡–„”ƒ‹ƒ”‡ƒ•…‘•‹•–•‘ˆƒš‘•ˆ”‘…‡ŽŽ„‘†‹‡•‹–Š‡•‡†‹‰ ’‘’—Žƒ–‹‘Šƒ˜‹‰ƒš‘–‡”‹ƒŽ•–Šƒ–•›ƒ’•‡‘’‘•–•›ƒ’–‹…‡—”‘•‹–Š‡ ”‡…‡‹˜‹‰’‘’—Žƒ–‹‘–‘™Š‹…Š–Š‡’ƒ–Š™ƒ›‹•†‹”‡…–‡†Ǥ‡‡”‡••Ž‡”ȏͶͻȐˆ‘”ƒ ‡š’‘•‹–‹‘‘ˆ™Š›‹–‡”ƒ…–‹‘•„‡–™‡‡„”ƒ‹ƒ”‡ƒ•ƒ”‡–Š‘—‰Š––‘‘……—”ƒ––Š‡Ž‡˜‡Ž ‘ˆ–Š‡‡—”‘ƒŽ’‘’—Žƒ–‹‘ǡƒ†‘––Š‡•‹‰Ž‡‡—”‘ǤŠ‡’”‡†‘‹ƒ–’ƒ––‡”‘ˆ ƒƒ–‘‹…ƒŽ…‘‡…–‹˜‹–›„‡–™‡‡’‘’—Žƒ–‹‘•‹•–Šƒ–‘ˆ”‡…‹’”‘…ƒŽȋ„‹Ǧ†‹”‡…–‹‘ƒŽȌ ’”‘Œ‡…–‹‘ǡ™‹–Šƒ”‡–—”’ƒ–Š™ƒ›ˆ”‘–Š‡”‡…‡‹˜‹‰’‘’—Žƒ–‹‘–‘–Š‡•‡†‹‰ ’‘’—Žƒ–‹‘ǤŠ—•ǡ’ƒ‹”•‘ˆ‡—”‘ƒŽ’‘’—Žƒ–‹‘•–›’‹…ƒŽŽ›„‘–Š•‡†’”‘Œ‡…–‹‘•–‘ǡ ƒ†”‡…‡‹˜‡–Š‡ˆ”‘ǡ‘‡ƒ‘–Š‡”ǡƒŽ–Š‘—‰Š‹†‹˜‹†—ƒŽ‡—”‘•‹–Š‘•‡ƒ”‡ƒ•ƒ”‡ ‘–‡…‡••ƒ”‹Ž›”‡…‹’”‘…ƒŽŽ›…‘‡…–‡†Ǥƒ–‘‹…ƒŽ’”‘Œ‡…–‹‘•‹–Š‡„”ƒ‹•—’’‘”– ˆ—…–‹‘ƒŽ‹–‡”ƒ…–‹‘•ǡƒ†’”‘Œ‡…–‹‘’ƒ–Š™ƒ›••—’’‘”––Š‡–”ƒ•‹••‹‘‘ˆ•’‹‡ ȋƒ…–‹‘’‘–‡–‹ƒŽȌ–”ƒ‹•‘ƒŽŽ–Š‡ƒš‘•ˆ”‘ƒ•‡†‹‰–‘ƒ”‡…‡‹˜‹‰’‘’—Žƒ–‹‘Ǥ ‡…‹’”‘…ƒŽƒš‘ƒŽ’ƒ–Š™ƒ›•–Š—••—’’‘”–„‹Ǧ†‹”‡…–‹‘ƒŽŽ›–”ƒ•‹––‡†•’‹‡–”ƒ‹•Ǥ ‘’—Žƒ–‹‘•‹–™‘‹–‡”…‘‡…–‡†ƒ”‡ƒ•interact™Š‡–Š‡›ƒ…–‹˜‡Ž›–”ƒ•‹–•’‹‡• –‘‘‡ƒ‘–Š‡”–Šƒ–ƒˆˆ‡…–‡ƒ…Š‘–Š‡”ǯ•ˆ—…–‹‘Ǥ‡—”‘ƒŽ’‘’—Žƒ–‹‘•‹—Ž–‹’Ž‡ ƒ”‡ƒ•–›’‹…ƒŽŽ›‹–‡”ƒ…–ƒ•’ƒ”–‘ˆ–Š‡‘”ƒŽˆ—…–‹‘‘ˆƒ„”ƒ‹•›•–‡ȏͷͶǡͷͷȐǤ Š‡Žƒ”‰‡Ǧ•…ƒŽ‡ƒƒ–‘‹…ƒŽ…‘‡…–‹˜‹–›‘ˆƒ„”ƒ‹•›•–‡”‡ˆ‡”•–‘–Š‡ ’ƒ––‡”‘ˆƒš‘ƒŽ’ƒ–Š™ƒ›•–Šƒ–’”‘Œ‡…–„‡–™‡‡–Š‡‡—”‘ƒŽ’‘’—Žƒ–‹‘•‹‹–• †‹ˆˆ‡”‡–ƒ”‡ƒ•Ǥƒ–‘‹…ƒŽ…‘‡…–‹˜‹–›‹•’”‹ƒ”‹Ž›‹†‡–‹ˆ‹‡†„›ƒƒ–‘‹…ƒŽ–”ƒ…–Ǧ 

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–”ƒ…‹‰–‡…Š‹“—‡•ǡƒ†„›ƒ–Š‡ƒ–‹…ƒŽƒƒŽ›•‹•‘ˆƒš‘ƒŽ–”ƒ…–•—•‹‰•–”—…–—”ƒŽ ‡—”‘‹ƒ‰‹‰Ǥƒ—•ƒŽŽ›†‹”‡…–‡†’Š›•‹‘Ž‘‰‹…ƒŽ‹ˆŽ—‡…‡•ƒ”‡‡š‡”–‡†„›‡—”‘ƒŽ ’‘’—Žƒ–‹‘•‹†‹ˆˆ‡”‡–„”ƒ‹ƒ”‡ƒ•‘‘‡ƒ‘–Š‡”ǤŠ‡›ƒ”‡‹†‡–‹ˆ‹‡†„› •–‹—Žƒ–‹‘–‡…Š‹“—‡•ƒ’’Ž‹‡†‹–Š‡•›•–‡ǡ„›•–ƒ–‹•–‹…ƒŽ…ƒ—•ƒŽ‹–›ƒƒŽ›•‹•‘ˆ ‡—”ƒŽ–‹‡•‡”‹‡•ˆ”‘–Š‡•›•–‡ǡƒ†„›‘†‡Ž‹‰‘ˆ†‹”‡…–‡†‹–‡”ƒ…–‹‘• „‡–™‡‡‡—”‘ƒŽ’‘’—Žƒ–‹‘•‹–Š‡•›•–‡Ǥƒ–‘‹…ƒŽ…‘‡…–‹˜‹–›•—’’‘”–• …ƒ—•ƒŽŽ›†‹”‡…–‡†’Š›•‹‘Ž‘‰‹…ƒŽ‹ˆŽ—‡…‡••‹…‡‡—”‘•…ƒ‘Ž›‹ˆŽ—‡…‡‘‡ ƒ‘–Š‡”™Š‡˜‹ƒ„Ž‡ƒš‘ƒŽ’ƒ–Š™ƒ›•‡š‹•–„‡–™‡‡–Š‡ǤŠ‡‡ƒ•—”‡‡–‘ˆ …ƒ—•ƒŽ‹ˆŽ—‡…‡„‡–™‡‡‡—”‘ƒŽ’‘’—Žƒ–‹‘•‹†‹ˆˆ‡”‡–„”ƒ‹ƒ”‡ƒ•ˆ”‘–Š‡ •–ƒ–‹•–‹…ƒŽƒƒŽ›•‹•‘ˆ‡—”ƒŽ–‹‡•‡”‹‡•…ƒ•—‰‰‡•–ǡ„—–‘–’”‘˜‡ǡ–Š‡‡š‹•–‡…‡‘ˆ …ƒ—•ƒŽŽ›†‹”‡…–‡†’Š›•‹‘Ž‘‰‹…ƒŽ‹ˆŽ—‡…‡•ǤŠ‡‹”‡š‹•–‡…‡…ƒ„‡‘”‡ˆ‹”Ž› ‡•–ƒ„Ž‹•Š‡†‹ˆ–Š‡”‡•—Ž–•‘ˆ•–ƒ–‹•–‹…ƒŽ…ƒ—•ƒŽ‹–›ƒƒŽ›•‹•ƒ”‡˜ƒŽ‹†ƒ–‡†„›‘–Š‡” ‡–Š‘†•Ž‹‡ȋ‡Ž‡…–”‹…ƒŽǡƒ‰‡–‹…ǡ‘”’Šƒ”ƒ…‘Ž‘‰‹…ƒŽȌ•–‹—Žƒ–‹‘‘”‹–‡”ƒ…–‹‘ ‘†‡Ž‹‰Ǥ  5.1 Causality in Large-Scale Brain Networks —”˜‹‡™‹•–Šƒ––Š‡„”ƒ‹•Š‘—Ž†„‡–”‡ƒ–‡†ƒ•ƒ…‘’Ž‡š•›•–‡ǡƒ†–Šƒ–ƒ ’”‘„ƒ„‹Ž‹•–‹…†‡ˆ‹‹–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹•„‡––‡”•—‹–‡†–Šƒƒ†‡–‡”‹‹•–‹…‘‡ˆ‘” ‡š’Žƒ‹‹‰…ƒ—•ƒŽ‹–›‹–Š‡„”ƒ‹Ǥ‡–ƒ‡‹–ƒ•ƒš‹‘ƒ–‹…–Šƒ–‡—”‘ƒŽ’‘’—Žƒ–‹‘• ‹†‹ˆˆ‡”‡–„”ƒ‹ƒ”‡ƒ•…ƒ—•ƒŽŽ›‹ˆŽ—‡…‡‘‡ƒ‘–Š‡”‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”• ȏͷ͵ȐǤ‘•‹†‡”ƒ„Ž‡‡’‹”‹…ƒŽ”‡•‡ƒ”…Šˆ”‘•–—†‹‡•‘ˆŠ—ƒƒ†‘ǦŠ—ƒ ’”‹ƒ–‡•‡‰ƒ‰‡†‹ƒ˜ƒ”‹‡–›‘ˆ…‘‰‹–‹˜‡ˆ—…–‹‘••—’’‘”–•–Š‡‹†‡ƒ‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹‡–™‘”•ȏͷ͸Ǧ͸͹ȐǤ—…Š‡–™‘”•ƒ›„‡—•‡ˆ—ŽŽ›†‡•…”‹„‡†ǡ„ƒ•‡†‘‰”ƒ’Š –Š‡‘”›ȏ͸ʹǡ͸͸Ǧ͸ͺȐ‹–‡”•‘ˆ•’‡…‹ˆ‹…„”ƒ‹”‡‰‹‘•ǡ…ƒŽŽ‡†‘†‡•ǡƒ†•’‡…‹ˆ‹… …‘‡…–‹‘•„‡–™‡‡–Š‘•‡”‡‰‹‘•ǡ…ƒŽŽ‡†‡†‰‡•Ǥ‘†‡•ƒ†‡†‰‡•ƒ”‡‹†‡–‹ˆ‹‡† ‡‹–Š‡”•–”—…–—”ƒŽŽ›ƒ•ƒƒ–‘‹…ƒŽ„”ƒ‹ƒ”‡ƒ•ƒ†…‘‡…–‹‰’ƒ–Š™ƒ›•ǡ‘” ˆ—…–‹‘ƒŽŽ›ƒ•‹–‡”ƒ…–‹‰„”ƒ‹”‡‰‹‘•ƒ†ˆ—…–‹‘ƒŽ…‘‡…–‹‘•ȋ‹–‡”ƒ…–‹‘•ȌǤ —…–‹‘ƒŽŽ›ǡ‡–™‘”‘†‡•ƒ›„‡”‡˜‡ƒŽ‡†„›˜ƒ”‹‘—•‡—”‘‹ƒ‰‹‰‡–Š‘†•ǡ ‡Ǥ‰Ǥǡ•‹‰ƒŽ•‹ˆ ǡ‘”‡–ƒ„‘Ž‹•‹Ǥ —…–‹‘ƒŽ‘†‡•ƒ”‡–Š—•„”ƒ‹ ”‡‰‹‘•–Šƒ–‹–‡”ƒ…–†—”‹‰„”ƒ‹ˆ—…–‹‘ȏ͸ͳǡ͹ʹǦ͹ͷȐǤ”—…‹ƒŽŽ›ǡ†‡ˆ‹‹‰–Š‡‘†‡• ƒ†‡†‰‡•ƒ•’”‡…‹•‡Ž›ƒ•’‘••‹„Ž‡ƒŽŽ‘™•‡–™‘”ˆ—…–‹‘ƒ††›ƒ‹…•–‘„‡ ‹ˆ‡””‡†Ǥ˜‘Ž˜‹‰”‡…‘”†‹‰–‡…Š‘Ž‘‰‹‡•ƒ†ƒƒŽ›–‹…ƒŽ–‡…Š‹“—‡•ƒ”‡…‘–”‹„—–‹‰ ‰”‡ƒ–Ž›–‘–Š‡‘†‡”—†‡”•–ƒ†‹‰‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ȏͷͺǦ͸Ͷǡ͹ͶǦͻͷȐǤ •‹–‡”…‘‡…–‡†•›•–‡•™‹–Šƒ›‹–‡”ƒ…–‹‰…‘’‘‡–•ǡŽƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹‡–™‘”•…‡”–ƒ‹Ž›“—ƒŽ‹ˆ›ƒ•…‘’Ž‡š•›•–‡•ǤŠ‡›ƒ”‡…Šƒ”ƒ…–‡”‹œ‡†„› ”‡…‹’”‘…ƒŽ…ƒ—•ƒŽ‹ˆŽ—‡…‡•„‡–™‡‡‡–™‘”‘†‡•„”‘—‰Š–ƒ„‘—–„›„‹Ǧ†‹”‡…–‹‘ƒŽ ’Š›•‹‘Ž‘‰‹…ƒŽ‹ˆŽ—‡…‡•Ǥ‡–ǡ–Š‡•‡‡‹‰Ž›•‹’Ž‡’Š‡‘‡‘‘ˆ‹–‡”ƒ…–‹‘ ”‡…‹’”‘…‹–›‰”‡ƒ–Ž›–ƒš‡•‘—”—†‡”•–ƒ†‹‰‘ˆ…ƒ—•ƒŽ‹–›Ǥ—”‡Ž›’Š›•‹‘Ž‘‰‹…ƒŽ ‹ˆŽ—‡…‡•ƒ”‡…ƒ—•ƒŽǡ„—–‘—”—•—ƒŽ—†‡”•–ƒ†‹‰‘ˆ…ƒ—•ƒŽ‹–›„”‡ƒ•†‘™‹ˆ‘‡ ‘†‡…ƒ—•ƒŽŽ›‹ˆŽ—‡…‡•ƒ‘–Š‡”™Š‹Ž‡–Šƒ–•‡…‘†•‹—Ž–ƒ‡‘—•Ž›…ƒ—•ƒŽŽ› ‹ˆŽ—‡…‡•–Š‡ˆ‹”•–ǤŠ‹•’Š‡‘‡‘‹•…ƒŽŽ‡†mutual causalityȏͻ͸ȐǤ –Š‡„”ƒ‹ǡ —–—ƒŽ…ƒ—•ƒŽ‹–›‘……—”•™Š‡‘‡‘†‡‹ˆŽ—‡…‡•–Š‡ƒ…–‹˜‹–›‘ˆƒ‘–Š‡”ǡƒ†˜‹…‡ ˜‡”•ƒȋ…ƒ—•‡•ƒ†…ƒ—•‡•ȌǤ‹…‡‹–‹•Ž‘‰‹…ƒŽŽ›‹’‘••‹„Ž‡ˆ‘”–Š‡”‡–‘„‡ 

