hello Internet today's video comes to you from the world of formal logic today we're going to learn about the three forms of logical inference deduction induction and abduction this is not as dry as you might think buried underneath all that jargon are some really important ideas for understanding how we think how we make meaning out of the world especially abduction most people have never heard of abduction before because it's not really logic in the way that we normally think about logic you can never really prove anything with abduction instead abduction tells us how things are like how they're similar to other things it gives us categories classes and maybe just maybe abduction forms the base of all other kinds of thinking but let's start at the other end here is a deductive syllogism from ancient Greece all humans die Socrates is a human Socrates will die this seems simple enough but there are two really powerful words snuck in there which make the whole thing tick those words are human and all what does all mean how do we refer to every single one abstractly in my mind I know that all humans exist but I've never seen all humans I've only seen specific instances like Maximus or Socrates maybe specific instances are all that exist all might be too abstract an idea to actually exist physically in the world it means totality infinity even allness is very difficult for us to symbolize clearly so if we want to use all as a premise in our deductive syllogism all humans die we need another syllogism a simpler syllogism to tell us what all means in this context that's where induction comes in Socrates was a human and Socrates died plato was a human and plato died Aristotle was a human and Aristotle died so all humans die our inductive syllogism doesn't seem as ironclad as our deductive syllogism because there's this jump in its reasoning we jump from three specific instances Socrates Aristotle and Plato to a general claim about all humans in deduction we know that our conclusion must be true as long as the premises are but with induction we can't be so confident all we can say is that because we have several examples of humans dying and no counter examples of humans not dying we can confidently assume that all humans die we can make our assumptions even stronger by adding more examples of people who died achilles and hector in paris but the structure of inductive logic always requires that jump from specific examples to the general case because these particular people died all humans die induction is weaker than deduction because it's always susceptible to counter example but it turns out that our deductive syllogism is dependent on inductive reasoning what I actually meant when I premise the deductive syllogism with all humans die was actually I have several examples of humans dying and not that many examples actually no examples of humans not dying so I'm pretty sure that all humans die that's not the most satisfying way of reaching an idea of all assuming it based on incomplete evidence but in many cases that's the best we can did but it gets even worse both the inductive case and the deductive case assume that there was this unambiguous category human but how do we know what a human is like the inductive generalization of the word all it turns out that the concept human is defined by a kind of logic which is rather fuzzy here's an abductive of syllogism Socrates is a human who walks on two legs and talks Plato is a human who walks on two legs and talks Aristotle is a human who walks on two legs and talks Polly walks on two legs and talks Polly is human the logic of the abductive syllogism makes a similar jump to the logic of the inductive syllogism but the direction is reversed in the inductive syllogism we looked at a property that specific members of a class shared mortality and then induced that all members of that class share that property in the abductive syllogism we look at a property that specific members of a class share walking and talking and then AB deuce that another particular individual must also be a member of that class because they share those properties the problem of course is that Polly is a parent abductive logic is obviously fallible we can make it stronger by adding more traits like humans don't just walk and talk they also have fingers and they think about logical reasoning and when we add these traits we can disqualify Polly but still the abductive jump remains classes just like the concept all are abstract ideas that we never have physical access to all we ever have physical access to are specific instances and yet when we generalize those specific instance in two categories we run the risk of making mistakes yet that's a risk we have to take we need categories if we want to think clearly about the world we certainly need them if we want to use logical deduction but it seems like the only way to establish categories is by fallible abduction the boundaries of categories are always going to be fuzzy because thought is fuzzy this isn't always a bad thing let's look at one more abductive syllogism grass dies humans die humans are grass of course this is not literally true but it does seem that there's some quality of the frailness and impermanence of grass that maps on to something about the impermanence of the human experience abduction may not have the stern authority of deductive logic but maybe it gives us something that is even more important metaphor perhaps even meaning [Music] [Music]