Soul that transmigrates? In Timsa Sutta Buddha says:

"What do you think, monks? Which is greater, the blood you have shed from having your heads cut off while transmigrating &amp; wandering this long, long time, or the water in the four great oceans?"

Furthermore he also says:

"The blood you have shed when, being water buffaloes, you had your water buffalo-heads cut off... when, being rams, you had your ram-heads cut off... when, being goats, you had your goat-heads cut off... when, being deer, you had your deer-heads cut off... when, being chickens, you had your chicken-heads cut off... when, being pigs, you had your pig-heads cut off: Long has this been greater than the water in the four great oceans."

Doesn't this mean that there is a soul in Buddhism?
A literal reading of this translation brings the conclusion there is the same person transmigrating or reincarnating from life to life. Therefore, there will obviously be the impression of a permanent substance, such as a "soul", reincarnating from life to life. The Neo-Buddhists can argue until they are blue in the face that what transmigrates is a "re-linking consciousness" (which the Buddha did not teach) but, whatever it is called, it retains the characteristics of a soul (which is probably why Buddhism became extinct in India, given the common person could not distinguish between Neo-Buddhism &amp; Hinduism). 



Personally, I regard Chapter 15 of the SN to be either "fake dhamma" or, otherwise, mostly metaphorical language. For example: 


Literally, the word "saṃsāro" does not mean "transmigration". It merely means "continuance". SN 22.99 is a sutta using similar language to SN 15.13 yet describes samsaro as the ignorant mind, similar to a dog tied to a post, continually circling around &amp; attaching to the same aggregates as "self". 
Literally, the word "satta" ("beings") does not refer to "sentient beings" but merely refers to a "self-view" produced by ignorance &amp; craving (refer to SN 23.2 &amp; SN 5.10, which define what a "satta" or "being" is). Therefore, what is continuing from an inconceivable beginning might be the production of self-views. 
Metaphorically, SN 47.20 uses the metaphor of a "head chopped off" for a loss of mindfulness. Therefore, when SN 15.13 refers to continually being beheaded, this may refer to continually lacking mindfulness. 
Metaphorically, suttas such as Lokapala Sutta refer to goats, sheep, chickens, pigs, dogs and jackals as representing sexual promiscuity (or unwholesome non-humane behaviours). 
Literally, similar to the Lokapala Sutta, SN 15.13 thus continues by referring to thieves, highway thieves, adulterers, which are unwholesome behaviours bringing punishment and even execution by the king. There are many suttas referring to the king cutting off the head of thieves, murderers &amp; adulterers.