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—–—ƒŽ†‡–‡”‹‹•ǡ™‡ƒ••‡”––Šƒ–—–—ƒŽ…ƒ—•ƒŽ‹–›‹–Š‡„”ƒ‹—•–„‡ ’”‘„ƒ„‹Ž‹•–‹…ǡ™‹–Š–Š‡‹ˆŽ—‡…‡‘ˆ‡ƒ…Š‘†‡‘…‘‡…–‡†‘†‡•Šƒ˜‹‰ƒ…‡”–ƒ‹ Ž‹‡Ž‹Š‘‘†‘ˆ…ƒ—•‹‰ƒ‡ˆˆ‡…–ǡ‘”‡“—‹˜ƒŽ‡–Ž›ǡŠƒ˜‹‰ƒ…‡”–ƒ‹‹ˆŽ—‡…‡•–”‡‰–ŠǤ •‡…‘†ˆ‡ƒ–—”‡‘ˆ…‘’Ž‡š„”ƒ‹‡–™‘”•–Šƒ–’”‡•‡–•ƒ…ŠƒŽŽ‡‰‡ˆ‘” –Š‡…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›‹•–Š‡convergence‘ˆ’”‘Œ‡…–‹‘•‹–Š‡Žƒ”‰‡Ǧ•…ƒŽ‡ ƒƒ–‘‹…ƒŽ…‘‡…–‹˜‹–›‘ˆ–Š‡„”ƒ‹ȏͻ͹ǡͻͺȐǤ‹–ƒ”›…ƒ—•ƒŽ’ƒ–Š•‘ˆ‹ˆŽ—‡…‡ …ƒ‘–„‡–”ƒ…‡†‹ƒ…‘’Ž‡š•›•–‡‹™Š‹…Š—Ž–‹’Ž‡‡–™‘”‘†‡•…‘…—””‡–Ž› •‡†…ƒ—•ƒŽ‹ˆŽ—‡…‡•–‘ƒ•‹‰Ž‡”‡…‡‹˜‹‰‘†‡ǤŠ‹•–‘’‘Ž‘‰‹…ƒŽƒ””ƒ‰‡‡–ǡ ™Š‹…Š‹˜‘Ž˜‡•–Š‡…‘˜‡”‰‡…‡‘ˆ—Ž–‹’Ž‡‹’—–•‘–‘ƒ•‹‰Ž‡”‡…‡‹˜‹‰‘†‡ǡ‹• …‘‘‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ǤŠ‡…ƒ—•ƒŽ‹ˆŽ—‡…‡•„‡–™‡‡‘†‡•—•– „‡’”‘„ƒ„‹Ž‹•–‹…‹•—…Šƒ•›•–‡•‹…‡–Š‡‹ˆŽ—‡…‡ˆ”‘ƒ•‡†‹‰‘†‡–‘ƒ ”‡…‡‹˜‹‰‘†‡‹•‘Ž›‘‡‘ˆƒ›…‘˜‡”‰‹‰‹ˆŽ—‡…‡•‘–Š‡”‡…‡‹˜‹‰‘†‡͹Ǥ –Š‹”†ˆ‡ƒ–—”‡‘ˆ…‘’Ž‡š„”ƒ‹‡–™‘”•‹•–Š‡„‡Šƒ˜‹‘”‘ˆ‡—”‘•ƒ• –Š”‡•Š‘Ž†—‹–•ǤŠ‡•—‘ˆ’‘•–•›ƒ’–‹…‡ˆˆ‡…–•ƒ›„‡•—„–Š”‡•Š‘Ž†ǡ‹™Š‹…Š…ƒ•‡ ‘‘„•‡”˜ƒ„Ž‡…Šƒ‰‡‹–Š‡’‘•–•›ƒ’–‹…•’‹‡ˆ‹”‹‰’ƒ––‡”‘……—”•ǤŠ‹•ˆ‡ƒ–—”‡ ‡ƒ•–Šƒ–…ƒ—•ƒŽ‹ˆŽ—‡…‡•ˆ”‘‘‡‡—”‘ƒŽ’‘’—Žƒ–‹‘–‘ƒ‘–Š‡”ƒ›Šƒ˜‡‘ ‘„•‡”˜ƒ„Ž‡‡ˆˆ‡…–ǤŠ‹•‹•‘––‘•ƒ›–Šƒ––Š‡‹ˆŽ—‡…‡•Šƒ˜‡‘‡ˆˆ‡…–ƒ–ƒŽŽǣ–Š‡ ’‘•–•›ƒ’–‹…‡„”ƒ‡’‘–‡–‹ƒŽ•‘ˆ–Š‡”‡…‡‹˜‹‰‡—”‘•ƒ›„‡”ƒ‹•‡†…Ž‘•‡”–‘ –Š”‡•Š‘Ž†ȋ‹–Š‡…ƒ•‡‘ˆ‡š…‹–ƒ–‘”›•›ƒ’•‡•Ȍǡ‘”Ž‘™‡”‡†ƒ™ƒ›ˆ”‘–Š”‡•Š‘Ž†ȋˆ‘” ‹Š‹„‹–‘”›•›ƒ’•‡•ȌǤŠ‡•‡•—„–Š”‡•Š‘Ž†‡—”‘ƒŽDz’”‹‹‰dz‹ˆŽ—‡…‡•ƒ›Šƒ˜‡ •—„–Ž‡„—–‹’‘”–ƒ–‡ˆˆ‡…–•–Šƒ–ƒ”‡‘–‘„•‡”˜ƒ„Ž‡„›•–ƒ†ƒ”†‡–Š‘†•Ǥ ˆ…‘—”•‡ǡ’”‘„ƒ„‹Ž‹•–‹……ƒ—•‡•™‹–Š’”‘„ƒ„‹Ž‹–‹‡•–Šƒ–ƒ”‡…Ž‘•‡–‘‘‡ƒ”‡ ‘–†‹ˆˆ‡”‡–ˆ”‘†‡–‡”‹‹•–‹……ƒ—•‡•Ǥ‘‡–Š‡Ž‡••ǡ™‡ƒ”‰—‡–Šƒ––Š‡’”‡˜ƒŽ‡…‡ ‘ˆ—–—ƒŽ…ƒ—•ƒŽ‹–›ǡ’”‘Œ‡…–‹‘…‘˜‡”‰‡…‡‹„”ƒ‹…‘‡…–‹˜‹–›ǡƒ†•—„–Š”‡•Š‘Ž† ‡ˆˆ‡…–•‡…‡••‹–ƒ–‡•–Šƒ–…ƒ—•ƒŽ‹–›„‡–”‡ƒ–‡†ƒ•’”‘„ƒ„‹Ž‹•–‹…Ǥ ‹˜‡–Šƒ––Š‡…ƒ—•ƒŽ ‹ˆŽ—‡…‡•‹ƒŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”ƒ›Šƒ˜‡’”‘„ƒ„‹Ž‹–‹‡•–Šƒ–ƒ”‡ •‹‰‹ˆ‹…ƒ–Ž›„‡Ž‘™‘‡ǡ–Š‡ƒ’”‘„ƒ„‹Ž‹•–‹…ˆ”ƒ‡™‘”‹•…ƒŽŽ‡†ˆ‘”Ǥ Š‡…‘…‡’–‘ˆŠƒ‘‡–”‘’›‹•ƒŽ•‘—•‡ˆ—Žˆ‘”†‡•…”‹„‹‰…ƒ—•ƒŽ ‹ˆŽ—‡…‡•‹…‘’Ž‡š„”ƒ‹‡–™‘”•ȋ•‡‡†‹•…—••‹‘‘–”ƒ•ˆ‡”‡–”‘’›„‡Ž‘™ȌǤ – Šƒ•„‡‡’”‘’‘•‡†–Šƒ–‡–™‘”‘†‡•‡š’”‡••‹ˆ‘”ƒ–‹‘„›‡–‡”‹‰†‹ˆˆ‡”‡– ƒ…–‹˜‹–›•–ƒ–‡•ǡƒ†–Šƒ–ƒ›‘†‡…ƒ’‘–‡–‹ƒŽŽ›‡š’”‡••ƒ—Ž–‹’Ž‹…‹–›‘ˆ•—…Š•–ƒ–‡• ȏͻͻǡͳͲͲȐǤŠƒ‘‡–”‘’›“—ƒ–‹ˆ‹‡•–Š‡‹ˆ‘”ƒ–‹‘‡š’”‡••‡†„›–Š‡‘†‡ǡ †‡ˆ‹‹‰‹–ƒ•ƒ”‡†—…–‹‘‹–Š‡—…‡”–ƒ‹–›‘ˆ‹ˆ‘”ƒ–‹‘‡š’”‡••‹‘ǤŠ‡ƒŽŽ ’‘••‹„Ž‡ƒ…–‹˜‹–›•–ƒ–‡•‘ˆ–Š‡‘†‡Šƒ˜‡ƒ’’”‘š‹ƒ–‡Ž›–Š‡•ƒ‡Ž‹‡Ž‹Š‘‘†‘ˆ  ͹ –ƒ›ƒ…–—ƒŽŽ›’”‘˜‡‘”‡ˆ”—‹–ˆ—Ž‹–Š‡Ž‘‰”—–‘ƒ„ƒ†‘–Š‡Žƒ‰—ƒ‰‡‘ˆcausalityƒŽŽ–‘‰‡–Š‡”ǡ

ƒ†”‡’Žƒ…‡‹–„›–Š‡Žƒ‰—ƒ‰‡‘ˆ’ƒ––‡”‰‡‡”ƒ–‹‘ƒ†…‘•–”ƒ‹–ȏͷ͸ȐǤ ˆƒ…–ǡ’ƒ––‡”…‘•–”ƒ‹– ƒ›„‡‘”‡…Ž‘•‡Ž›”‡Žƒ–‡†–‘–Š‡’Š›•‹‘Ž‘‰‹…ƒŽ‡…Šƒ‹••–Šƒ–•—’’‘”–‹–‡”ƒ…–‹‘•‹Žƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹‡–™‘”•–Šƒ…ƒ—•ƒŽ‹–›ǤŠ‡…‘…‡’–‘ˆ…‘•–”ƒ‹––Š—•†‡•‡”˜‡•…Ž‘•‡”‹•’‡…–‹‘•‹…‡‹–ƒ› „‡…Ž‘•‡Ž›ƒŽ‹‰‡†™‹–Š–Š‡’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǣ„‘–Š…‘•–”ƒ‹–ƒ†’”‘„ƒ„‹Ž‹–›ƒ”‡ ‰”ƒ†‡†“—ƒ–‹–‹‡•ǡ”ƒ‰‹‰ˆ”‘™‡ƒ–‘•–”‘‰Ǥ





ͳͷ

‡š’”‡••‹‘ǡŠƒ‘‡–”‘’›‹•ƒš‹ƒŽ„‡…ƒ—•‡–Š‡”‡‹•ƒš‹ƒŽ—…‡”–ƒ‹–› ƒ„‘—–™Šƒ–‹–••–ƒ–‡™‹ŽŽ„‡ȏͻͻȐǤŠ‡•–”‡‰–Š‡‹‰‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡•‘–‘–Š‡ ‘†‡ƒ›…ƒ—•‡•‘‡•–ƒ–‡•–‘‹…”‡ƒ•‡‹Ž‹‡Ž‹Š‘‘†ƒ†‘–Š‡”•–‘†‡…”‡ƒ•‡Ǥ –Šƒ– …ƒ•‡ǡ‹ˆ‘”ƒ–‹‘‡š’”‡••‹‘„›–Š‡‘†‡„‡…‘‡•‘”‡…‡”–ƒ‹ǡƒ†Šƒ‘ ‡–”‘’›†‡…”‡ƒ•‡•ǤŠ‡•–”‡‰–Š‡‹‰‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹ƒ›…‘‡ ƒ„‘—–™‹–ŠŽ‡ƒ”‹‰Ǥ –Š‹••…‡ƒ”‹‘ǡŽ‡ƒ”‹‰…ƒ—•‡•…‡”–ƒ‹•–ƒ–‡•–‘„‡̶•‡Ž‡…–‡†̶ ˆ‘”‡š’”‡••‹‘–‘–Š‡‡š…Ž—•‹‘‘ˆ‘–Š‡”•ǡƒ†–Š—•–Š‡†‹•–”‹„—–‹‘‘ˆƒ…–‹˜‹–›•–ƒ–‡• –‘„‡…‘‡‘”‡‘Ǧ—‹ˆ‘”Ǥ‹…‡Ž‡ƒ”‹‰‹•‡š’‡…–‡†–‘‹˜‘Ž˜‡ƒŽŽ–Š‡‘†‡•‹ƒ Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”ǡ–Š‡‡ƒ‡–”‘’›Ž‡˜‡Ž‘ˆ–Š‡‡–™‘”‹•’”‡†‹…–‡†–‘ †‡…”‡ƒ•‡ǡƒ†–Š‡‡–™‘”–‘„‡…‘‡‘”‡‘”†‡”‡†ǡƒ•ƒ”‡•—Ž–‘ˆŽ‡ƒ”‹‰Ǥ  5.2 Quantification of Probabilistic Causality in the Brain –‹•ƒ™‡ŽŽǦ‘™’”‘’‡”–›‘ˆ•–‘…Šƒ•–‹…’”‘…‡••‡•–Šƒ––Š‡’ƒ•–˜ƒŽ—‡•‹ –Š‡‹”–‹‡•‡”‹‡•…ƒŠƒ˜‡…ƒ—•ƒŽǡ„—–‘Ǧ†‡–‡”‹‹•–‹…ǡ‡ˆˆ‡…–•‘ˆ—–—”‡˜ƒŽ—‡•‹ –Š‡‹”–‹‡•‡”‹‡•ƒ†‹–Š‡–‹‡•‡”‹‡•‘ˆ‘–Š‡””‡Žƒ–‡†’”‘…‡••‡•Ǥ—…Š’”‘„ƒ„‹Ž‹•–‹… ‡ˆˆ‡…–•…ƒ„‡‡ƒ•—”‡†„›‡–Š‘†•–Šƒ–‹˜‘Ž˜‡–‹‡•‡”‹‡•‘†‡Ž‹‰ȏͳͲͳȐǤŠ‡ –Š‡–‹‡•‡”‹‡•ƒ”‡‡ƒ•—”‡†ˆ”‘–Š‡‘†‡•‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ǡƒ …‘””‡•’‘†‡…‡ƒ›„‡‘„•‡”˜‡†„‡–™‡‡‘†‡ŽǦ†‡”‹˜‡†…ƒ—•ƒŽ‹–›‡ƒ•—”‡•ƒ† …ƒ—•ƒŽ‹ˆŽ—‡…‡•„‡–™‡‡‡–™‘”‘†‡•ȏͳͲͳǦͳͲͶȐǤ‹”‡…–‡†ˆ—…–‹‘ƒŽ‡†‰‡•‹ Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ƒ”‡–Š—•…‘‘Ž›”‡’”‡•‡–‡†„›•–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ–‡ˆˆ‡…–•†‡”‹˜‡†ˆ”‘–‹‡•‡”‹‡•‘†‡Ž•ȋ ‹‰—”‡ʹȌǤŠ‡•‡‡†‰‡•ǡ ”‡’”‡•‡–‹‰†‹”‡…–‡†‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹ǡƒ”‡…‘•‹•–‡–™‹–Š–Š‡†‹”‡…–‡†ƒ† ’”‘„ƒ„‹Ž‹•–‹…ƒ‡”‹™Š‹…Š‡–™‘”‘†‡•ƒˆˆ‡…–‘‡ƒ‘–Š‡”ǤŠ‡•—……‡••‘ˆ –Š‡•‡•–ƒ–‹•–‹…ƒŽ‡ƒ•—”‡‡–‡–Š‘†••—’’‘”–•–Š‡’”‘„ƒ„‹Ž‹•–‹…ƒ–—”‡‘ˆ–Š‡ …ƒ—•ƒŽ‡ˆˆ‡…–•–Šƒ––Š‡›”‡˜‡ƒŽǤ –Šƒ•„‡‡ƒ”‰—‡†–Šƒ–‡ƒ•—”‹‰…ƒ—•ƒŽ‹ˆŽ—‡…‡• ‹…‘’Ž‡š„”ƒ‹‡–™‘”•”‡“—‹”‡•“—ƒ–‹ˆ‹…ƒ–‹‘‡–Š‘†•–Šƒ–‡‡–•‡˜‡”ƒŽ —†‡”Ž›‹‰…”‹–‡”‹ƒȏͳͲʹȐǤŠ‡•‡…”‹–‡”‹ƒ‹…Ž—†‡ǣŠƒ˜‹‰ƒ‡ƒ•—”ƒ„Ž‡strength‘ˆ ƒ••‘…‹ƒ–‹‘„‡–™‡‡…ƒ—•‡ƒ†‡ˆˆ‡…–Ǣ–Š‡‡ƒ•—”‡†…ƒ—•ƒŽ”‡Žƒ–‹‘Šƒ˜‹‰ consistencyǢ–Š‡”‡Žƒ–‹‘Šƒ˜‹‰specificityǢƒ†‹–Šƒ˜‹‰temporalityȋ…ƒ—•‡ ’”‡…‡†‹‰‡ˆˆ‡…–ȌǤƒ–Š‡ƒ–‹…ƒŽƒƒŽ›•‹•‹•ƒ––Š‡Š‡ƒ”–‘ˆƒ—„‡”‘ˆ†‹ˆˆ‡”‡– ‡–Š‘†•—•‡†–‘—…‘˜‡”…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹Ǥ”‘‹‡–ƒ‘‰–Š‡•‡ƒ”‡ ‡‹‡”Ǧ ”ƒ‰‡”ƒ—•ƒŽ‹–›ȋ Ȍǡ›ƒ‹…ƒ—•ƒŽ‘†‡Ž‹‰ȋȌǡƒ†”ƒ•ˆ‡” –”‘’›ȋȌȏʹͶǡͷ͹ǡ͹ͳǡͳͲ͸ȐǤ‡™‹ŽŽ†‹•…—••ƒŽŽ–Š”‡‡ƒ’’”‘ƒ…Š‡•ǡ„—–™‡ˆ‘…—• ˆ‘”‡‘•–‘ ƒ•ƒ“—ƒ–‹ˆ‹…ƒ–‹‘‡–Š‘†–Šƒ–‹ˆ‡”•’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›„› ƒ’’Ž›‹‰ƒ–Š‡ƒ–‹…ƒŽ‡–Š‘†•–‘‡—”ƒŽ–‹‡•‡”‹‡•†ƒ–ƒǡ–Š—•…‘„‹‹‰ ‡’‹”‹…ƒŽ†ƒ–ƒ™‹–Ša prioriƒƒŽ›–‹…–‡…Š‹“—‡•Ǥ

”ƒ‰‡”ȏʹͶǡͳͲ͹ǦͳͲͺȐ—•‡†ƒ…‘…‡’–—ƒŽ‘–‹‘’”‘˜‹†‡†„›‹‡‡”ȏͳͲͻȐ –‘ƒ’’Ž›ƒ‘’‡”ƒ–‹‘ƒŽ†‡ˆ‹‹–‹‘‘ˆ…ƒ—•ƒŽ‹–›–‘‡…‘‘‹…–‹‡•‡”‹‡•†ƒ–ƒ„ƒ•‡†‘ –‹‡•‡”‹‡•’”‡†‹…–‹‘ȋƒŽ•‘…ƒŽŽ‡†ˆ‘”‡…ƒ•–‹‰ȌǤ –Š‡‡…‘‘‹……‘–‡š–ǡ‹ˆ‡”‡…‡ ƒ„‘—–…ƒ—•ƒŽ‹ˆŽ—‡…‡‹•ƒ†‡•‘Ž‡Ž›ˆ”‘–‹‡•‡”‹‡•†ƒ–ƒǡDz™‹–Š‘—–ƒ›†‹”‡…– ”‡ˆ‡”‡…‡–‘„ƒ…‰”‘—†‡…‘‘‹…–Š‡‘”›dzȏʹͶȐǤŠ‡•ƒ‡‹•–”—‡™Š‡ƒ’’Ž›‹‰  –‘‡—”ƒŽ–‹‡•‡”‹‡•†ƒ–ƒȂ†‹”‡…–”‡ˆ‡”‡…‡–‘„ƒ…‰”‘—†‡—”‘•…‹‡–‹ˆ‹… ’”‹…‹’Ž‡•…ƒ‡••‡–‹ƒŽŽ›„‡‹‰‘”‡†Ǥ 

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”ƒ‰‡”ǯ•ƒ’’”‘ƒ…Šǡˆ‘”–™‘–‹‡•‡”‹‡•ǡ‹•–‘†‡–‡”‹‡™Š‡–Š‡”‘‡–‹‡ •‡”‹‡•‹•’”‡†‹…–‹˜‡‘ˆ–Š‡‘–Š‡”„›—•‹‰Ž‹‡ƒ””‡‰”‡••‹‘‘†‡Ž•ȏͳͳͲǦͳͳʹȐǤ‘”‡ •’‡…‹ˆ‹…ƒŽŽ›ǡˆ‘”–‹‡•‡”‹‡•ͳƒ†ʹǡ‹ˆ‘‡…ƒ„‡––‡”’”‡†‹…–ʹƒ–‘‡–‹‡—•‹‰ ‡ƒ”Ž‹‡”–‹‡˜ƒŽ—‡•‘ˆʹƒ†ͳǡ–Šƒ„›•‹’Ž›—•‹‰‡ƒ”Ž‹‡”˜ƒŽ—‡•‘ˆʹƒŽ‘‡ǡ–Š‡ ͳ…‘–ƒ‹•‹ˆ‘”ƒ–‹‘—•‡ˆ—Žˆ‘”’”‡†‹…–‹‰ʹǤ˜‡‹ˆ–Š‡…ƒ—•ƒŽ‡…Šƒ‹•‹• —‘™ǡ‹–‹••ƒ‹†–Šƒ–ͳGranger-causesʹǤ ”ƒ‰‡”—•‡†Ž‹‡ƒ”ƒ—–‘”‡‰”‡••‹˜‡ –‹‡•‡”‹‡•‘†‡Ž‹‰–‘ˆ‘”ƒŽ‹œ‡–Š‡‘–‹‘ǤŠ—•ǡ•—’’‘•‡–Šƒ–X1(t)ƒ†X2(t)ƒ”‡ ‘†‡Ž‡†„›–Š‡•—ƒ–‹‘•‘–Š‡”‹‰Š–ǦŠƒ†•‹†‡•‘ˆ–Š‡‡“—ƒ–‹‘•ǣ







ȋͳȌ

™Š‡”‡X1(t)ƒ†X2(t)ƒ”‡–Š‡’”‡†‹…–‡†˜ƒŽ—‡•‘ˆ™‹†‡Ǧ•‡•‡•–ƒ–‹‘ƒ”›•–‘…Šƒ•–‹… –‹‡•‡”‹‡•ͳƒ†ʹǢp‹•–Š‡ƒš‹—–‹‡Žƒ‰‹–Š‡‘†‡Žȋ…ƒŽŽ‡†–Š‡‘†‡Ž ‘”†‡”ȌǢA‹•–Š‡ƒ–”‹š…‘–ƒ‹‹‰–Š‡…‘‡ˆˆ‹…‹‡–•‘ˆ–Š‡‘†‡ŽǡX1(t-j)ƒ†X2(t-j) ”‡’”‡•‡––Š‡’ƒ•–˜ƒŽ—‡•‘ˆͳƒ†ʹǡƒ†E1(t)ƒ†E2(t)ƒ”‡–Š‡’”‡†‹…–‹‘‡””‘”• ‘ˆ–Š‡‘†‡Ž•ȋƒŽ•‘…ƒŽŽ‡†‹‘˜ƒ–‹‘•Ȍȋƒ†ƒ’–‡†ˆ”‘ȏͳͳͲǡͳͳͳȐȌǤ ˆ–Š‡˜ƒ”‹ƒ…‡‘ˆ –Š‡’”‡†‹…–‹‘‡””‘”‘ˆ–Š‡‘†‡Ž‘ˆʹ‹••‹‰‹ˆ‹…ƒ–Ž›”‡†—…‡†„›‹…Ž—†‹‰’ƒ•– ˜ƒŽ—‡•‘ˆͳǡƒ•…‘’ƒ”‡†–‘‘–‹…Ž—†‹‰–Š‡ǡ–Š‡ͳ ”ƒ‰‡”Ǧ…ƒ—•‡•ʹǤ ˆ–Š‡ ƒ••—’–‹‘•‘ˆ•–‘…Šƒ•–‹…‹–›ǡ™‹†‡Ǧ•‡•‡•–ƒ–‹‘ƒ”‹–›ǡƒ†Ž‹‡ƒ”‹–›ƒ”‡˜ƒŽ‹†ǡ–Š‡ –Š‡—ŽŽŠ›’‘–Š‡•‹•‘ˆ‘•‹‰‹ˆ‹…ƒ– ”ƒ‰‡”…ƒ—•ƒŽ”‡Žƒ–‹‘…ƒ„‡–‡•–‡†™‹–Šƒ Ǧ –‡•–ȏͳͳͳȐǤ Ž–Š‘—‰Š–Š‡ƒˆ‘”‡‡–‹‘‡†ƒ—–‘”‡‰”‡••‹˜‡ˆ‘”—Žƒ–‹‘‹•„‹˜ƒ”‹ƒ–‡ȋͳ ƒ†ʹȌǡ–Š‡–‡…Š‹“—‡…ƒ„‡‰‡‡”ƒŽ‹œ‡†–‘ƒ—Ž–‹˜ƒ”‹ƒ–‡ƒ—–‘”‡‰”‡••‹˜‡ȋȌ ‘†‡Ž‹™Š‹…Š–Š”‡‡‘”‘”‡–‹‡•‡”‹‡•ƒ”‡”‡’”‡•‡–‡†ȏͻͺȐǤ‡—•‡ˆ‘”–Š‡ ‘†‡Ž‹•–‘…‘’—–‡–Š‡…‘†‹–‹‘ƒŽ Ǥ ˆ–Š”‡‡–‹‡•‡”‹‡•ƒ”‡ͳǡʹǡƒ† ͵ǡ–Š‡ …ƒ„‡…‘’—–‡†ˆ”‘ͳ–‘ʹ…‘†‹–‹‘ƒŽ‘͵ȏͳͲͻȐǤ –‡”‡•–‹‰Ž›ǡ –Š‡„‹˜ƒ”‹ƒ–‡…ƒ•‡‹•‘ˆ–‡‘–ƒ„Ž‡–‘†‹•–‹‰—‹•Š„‡–™‡‡•‹‹Žƒ”…ƒ—•ƒŽ …‘‡…–‹˜‹–›’ƒ––‡”•ȋ•‡‡†‹•…—••‹‘„‡Ž‘™ȌǤ ‘”‹•–ƒ…‡ǡ‹ˆƒ’ƒ‹”™‹•‡ƒƒŽ›•‹• ”‡˜‡ƒŽ•ƒ…ƒ—•ƒŽ…‘‡…–‹˜‹–›’ƒ––‡”ˆ”‘ͳ–‘ʹǡ–Š‡…ƒ—•ƒŽ‹ˆŽ—‡…‡…‘—Ž†„‡ †‹”‡…–ǡ‘”‹†‹”‡…–Ž›‡†‹ƒ–‡†„›ƒ–Š‹”†–‹‡•‡”‹‡•͵ǤŠ‡ ˆ”‘ͳ–‘ʹǡ …‘†‹–‹‘ƒŽ‘͵ǡ…ƒ†‹•–‹‰—‹•Š™Š‡–Š‡”–Š‡‹ˆŽ—‡…‡ˆ”‘ͳ–‘ʹ‹•†‹”‡…–‘” ‡†‹ƒ–‡†„›–Š‡–Š‹”†–‹‡•‡”‹‡•͵ǡ™Š‡”‡͵ƒ›„‡ƒ›”‡…‘”†‡†–‹‡•‡”‹‡• ȏͳͳͳǡͳͳͶȐǤ‡…‡ǡƒƒŽ›•‹•”‡˜‡ƒŽ•ƒ…ƒ—•ƒŽ‹ˆŽ—‡…‡ˆ”‘ͳ–‘ʹ‹ˆ ‹ˆ‘”ƒ–‹‘ˆ”‘ͳ‹•—•‡ˆ—Žˆ‘”’”‡†‹…–‹‰ʹǡƒ†ǡ„›…‘’—–‹‰…‘†‹–‹‘ƒŽ •ǡ ™‡…ƒ†‡–‡”‹‡‹ˆ–Šƒ–‹ˆŽ—‡…‡‹•‡†‹ƒ–‡†„›ƒ›—„‡”‘ˆ‘–Š‡””‡…‘”†‡† ’”‘…‡••‡•Ǥ‘•‡“—‡–Ž›ǡƒƒŽ›•‹•ƒ›„‡—•‡ˆ—ŽŽ›‡’Ž‘›‡†ˆ‘”‹˜‡•–‹‰ƒ–‹‰ –Š‡…ƒ—•ƒŽ‹ˆŽ—‡…‡•ƒ–’Žƒ›„‡–™‡‡–Š‡‘†‡•‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ȏ͸ͻǦ ͹ͳȐǤ



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Š‡•‡…‘•‹†‡”ƒ–‹‘•Ž‡ƒ†–‘–Š‡“—‡•–‹‘‘ˆ–Š‡‡ƒ‹‰‘ˆ ”ƒ‰‡” …ƒ—•ƒŽ‹–›ǣ‹••ƒ›‹‰Granger-causes‡“—‹˜ƒŽ‡––‘•ƒ›‹‰causesǫ‘ ”‡…ƒ’‹–—Žƒ–‡–Š‡’”‡…‡†‹‰ǡ™‡Šƒ˜‡‡šƒ‹‡†˜ƒ”‹‘—•˜‹‡™•‘ˆ…ƒ—•ƒŽ‹–›ˆ”‘ ’Š‹Ž‘•‘’Š›ǡ’Š›•‹…•ǡ…‘’Ž‡š•›•–‡•ǡƒ†‡—”‘•…‹‡…‡–Šƒ–Ž‡ƒ†—•–‘•—’’‘”––Š‡ ‹†‡ƒ‘ˆ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›Ǥ‡ƒ•™‡”‹–Š‡ƒˆˆ‹”ƒ–‹˜‡ǡƒ†…‘…Ž—†‡–Šƒ–  ‹•‡–‹”‡Ž›…‘•‹•–‡–™‹–Š–Š‡‹†‡ƒ‘ˆ’”‘„ƒ„‹Ž‹•–‹……ƒ—•ƒŽ‹–›Ǥ –Š‹•ǡ™‡ˆ‘ŽŽ‘™ ‘‘˜‡”ȏͳͳ͸Ȑ‹‘–‹‰–Šƒ––Š‡’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›‹•ƒDzƒ–—”ƒŽ •—……‡••‘”–‘—‡dzǡƒ†‘–‡–Šƒ–—‡ǯ•…‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›‹•ǡƒ•‡–‹‘‡† ƒ„‘˜‡ǡˆ”ƒ—‰Š–™‹–Š†‹ˆˆ‹…—Ž–‹‡•ǡ‹…Ž—†‹‰•’—”‹‘—•”‡‰—Žƒ”‹–‹‡•Ǥ —”–Š‡”ǡ•–—†‹‡•‘ˆ Š‡–‡”‘‰‡‡‘—•ˆ—…–‹‘ƒŽ‹–‡”ƒ…–‹‘•„‡–™‡‡„”ƒ‹ƒ”‡ƒ•ȏͳͳͳȐ•Š‘™–Šƒ–ƒ ’”‘„ƒ„‹Ž‹•–‹…˜‹‡™‘ˆ…ƒ—•ƒŽ‹ˆŽ—‡…‡‹•‡…‡••ƒ”›Ǥ –‡”‡•–‹‰Ž›ǡ’”‘„Ž‡•ƒ”‹•‡‹ •—…Š•–—†‹‡•ȋ ‹‰—”‡͵Ȍ–Šƒ–ƒ”‡ƒƒŽ‘‰‘—•–‘‹–…Š…‘…ǯ•‡–‡‘”‘Ž‘‰‹…ƒŽ‡šƒ’Ž‡ǣ ‘‡„”ƒ‹ƒ”‡ƒƒ›„‡•’—”‹‘—•Ž›‹†‡–‹ˆ‹‡†ƒ•„‡‹‰…ƒ—•ƒŽ–‘ƒ‘–Š‡”ǡ™Š‡‹ˆƒ…–ǡ –Š‡…ƒ—•ƒŽ‹ˆŽ—‡…‡ƒ…–—ƒŽŽ›ƒ”‹•‡•ˆ”‘ƒ–Š‹”†ƒ”‡ƒǤŠ—•ǡ‹ƒ‰”‡‡‡–™‹–Š ‹–…Š…‘…ǡ™‡ƒ”‰—‡ƒ‰ƒ‹•––Š‡ƒ’’Ž‹…ƒ–‹‘‘ˆƒ›”‡‰—Žƒ”‹–›–Š‡‘”›–‘…ƒ—•ƒŽ ”‡Žƒ–‹‘•‹–Š‡„”ƒ‹Ǥ‘†‹–‹‘ƒŽ ”ƒ‰‡”…ƒ—•ƒŽ‹–›†‹•ƒ„‹‰—ƒ–‡•–Š‡•‡•‹–—ƒ–‹‘• „›‹…Ž—†‹‰–Š‡•‹—Ž–ƒ‡‘—•Ž›”‡…‘”†‡†–‹‡•‡”‹‡•ˆ”‘–Š‡–Š‹”†ƒ”‡ƒȏͻ͹ǡͻͺȐǡ‹ Ž‹‡ƒ‡”–‘–Š‡’”‡˜‹‘—•Ž›†‹•…—••‡†‹…Ž—•‹‘‘ˆ‡‹…Š‡„ƒ…Šǯ•…‘‘…ƒ—•‡ ‹•…”‡‡‹‰‘ˆˆǤ …‘…Ž—•‹‘ǡ™‡ƒ‰”‡‡™‹–Š ”ƒ‰‡”ǯ•…Žƒ‹–Šƒ––Š‡Dz™‡‹‰Š–Ǧ‘ˆǦ ‡˜‹†‡…‡dzŒ—•–‹ˆ‹‡•–Šƒ–…ƒ—•ƒŽ‹–›…ƒ„‡‹ˆ‡””‡†ˆ”‘•–ƒ–‹•–‹…ƒŽ†ƒ–ƒȏʹͶȐǤ‡ ˆ—”–Š‡”’”‘’‘•‡–Šƒ–…‘†‹–‹‘ƒŽ ǡƒ†‘–Š‡”“—ƒ–‹ˆ‹…ƒ–‹‘‡–Š‘†•Ž‹‡‹–ǡ†‘ǡ ‹ˆƒ…–ǡ‡ƒ•—”‡…ƒ—•ƒŽ‹ˆŽ—‡…‡•–Šƒ–ƒ”‡†‡ˆ‹‡†’”‘„ƒ„‹Ž‹•–‹…ƒŽŽ›Ǥ••—…Šǡ–Š‡•‡ ‡ƒ•—”‡•ƒ”‡™‡ŽŽ•—‹–‡†–‘“—ƒ–‹ˆ›‹‰…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹Ǥ ‹‡ ǡ†›ƒ‹…ƒŽ…ƒ—•ƒŽ‘†‡Ž‹‰ȋȌ‹•ƒƒ–Š‡ƒ–‹…ƒŽŽ›„ƒ•‡†ǡ –‡•–ƒ„Ž‡‡–Š‘†‘Ž‘‰›—•‡†–‘‹ˆ‡”†‹”‡…–‡†‹ˆŽ—‡…‡•‹Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹ ‡–™‘”•Ǥ ǡ•‡‰”‡‰ƒ–‡†„”ƒ‹”‡‰‹‘•–Šƒ–•Š‘™ƒ…–‹˜ƒ–‹‘‹˜ƒ”‹‘—• ‡—”‘‹ƒ‰‹‰–‡…Š‹“—‡•ƒ”‡”‡’”‡•‡–‡†ƒ•…‘—’Ž‡††›ƒ‹…ƒŽ•›•–‡•–Šƒ– ‹ˆŽ—‡…‡‘‡ƒ‘–Š‡”Ǥ‡ƒ‹†‹ˆˆ‡”‡…‡„‡–™‡‡ƒ†Ǧ„ƒ•‡†…ƒ—•ƒŽ ‹ˆ‡”‡…‡‹•–Šƒ––Š‡‡š–‡”ƒŽ‹’—–•–‘–Š‡•›•–‡–Šƒ–‰‡‡”ƒ–‡–Š‡‡—”‘‹ƒ‰‹‰ †ƒ–ƒƒ”‡•’‡…‹ˆ‹‡†‹‹‘”†‡”–‘—…‘˜‡”Š‹††‡•–ƒ–‡˜ƒ”‹ƒ„Ž‡•Ǥ Š‹•‘”‹‰‹ƒŽ ’ƒ’‡”‘ǡ ”‹•–‘•–ƒ–‡•–Šƒ–ǡDzŠ‡—•‡‘ˆ†‡•‹‰‡†ƒ†‘™‹’—–•‹ …Šƒ”ƒ…–‡”‹œ‹‰‡—”‘‹ƒ‰‹‰†ƒ–ƒ™‹–Šǥ‹•ƒ‘”‡ƒ–—”ƒŽ™ƒ›–‘ƒƒŽ›œ‡†ƒ–ƒ ˆ”‘†‡•‹‰‡†‡š’‡”‹‡–•ǥ‰‹˜‡–Šƒ––Š‡˜ƒ•–ƒŒ‘”‹–›‘ˆ‹ƒ‰‹‰‡—”‘•…‹‡…‡ ”‡Ž‹‡•—’‘†‡•‹‰‡†‡š’‡”‹‡–•dzȏͳͳ͹ǦͳʹͲȐǤ‘–Š‡”†‹ˆˆ‡”‡…‡‹•–Šƒ–…ƒ—•ƒŽ ‹ˆŽ—‡…‡•‹ƒ”‡…‘•‹†‡”‡†–‘„‡†‡–‡”‹‹•–‹…ǣ ”‹•–‘ˆ—”–Š‡”•–ƒ–‡•–Šƒ– DzŠ‡…‡–”ƒŽ‹†‡ƒ„‡Š‹††›ƒ‹……ƒ—•ƒŽ‘†‡ŽŽ‹‰ȋȌ‹•–‘–”‡ƒ––Š‡„”ƒ‹ƒ•ƒ †‡–‡”‹‹•–‹…‘Ž‹‡ƒ”†›ƒ‹…•›•–‡–Šƒ–‹••—„Œ‡…––‘‹’—–•ƒ†’”‘†—…‡• ‘—–’—–•dzȏͳʹͳȐǤ ˆ—†ƒ‡–ƒŽ“—‡•–‹‘ƒ„‘—–…‘…‡”•–Š‡™ƒ›–Šƒ–‹––”‡ƒ–•–Š‡ …‘…‡’–‘ˆ…ƒ—•ƒŽ‹–›Ǥ ‹˜‡–Šƒ–…‘•‹†‡”•–Š‡„”ƒ‹–‘„‡ƒ†‡–‡”‹‹•–‹… •›•–‡ǡ…ƒ‹–ƒ……‘‘†ƒ–‡ƒ’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǫŠ‡‡š–‡”ƒŽ‹’—–• –‘–Š‡•›•–‡‹ƒ”‡…Ž‡ƒ”Ž›†‡–‡”‹‹•–‹…ǡ‹–Šƒ––Š‡›ƒ”‡‘™ƒ† ‡š’‡”‹‡–ƒŽŽ›†‡•‹‰‡†Ǥ —”–Š‡”‘”‡ǡ–Š‡Š‹††‡•–ƒ–‡•ƒ”‡ƒŽ•‘†‡–‡”‹‹•–‹… •‹…‡–Š‡›ƒ”‡‰‘˜‡”‡†„›ƒ‘Ž‹‡ƒ”†‡–‡”‹‹•–‹…‡“—ƒ–‹‘‘ˆ‘–‹‘ǤŠ—•ǡ‹‹–•



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•–ƒ†ƒ”†ˆ‘”ǡ”‡–ƒ‹•–Š‡…Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›Ǥ‘™‡˜‡”ǡ ™‡†‘‘–…‘…Ž—†‡–Šƒ–‹–•‹Š‡”‡–†‡–‡”‹‹•ƒ‡•ƒ‹˜ƒŽ‹† ‡–Š‘†‘Ž‘‰›ˆ‘”‹ˆ‡””‹‰Žƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•ƒ†…ƒ—•ƒŽ‡…Šƒ‹••‹–Š‡ „”ƒ‹Ǥƒ–Š‡”ǡ™‡ƒ••‡”––Šƒ–ǡ‹‹–•…—””‡–ˆ‘”ǡ†‘‡•‘–ƒŽŽ‘™ˆ‘”ƒ ’”‘„ƒ„‹Ž‹•–‹…‹–‡”’”‡–ƒ–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǤŠ‹••‹–—ƒ–‹‘‹‰Š–„‡”‡‡†‹‡†„›ƒ††‹‰ ƒ•–‘…Šƒ•–‹…–‡”–‘–Š‡•–ƒ–‡‡“—ƒ–‹‘‹Ǥ  •ˆ‘”–Š‡”‡Žƒ–‹‘„‡–™‡‡–Š‡ ƒ†‡–Š‘†‘Ž‘‰‹‡•ǡ™‡ƒ‰”‡‡™‹–Š ”‹•–‘ƒ†‡–Š–Šƒ––Š‡›ƒ”‡…‘’Ž‹‡–ƒ”›ȏͳͳͺȐǤ˜‡–Š‘—‰Š–Š‡ƒ–—”‡‘ˆ …ƒ—•ƒŽ‹–›‹–Š‡–™‘‡–Š‘†•‹•ˆ—†ƒ‡–ƒŽŽ›†‹ˆˆ‡”‡–ǡ™‡„‡Ž‹‡˜‡–Šƒ–‡ƒ…Š ƒ’’”‘ƒ…Š‹•˜ƒŽ‹†ǡ‘‡ˆ‘”†ƒ–ƒ‡š’Ž‘”ƒ–‹‘ƒ†–Š‡‘–Š‡”ˆ‘”•—„•‡“—‡–†‡–ƒ‹Ž‡† ‘†‡Ž‹‰Ǥ ˆƒ…–ǡ™‡‡˜‹•‹‘–Š‡„‡‹‰—•‡†‹–ƒ†‡–‘—†‡”•–ƒ†…‘’Ž‡š „”ƒ‹•›•–‡•Ǥ ƒ•–Ž›™‡„”‹‡ˆŽ›…‘•‹†‡”–”ƒ•ˆ‡”‡–”‘’›ȋȌǡƒ‹ˆ‘”ƒ–‹‘Ǧ–Š‡‘”‡–‹… ‡ƒ•—”‡‘ˆ–Š‡–”ƒ•ˆ‡”‘ˆ‹ˆ‘”ƒ–‹‘„‡–™‡‡–™‘–‹‡•‡”‹‡•ǤŠƒ•„‡‡•Š‘™ –‘„‡‡“—‹˜ƒŽ‡––‘ —†‡”‘”ƒŽ…‘†‹–‹‘•ȏͳͲ͸ǡͳʹ͵ȐǤŠ‡”‡ƒ•  ƒ••‡••‡•…ƒ—•ƒŽ‹–›„›–Š‡”‡†—…–‹‘‘ˆ’”‡†‹…–‹‘‡””‘”‹ƒ—–‘”‡‰”‡••‹˜‡‘†‡Ž•ǡ ‡ƒ•—”‡•‹–ƒ•”‡†—…‡†—…‡”–ƒ‹–›ǤŠ‡–”ƒ•ˆ‡”‘ˆ‡–”‘’›ˆ”‘–‹‡•‡”‹‡•ʹ–‘ –‹‡•‡”‹‡•ͳ‹•–Š‡‡š–‡––‘™Š‹…Šʹ”‡†—…‡•–Š‡—…‡”–ƒ‹–›‘ˆˆ—–—”‡ͳ˜ƒŽ—‡•ǡ „‡›‘†–Š‡‹ˆ‘”ƒ–‹‘’”‘˜‹†‡†„›ͳ‹–•‡ŽˆȏͳͲʹȐǤ—…Š‘ˆ–Š‡…‘…‡’–—ƒŽƒƒŽ›•‹• †‹•…—••‡†ƒ„‘˜‡ˆ‘” ƒŽ•‘ƒ’’Ž‹‡•ǣ’”‘˜‹†‡•ƒ’”‘„ƒ„‹Ž‹•–‹…‹ˆ‡”‡…‡‘ˆ …ƒ—•ƒŽ‹–›ƒ‘‰–‹‡•‡”‹‡•ˆ”‘‡—”‘ƒŽ’‘’—Žƒ–‹‘•‹–‡”ƒ…–‹‰‹ƒŽƒ”‰‡Ǧ•…ƒŽ‡ „”ƒ‹‡–™‘”Ǥ ‘•—ƒ”‹œ‡ǡ‡–Š‘†•Ž‹‡ ƒ†“—ƒ–‹ˆ›–Š‡•–ƒ–‹•–‹…ƒŽŽ‹‡Ž‹Š‘‘† –Šƒ–ƒ…Šƒ‰‡‹ƒ…–‹˜‹–›‹‘‡‘†‡‘ˆƒ„”ƒ‹‡–™‘”Šƒ•ƒ…ƒ—•ƒŽ‡ˆˆ‡…–‹ ƒ‘–Š‡”Ǥ‹…‡–Š‡•‡‡ƒ•—”‡•ƒ”‡‹Š‡”‡–Ž›’”‘„ƒ„‹Ž‹•–‹…ǡ™‡„‡Ž‹‡˜‡–Šƒ––Š‡›ƒ”‡ ‰‡‡”ƒŽŽ›„‡––‡”•—‹–‡†–Šƒ†‡–‡”‹‹•–‹…‡ƒ•—”‡•ˆ‘”‹†‡–‹ˆ›‹‰…ƒ—•ƒŽ‹–›‹–Š‡ „”ƒ‹Ǥ‡–ǡ™Š‹Ž‡”‘‘–‡†‹†‡–‡”‹‹•ǡƒ›‘‡–Š‡Ž‡••„‡—•‡ˆ—ŽŽ›‡’Ž‘›‡† –‘†‡–‡”‹‡…ƒ—•ƒŽ‹ˆŽ—‡…‡•ƒ‘‰ƒŽ‹‹–‡†—„‡”‘ˆ‡–™‘”‘†‡•–Šƒ–Šƒ˜‡ ’”‡˜‹‘—•Ž›„‡‡‹†‡–‹ˆ‹‡†„›‘–Š‡”‡ƒ•Ǥ  6. Conclusions

”ƒ‰‡”ȏʹͶȐƒ†‡ƒ’‘‹‰ƒ–”‡ƒ”…‘…‡”‹‰…ƒ—•ƒŽ‹–›–Šƒ–Šƒ•‘ˆ–‡ „‡‡‘˜‡”Ž‘‘‡†‹–Š‡‹Ž‹‡—‘ˆ–Š‡‘™’‘’—Žƒ”—•‡‘ˆŠ‹•‡–Š‘†‘Ž‘‰›‹ ‡—”‘•…‹‡…‡ǣ  „‡Ž‹‡˜‡ –Šƒ– †‡ˆ‹‹–‹‘• •Š‘—Ž† „‡ ƒŽŽ‘™‡† –‘ ‡˜‘Ž˜‡ †—‡ –‘ †‡„ƒ–‡ ”ƒ–Š‡”–Šƒ„‡Œ—†‰‡†•‘Ž‡Ž›‘ƒ–”—–Š‘”‘–•…ƒŽ‡Ǥ ‡Šƒ˜‡ƒ”‰—‡†Š‡”‡–Šƒ–…Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹…‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›‰‡‡”ƒŽŽ›ˆƒ‹Ž ™Š‡†‡•…”‹„‹‰…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹…‘’Ž‡š•›•–‡•ǡƒ†’ƒ”–‹…—Žƒ”Ž›•‘ˆ‘”…ƒ—•ƒŽ ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹ǤŽ–Š‘—‰Š†‡–‡”‹‹•–‹……ƒ—•ƒŽ‹–›ƒ›„‡—•‡ˆ—Ž—†‡”•‘‡ 

ͳͻ

…‹”…—•–ƒ…‡•ˆ‘”†‡•…”‹„‹‰‡—”ƒŽ‹ˆŽ—‡…‡•ǡprobabilistic causality‹•–Š‡‘”‡ …‘…‡’–—ƒŽŽ›ƒ’’”‘’”‹ƒ–‡„ƒ•‹•ˆ‘”†‡•…”‹„‹‰‹ˆŽ—‡…‡•‹…‘’Ž‡š•›•–‡••—…Šƒ• –Š‡„”ƒ‹Ǥ Š‡„”ƒ‹‹•ƒ•‡ŽˆǦ‘”‰ƒ‹œ‹‰•›•–‡™‹–Šƒƒ•–”‘‘‹…ƒŽŽ›Š‹‰Š—„‡”‘ˆ ‹–‡”ƒ…–‹‰…‘’‘‡–•ǡ™‹–Š„‘–ŠŠ‹‡”ƒ”…Š‹…ƒŽƒ†Š‡–‡”ƒ”…Š‹…ƒŽ‘”‰ƒ‹œƒ–‹‘ǡ ‘’‡”ƒ–‹‰‹„‘–ŠŽ‹‡ƒ”ƒ†‘Ž‹‡ƒ”†‘ƒ‹•ǡƒ†‘—Ž–‹’Ž‡–‹‡•…ƒŽ‡•Ǥ Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹…‘–‹‘•‘ˆ…ƒ—•ƒŽ‹–›ƒ”‡•‹’Ž›‘–’Žƒ—•‹„Ž‡ˆ‘”†‡•…”‹„‹‰ ƒ†‡š’Žƒ‹‹‰…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡„”ƒ‹Ǥ–ƒ–‡‡–•Ž‹‡Dz”ƒ‹”‡‰‹‘Šƒ•ƒ …ƒ—•ƒŽ‹ˆŽ—‡…‡‘„”ƒ‹”‡‰‹‘dzƒ†DzŠ‡„ƒ•‡„ƒŽŽ…ƒ—•‡•–Š‡™‹†‘™–‘•Šƒ––‡”dz Šƒ˜‡†‹ˆˆ‡”‡–‡ƒ‹‰•Ǥ –Š‡•‡…‘†•–ƒ–‡‡–ǡ–Š‡”‡‹•ƒ‹–—‹–‹˜‡‘–‹‘ȋ–Šƒ– —‡™‘—Ž†’”‡ˆ‡”Ȍƒ„‘—–‡˜‡”›†ƒ›…ƒ—•‡•ǡ™Š‡”‡ƒ•‹–Š‡ˆ‹”•–•–ƒ–‡‡––Š‡”‡‹• ‘–ǤŠƒ–Dz…ƒ—•ƒŽ‹ˆŽ—‡…‡dz‡ƒ•‹–Š‡…‘–‡š–‘ˆŽƒ”‰‡Ǧ•…ƒŽ‡„”ƒ‹‡–™‘”•‹• ‘––Š‡•ƒ‡ƒ•–Š‡…Žƒ••‹…ƒŽ†‡–‡”‹‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǤŽ–Š‘—‰Š•‘‡ –Š‹‡”•Šƒ˜‡†‡‡‡†…ƒ—•ƒŽ‹–›–‘„‡—ƒƒŽ›œƒ„Ž‡ȏͳȐǡ™‡ƒ”‰—‡–Šƒ–…ƒ—•ƒŽ‹–›†‘‡• ‡š‹•–‹–Š‡Š—ƒ„”ƒ‹ǡƒ†…ƒǡ‹ˆƒ…–ǡ„‡‡ƒ•—”‡†Ǥ ‡Šƒ˜‡‘––”‹‡†–‘ƒ•™‡”–Š‡“—‡•–‹‘‘ˆ™Š‡–Š‡”–Š‡„”ƒ‹‹•‹Š‡”‡–Ž› ƒ†‡–‡”‹‹•–‹…‘”•–‘…Šƒ•–‹…•›•–‡ǤŠ‹•“—‡•–‹‘‹••–‹ŽŽ„‡‹‰†‡„ƒ–‡†ǤŠ‡„”ƒ‹ ‹•…Ž‡ƒ”Ž›ƒŠ‹‰Š†‹‡•‹‘ƒŽ•›•–‡ǡ„—–‹–‹•†‹ˆˆ‹…—Ž––‘†‹•–‹‰—‹•Š„‡–™‡‡Š‹‰ŠǦ †‹‡•‹‘ƒŽ†‡–‡”‹‹•ƒ†•–‘…Šƒ•–‹…‹–›Ǥ‡˜‡”–Š‡Ž‡••ǡƒ•™‡Šƒ˜‡ƒ”‰—‡†ǡ •–ƒ–‹•–‹…ƒŽ–‡…Š‹“—‡••—…Šƒ• Šƒ˜‡’”‘˜‡–‘„‡‡’‹”‹…ƒŽŽ›—•‡ˆ—Ž‹ ’”‡†‹…–‹‘ǡ†‡•…”‹’–‹‘ǡƒ†‡š’Žƒƒ–‹‘Ǥ‘”‡‘˜‡”ǡ‡˜‡‹ˆ–Š‡„”ƒ‹†‘‡•‡’Ž‘› †‡–‡”‹‹•–‹…‹ˆŽ—‡…‡•ǡ‹–•Š‹‰Š†‹‡•‹‘ƒŽ‹–›‰‹˜‡•–Š‡ƒ’’‡ƒ”ƒ…‡‘ˆ •–‘…Šƒ•–‹…‹–›ǡƒ†–Š—•”‡“—‹”‡•–Šƒ–…ƒ—•ƒŽ„”ƒ‹‡ƒ•—”‡•ˆ‘—†ƒ–‹‘ƒŽŽ›”‡Ž›‘ƒ ’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›Ǥ’”‘„ƒ„‹Ž‹•–‹…ˆ”ƒ‡™‘”ˆ‘”†‡•…”‹„‹‰…ƒ—•ƒŽ‹–› ‹–Š‡„”ƒ‹‹•‘–‘Ž›…‘•‹•–‡–™‹–Š‘†‡”–”‡†•‹’Š‹Ž‘•‘’Š›Ǥ –‹•ƒŽ•‘ …‘’”‡Š‡•‹˜‡ǣ™‹–Š’”‘„ƒ„‹Ž‹•–‹…‹ˆŽ—‡…‡•Šƒ˜‹‰ƒ”ƒ‰‡‘ˆ•–”‡‰–Š•ǡ‹–‹•ƒ„Ž‡ –‘ƒ……‘‘†ƒ–‡‹ˆŽ—‡…‡•‘ˆ†‹ˆˆ‡”‡–•–”‡‰–Š•ǡ‹…Ž—†‹‰–Š‘•‡™‹–Šƒ’”‘„ƒ„‹Ž‹–› ‘ˆ‘‡ǡ™Š‹…Šƒ›ƒŽ•‘„‡…‘•‹†‡”‡†–‘„‡†‡–‡”‹‹•–‹…Ǥ 



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[98] Ding, M., Chen, Y., & Bressler, S.L. (2006). Granger causality: Basic theory and application to neuroscience. In Schelter. S., Winterhalder, N., & Timmer, J. Handbook of Time Series Analysis. [99] Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review, 5(1), 3-55. [100] Chornoboy, E. S., Schramm, L. P., & Karr, A. F. (1988). Maximum likelihood identification of neural point process systems. Biological Cybernetics 59, 265-75. [101] Chatfield, C. (2013). The analysis of time series: an introduction. CRC press. [102] Jansen, B.H. (1991. Time series analysis by means of linear modeling. In: Digital Biosignal Processing, Weitkunat, R. (ed.). Elsevier, Amsterdam, 157-180. [103] Kaminski, M.J., Blinowska, K.J. (1991). A new method of the description of the information flow in the brain structures. Biological Cybernetics, 65:203-210. [104] Valdes-Sosa, P.A., Roebroeck, A., Daunizeau, J., Friston, K. (2011). Effective connectivity: influence, causality and biophysical modeling. Neuroimage, 58:339361. [105] Wen X, Rangarajan G, Ding M (2013). Is Granger Causality a Viable Technique for Analyzing fMRI Data? PLoS ONE, 8(7): e67428. [106] Barnett L, Barrett AB, Seth AK (2009). Granger causality and transfer entropy are equivalent for Gaussian variables. Physical Review Letters, 103:238701. [107] Granger, C. W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society, 424-438. [108] Granger, C. W. J. (2001). Essays in Econometrics: The Collected Papers of Clive W.J. Granger. Cambridge: Cambridge University Press. [109] Wiener, N. (1956). The theory of prediction. In Modern Mathematics for Engineers, vol. 1 (ed. E. F. Beckenbach). New York: McGraw-Hill. [110] Cold, C. S. H. P. M., & Cold, C. S. H. H. B. (2007). Observed brain dynamics. Oxford University Press. [111] Tang W, Bressler SL, Sylvester CM, Shulman GL, Corbetta M (2012). Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO. PLoS Computational Biology, 8(5): e1002513. [112] Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77(378), 304313. [113] Chen, Y., Bressler, S. L., & Ding, M. (2006). Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. Journal of Neuroscience Methods, 150, 228-37. [114] Chen, Y., Rangarajan, G., Feng, J., & Ding, M. (2004). Analyzing multiple nonlinear time series with extended Granger causality. Physics Letters A, 324, 26-35. [115] Chicharro, D., & Ledberg, A. (2012). When two become one: The limits of causality analysis of brain dynamics. PloS ONE, 7(3), e32466. [116] Hoover, K. D. (2008). Causality in economics and econometrics. The new Palgrave dictionary of economics, 2. [117] Friston, K. J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling. Neuroimage, 19(4), 1273-1302. 

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[118] Friston, K., Moran, R., & Seth, A. K. (2013). Analysing connectivity with Granger causality and dynamic causal modelling. Current opinion in neurobiology, 23(2), 172-178. [119] Friston, K.J., (1994). Functional and effective connectivity in neuroimaging: a synthesis. Human Brain Mapping, 2, 56–78. [120] Friston, K.J., (1997). Imaging cognitive anatomy. Trends in Cognitive Sciences, 1, 21–27. [121] Friston, K. (2011). Dynamic causal modeling and Granger causality Comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage, 58(2-2), 303. [122] Stephan, K. E., Penny, W. D., Moran, R. J., den Ouden, H. E., Daunizeau, J., & Friston, K. J. (2010). Ten simple rules for dynamic causal modeling. Neuroimage, 49(4), 3099-3109. [123] Schreiber, T. (2000). Measuring information transfer. Physical review letters, 85(2), 461.



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Figure 1: † †‡–‡”‹‹•––‹…”‡‰—Žƒ”‹–› ›–Š‡‘”›‘ˆ…ƒ—•ƒŽ‹–›ȋ‡‡Ǥ‰Ǥǡ—‡ǯ•ƒ……‘—–Ȍ …ƒƒ‘–ƒ……‘— —–ˆ‘”ƒ…‘ ‘…ƒ—•‡‡‘ˆ–™‘†‹ˆˆˆ‡”‡–‡ˆˆ‡…–•Ǥ––‡’–••–‘ƒ’’Ž›ƒ †‡–‡”‹‹•–‹…–Š‡‘”›ƒƒ››‹‡Ž†•’—”‹‘—•”‡‰—Žƒƒ”‹–‹‡•ǡƒ ‡Ž›…‘…Ž—† †‹‰–Šƒ–ƒ †”‘’‹–Š‡……‘Ž—‘ˆ ‡”…—”›‹ƒ„ƒ”‘‡–‡”…ƒ—•‡•ƒ•–‘”Ǥ‡’”‹ –‡†™‹–Š ’‡”‹••‹‘ˆˆ”‘‹–…Š…‘…ǡʹͲͳʹǤ



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   …‡ƒ† ”ƒ ‰‡” Figure 2: –ƒƒ–‹•–‹…ƒŽŽ›•‹‹‰‹ˆ‹…ƒ–‡ˆˆˆ‡…–•ǡ•’‡…––”ƒŽ…‘Š‡”‡ …ƒƒ—•ƒŽ‹–›ǡ†‡”‹˜‡†ˆ”‘ƒƒ—–‘”‡‰”‡•••‹˜‡–‹‡•‡‡”‹‡•‘†‡Ž••ƒ’’Ž‹‡†–‘‡‘…‘”–‹…ƒŽŽ Ž‘ ‘…ƒŽˆ‹‡Ž†’‘ ‘–‡–‹ƒŽ†ƒ–ƒƒǤ‘Š‡”‡…‡‡‹•…‘‘ Ž›”‡’”‡•‡–‡†ƒ•ƒ— —†‹”‡…–‡† ˆ— —…–‹‘ƒŽ‡† †‰‡ǡƒ† ”ƒƒ‰‡”…ƒ—•ƒƒŽ‹–›ƒ•ƒ†‹””‡…–‡†ˆ—…–‹‘ƒŽ‡†‰‡‹‹Žƒ”‰‡Ǧ •……ƒŽ‡„”ƒ‹ ‡–™‘”•Ǥ‡‡’”‹–‡†™‹‹–Š’‡”‹••‹‹‘ˆ”‘””‘˜‡ŽŽ‹‡–ƒŽǡʹͲͲͶǤ



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Figure 3:™ ™‘†‹ˆˆ‡”‡––…‘‡…–‹˜‹––›’ƒ––‡”•–Šƒ–…‘—Ž†ŽŽ‡ƒ†–‘–Š‡ ‹† †‡–‹ˆ‹…ƒ–‹‘ ‘ˆ•’—”‹‘— —•…ƒ—•ƒŽ‹–›ȋˆ”‘–‘ ‹„‘–Šƒ†ȌǤ ‡’ ’”‹–‡†™‹–Š Š ’‡”‹••‹‘ˆˆ”‘ƒ‰‡‡–ƒŽǡʹͲͳʹǤ



͵ ͵Ͳ

Glossary Bi-directionality: –Š‡’”‡˜ƒŽ‡–’ƒ––‡”‘ˆ…‘‡…–‹˜‹–›‹–Š‡„”ƒ‹™Š‡”‡„›ˆ‹„‡” ’ƒ–Š™ƒ›•’”‘Œ‡…–‹„‘–Š†‹”‡…–‹‘•„‡–™‡‡‡—”‘•‘”‡—”‘ƒŽ’‘’—Žƒ–‹‘•Ǥ Causal asymmetry: –Š‡‘–‹‘‘ˆ–‹‡ƒ•›‡–”›™Š‡”‡„›…ƒ—•ƒŽ‹ˆŽ—‡…‡•‹–Š‡ ’ƒ•–ƒ†’”‡•‡–ƒ›…ƒ—•‡‡ˆˆ‡…–•‹–Š‡ˆ—–—”‡ǡ„—––Š‘•‡‹–Š‡ˆ—–—”‡ƒ›‘– …ƒ—•‡‡ˆˆ‡…–•‹–Š‡’ƒ•–‘”’”‡•‡–Ǥ Causal influence: –Š‡”‡•—Ž–ƒ–‡ˆˆ‡…–‡š‡”–‡†„›ƒ…ƒ—•ƒŽ–Š‹‰‘”‡˜‡–‘ƒ‘–Š‡” –Š‹‰‘”‡˜‡–Ǥ Complex system: ƒ•›•–‡…‘•‹•–‹‰‘ˆƒ›‹–‡”ƒ…–‹‰’ƒ”–•ǡ•—…Š–Šƒ––Š‡•‡ ’ƒ”–•ǡ™‘”‹‰–‘‰‡–Š‡”ǡ’”‘†—…‡’”‘’‡”–‹‡•™Š‹…Šƒ”‡‘–‹Š‡”‡–‹–Š‡’ƒ”–• –Š‡•‡Ž˜‡•Ǥ Constant conjunction: ƒ–‡”ˆ”‘ƒ˜‹†—‡ǡ”‡ˆ‡””‹‰–‘–Š‡ˆƒ…––Šƒ–Š—ƒ• †‘‘–’‡”…‡‹˜‡…ƒ—•ƒŽ”‡Žƒ–‹‘•„—–ǡ”ƒ–Š‡”‘Ž›–™‘‡˜‡–•™Š‹…ŠƒŽ™ƒ›••‡‡–‘ Šƒ’’‡‹–‡’‘”ƒŽ•‡“—‡…‡ǡˆ‘”‡šƒ’Ž‡ǡŽ‹‰Š–‡‹‰ǡ–Š‡–Š‡–Š—†‡”…Žƒ’Ǥ Convergence: –Š‡’”‡˜ƒŽ‡–’ƒ––‡”‘ˆ…‘‡…–‹˜‹–›‹–Š‡„”ƒ‹™Š‡”‡„›ˆ‹„‡” ’ƒ–Š™ƒ›•ˆ”‘—Ž–‹’Ž‡•‡†‹‰‡—”‘•‘”‡—”‘ƒŽ’‘’—Žƒ–‹‘•’”‘Œ‡…––‘–Š‡ •ƒ‡”‡…‡‹˜‹‰‡—”‘‘”‡—”‘ƒŽ’‘’—Žƒ–‹‘Ǥ Deterministic causalityǣ–Š‡’Š‡‘‡‘™Š‡”‡„›ƒ•’‡…‹ˆ‹……ƒ—•‡ƒŽ™ƒ›• †‡–‡”‹‡•ƒ•’‡…‹ˆ‹…‡ˆˆ‡…–Ǥ Dynamical Causal Modeling: ƒƒ–Š‡ƒ–‹…ƒŽ‡–Š‘†‘Ž‘‰›—•‡†–‘‹ˆ‡”‡ˆˆ‡…–‹˜‡ …‘‡…–‹˜‹–›„›•’‡…‹ˆ›‹‰ƒ‘†‡Žƒ†ƒ–…Š‹‰‹––‘‡’‹”‹…ƒŽ‡—”ƒŽ†ƒ–ƒǤ Effective connectivity: ƒƒ……‘—–‘ˆ–Š‡‹–‡”ƒ…–‹‘„‡–™‡‡„”ƒ‹”‡‰‹‘•ǡ—•—ƒŽŽ› ‡ƒ•—”‡†ˆ”‘ˆ—…–‹‘ƒŽ‡—”‘‹ƒ‰‹‰†ƒ–ƒǡ–Šƒ–”‡•–•‘ƒ‡…Šƒ‹•–‹…‘†‡Ž‘ˆ ™Šƒ–…ƒ—•‡†–Š‡‹–‡”ƒ…–‹‘Ǥ Functional connectivity: ƒ•–ƒ–‹•–‹…–Šƒ–‡ƒ•—”‡•–Š‡ˆ—…–‹‘ƒŽ”‡Žƒ–‹‘ǡ‡‹–Š‡” —†‹”‡…–‡†‘”†‹”‡…–‡†ǡ„‡–™‡‡„”ƒ‹”‡‰‹‘•Ǥ Granger, Clive: ƒʹͲ–Š…‡–—”›•–ƒ–‹•–‹…‹ƒ™Š‘…”‡ƒ–‡†ƒƒ–Š‡ƒ–‹…ƒŽˆ‘”—Žƒ–‹‘ ‘ˆ–Š‡…ƒ•—ƒŽ”‡Žƒ–‹‘•„‡–™‡‡–‹‡•‡”‹‡•Ǥ Ganger causalityǣ‹–Š‡‡ƒ•—”‡‡–‘ˆ•–‘…Šƒ•–‹…–‹‡•‡”‹‡•ǡ‘‡–‹‡•‡”‹‡•‹•

”ƒ‰‡”…ƒ—•ƒŽ–‘ƒ•‡…‘†‹ˆ‹…Ž—†‹‰‹ˆ‘”ƒ–‹‘ˆ”‘–Š‡ˆ‹”•–ƒŽŽ‘™•„‡––‡” ’”‡†‹…–‹‘‘ˆ–Š‡•‡…‘†–Šƒ‹ˆ‘Ž›‹ˆ‘”ƒ–‹‘ˆ”‘–Š‡•‡…‘†‹•‹…Ž—†‡†Ǥ Hume, Davidǣƒͳͺ–Š…‡–—”›‡’‹”‹…ƒŽƒ†•‡’–‹…ƒŽ’Š‹Ž‘•‘’Š‡”™Š‘’”‘’‘•‡†ƒ ”‡‰—Žƒ”‹–›–Š‡‘”›‘ˆ…ƒ—•ƒŽ‹–›ƒ•‡š‹•–‹‰‹Š—ƒ’‡”…‡’–‹‘Ǥ



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Imperfect regularity: ƒ†‹ˆˆ‹…—Ž–›ˆ‘””‡‰—Žƒ”‹–›–Š‡‘”‹‡•™Š‡”‡„›ƒ…ƒ—•‡‹•‘– ƒŽ™ƒ›•ˆ‘ŽŽ‘™‡†„›‹–•‡ˆˆ‡…–Ǥ Indeterminism: –Š‡’”‘’‡”–›‘ˆ•›•–‡•ǡ‘†‡Ž•ǡ‘”Žƒ™•Šƒ˜‹‰•–‘…Šƒ•–‹…ǡ ’”‘„ƒ„‹Ž‹•–‹…ǡ‘””ƒ†‘…‘’‘‡–•‹–Š‡Ǥ Kant, Immanuel: ƒͳͻ–Š…‡–—”›’Š‹Ž‘•‘’Š‡”™Š‘’‘’—Žƒ”Ž›Dz”‡•…—‡†dz…ƒ—•ƒŽ‹–› ˆ”‘—‡ǯ••‡’–‹…‹•ǢŠ‡˜‹‡™‡†…ƒ—•ƒŽ‹–›ƒ•‘–‘Ž›„‡‹‰ƒ’”‘†—…–‘ˆŠ—ƒ ’‡”…‡’–‹‘ǡƒ†’Žƒ…‡†‹–’ƒ”–‹ƒŽŽ›‹–Š‡‡š–‡”ƒŽ™‘”Ž†Ǥ Laplace’s demon: ƒŠ›’‘–Š‡–‹…ƒŽ‹†ǡ…‘Œ—”‡†„›‹‡””‡†‡ƒ’Žƒ…‡ǡ™Š‘ǡ‰‹˜‡ –Š‡‹‹–‹ƒŽ…‘†‹–‹‘•‘ˆ‡ƒ…Š’ƒ”–‹…Ž‡ƒ†Žƒ™•‰‘˜‡”‹‰–Š‡—‹˜‡”•‡ǡ…‘—Ž†–Š‡ ˆ‘”‡•‡‡ƒŽŽ–Šƒ–™‘—Ž†Šƒ’’‡ˆ‘”ƒŽŽˆ—–—”‡–‹‡Ǥ Large-scale brain network:•–”—…–—”ƒŽŽ›ǡƒ’Š›•‹…ƒŽ•›•–‡‹–Š‡„”ƒ‹‘ˆ‡–™‘” ‘†‡•ǡ”‡’”‡•‡–‹‰‡—”‘ƒŽ’‘’—Žƒ–‹‘•ǡ‹–‡”…‘‡…–‡†„›‡–™‘”‡†‰‡•ǡ ”‡’”‡•‡–‹‰ˆ‹„‡”’ƒ–Š™ƒ›•’”‘Œ‡…–‹‰ˆ”‘‘‡‘†‡–‘ƒ‘–Š‡”Ǣˆ—…–‹‘ƒŽŽ›ǡƒ •›•–‡‘ˆ‡–™‘”‘†‡•ǡ”‡’”‡•‡–‹‰‡—”‘ƒŽ’‘’—Žƒ–‹‘•–Šƒ–‹–‡”ƒ…–ƒ•’ƒ”–‘ˆ „”ƒ‹ˆ—…–‹‘ǡ–Š‡ˆ—…–‹‘ƒŽ‹–‡”ƒ…–‹‘•„‡‹‰”‡’”‡•‡–‡†„›‡–™‘”‡†‰‡•Ǥ Mutual causality: –Š‡—–—ƒŽŽ›†‹”‡…–‡†‹–‡”ƒ…–‹‘‘ˆ–™‘…‘’‘‡–•‹ƒ …‘’Ž‡š•›•–‡™Š‡”‡„›‡ƒ…Š…‘…—””‡–Ž›‡š‡”–•ƒ…ƒ—•ƒŽ‡ˆˆ‡…–‘–Š‡‘–Š‡”Ǣ‹ –Š‡„”ƒ‹ǡ‹––”ƒ•’‹”‡•„‡–™‡‡„‹Ǧ†‹”‡…–‹‘ƒŽŽ›…‘‡…–‡†‡—”‘ƒŽ’‘’—Žƒ–‹‘•Ǥ Neural causal influence: –Š‡‡ˆˆ‡…–‡š‡”–‡†„›ƒ‡—”‘‘”‡—”‘ƒŽ’‘’—Žƒ–‹‘‘ –Š‡ƒ…–‹˜‹–›‘ˆƒ‘–Š‡”‡—”‘‘”‡—”‘ƒŽ’‘’—Žƒ–‹‘Ǥ Network edge:ƒ‰”ƒ’ŠǦ–Š‡‘”‡–‹…”‡’”‡•‡–ƒ–‹‘‘ˆƒ…‘‡…–‹‘„‡–™‡‡‘†‡•‹ ƒ’Š›•‹…ƒŽ•›•–‡Ǥ Network node: ƒ‰”ƒ’ŠǦ–Š‡‘”‡–‹…”‡’”‡•‡–ƒ–‹‘‘ˆƒ…‘‡…–‡†—‹–‹ƒ’Š›•‹…ƒŽ •›•–‡Ǥ Probabilistic causalityǣ–Š‡’Š‡‘‡‘™Š‡”‡„›ƒ…ƒ—•‡”ƒ‹•‡•–Š‡’”‘„ƒ„‹Ž‹–›‘ˆ ‹–•‡ˆˆ‡…–Ǥ Regularity theory of causality: ƒ†‡–‡”‹‹•–‹…ƒ……‘—–‘ˆ…ƒ—•ƒŽ‹–›•’‡…‹ˆ›‹‰–Šƒ– ‡ˆˆ‡…–•”‡‰—Žƒ”Ž›ˆ‘ŽŽ‘™–Š‡‹”…ƒ—•‡•Ǥ Russell, Bertrand: ƒʹͲ–Š…‡–—”›’Š‹Ž‘•‘’Š‡”™Š‘ǡƒ‘‰‘–Š‡”–Š‹‰•ǡ™ƒ• •‡’–‹…ƒŽƒ„‘—––Š‡‡…‡••ƒ”›…‘‡…–‹‘„‡–™‡‡…ƒ—•ƒŽ‹–›ƒ††‡–‡”‹‹•Ǥ Screening off: ƒ’”‘„ƒ„‹Ž‹•–‹…‘–‹‘‘ˆ…ƒ—•ƒŽ‹–›ǡ’”‘ˆˆ‡”‡†„›ƒ•‡‹…Š‡„ƒ…Šǡ ƒ††”‡••‹‰–Š‡’”‘„Ž‡‘ˆ•’—”‹‘—•…‘””‡Žƒ–‹‘•Ǥ Shannon entropy: ƒ“—ƒ–‹–ƒ–‹˜‡‡ƒ•—”‡‘ˆ‹ˆ‘”ƒ–‹‘‡š’”‡••‹‘„ƒ•‡†‘–Š‡ †‡‰”‡‡‘ˆ—…‡”–ƒ‹–›‹–Šƒ–‡š’”‡••‹‘Ǥ



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Spurious regularity: …ƒ—•ƒŽ”‡Žƒ–‹‘•–Šƒ–ƒ›„‡‹•‹†‡–‹ˆ‹‡†ǡ•‹…‡ǡƒŽ–Š‘—‰Š‹– Ž‘‘•Ž‹‡–Š‡‡ˆˆ‡…–‹•”‡‰—Žƒ”Ž›ˆ‘ŽŽ‘™‡†„›‹–•…ƒ—•‡ǡ‹–‹•‘––Š‡…ƒ•‡–Šƒ––Š‡‡ˆˆ‡…– ƒ†–Š‡…ƒ—•‡ƒ”‡”‡Žƒ–‡†‹ƒ›™ƒ›Ǥ Stationary process:ƒ•–‘…Šƒ•–‹…’”‘…‡••ˆ‘”™Š‹…ŠƒŽŽ•–ƒ–‹•–‹…ƒŽ‡ƒ•—”‡•†‘‘– …Šƒ‰‡‘˜‡”–‹‡Ǥ Structural connectivity: –Š‡’ƒ––‡”‘ˆƒƒ–‘‹…ƒŽ’ƒ–Š™ƒ›•…‘‡…–‹‰”‡‰‹‘•‘ˆ ƒ„”ƒ‹•›•–‡Ǥ Transfer entropy: ƒ•–ƒ–‹•–‹…ƒŽ‡ƒ•—”‡‘ˆ…ƒ•—ƒŽ‹ˆŽ—‡…‡ǡ‡š’”‡••‡†ƒ•–Š‡ ”‡†—…–‹‘‘ˆ—…‡”–ƒ‹–›‹–Š‡‹ˆ‘”ƒ–‹‘‘ˆ‘‡–‹‡•‡”‹‡•ƒ––”‹„—–‡†–‘ƒ•‡…‘† –‹‡•‡”‹‡•ƒ†“—ƒ–‹ˆ‹‡†„›–Š‡ƒ‘—–‘ˆ–”ƒ•ˆ‡””‡†Šƒ‘‹ˆ‘”ƒ–‹‘Ǥ Wide-sense stationarity:ƒ™‡ƒˆ‘”‘ˆ•–ƒ–‹‘ƒ”‹–›”‡“—‹”‹‰‘Ž›–Šƒ––Š‡ˆ‹”•– ‘‡–ȋ‡ƒȌƒ†–Š‡ƒ—–‘…‘˜ƒ”‹ƒ…‡†‘‘–˜ƒ”›™‹–Š–‹‡Ǥ    



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