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    • The Philosopher’s Lexicon: A Priori and A Posteriori Knowledge

      Posted at 12:30 pm by Michelle Joelle, on May 29, 2015

      Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go. 

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      This week’s entry into the lexicon will be the last of a string of distinctions. I began some weeks ago by discussing the de dicto/de re distinction, then moved onto the distinction between ontology and epistemology, after which I tackled logical and causal possibly, and most recently I covered the difference between analytic and synthetic reasoning. To these, I add the distinction between a priori and a posteriori knowledge, a classification which I first encountered as a philosophy student in Kant’s Groundwork for the Metaphysics of Morals and A. C. Grayling’s An Introduction to Philosophical Logic, and is explained well in Nils Ch. Rauhut’s Ultimate Questions.

      In its weaker sense, a priori knowledge is knowledge that requires no external experience to comprehend. All you have to do is think things through according to the knowledge you already have. A priori knowledge can be verified without leaving your desk according to what you already know. This can refer to analytic deduction: no external validation is required to affirm the truth of tautological definitions like “A bachelor is an unmarried man” or equations like “10 + 10 = 20”. This is a weak definition of a priori knowledge because it refers only to knowledge that you learned earlier, meaning you could have learned that knowledge from earlier experience.

      The stronger sense of the word refers to knowledge that is innately held. This is obviously more controversial, as it assumes that we are born with knowledge prior to our experience with the world, usually eternal truths and immutable forms. Plato’s theory of knowledge is that when we learn anything in the world, what we’re really doing is recalling truths we already knew by virtue of have a knowing soul (nous). When we think we’re leaning from experience, we’re really just reminding ourselves of things we already knew, but haven’t yet named. While some versions of Platonism claim that this means we are born with perfect geometric forms in our minds, I tend to think Plato’s intention was that we were born with more abstract concepts of order and pattern. But that’s a post for another day.

      In contrast, a posteriori knowledge comes to us through our experience – literally, post or after our perceptions. A posteriori knowledge requires that we gather new information to verify, such as synthetic statements like “Bill is a bachelor” or “Bill has 10 apples in a basket, and 10 on the counter, making 20 in total”. We’ll have to go and consult with Bill to know if either of these statements are true – no amount of thinking can override our need to gather new information.

      While in philosophy the terms are mostly used in reference to logic and Kant, the difference between a priori and a posteriori knowledge is essential in machine learning and artificial intelligence. Siri, Google Now, and other new technologies rely on creating systems that mix pre-programmed structures (a priori knowledge) with millions of examples gathered from the real world (a posteriori knowledge).

      These terms may seem redundant when placed in context with “analytic and synthetic reasoning” and “logical and causal possibility,” but there are a few different ways frame these distinctions in context with each other. Next week, I will attempt to put all of the distinctions I’ve covered into context with each other in order to explore the various ways these terms can overlap and conflict.

      Posted in Series | 29 Comments | Tagged a posteriori, a priori, academia, epistemology, knowledge, lexicon, philosophy, vocabulary
    • The Philosopher’s Lexicon: Analytic and Synthetic Reasoning

      Posted at 12:30 pm by Michelle Joelle, on May 8, 2015

      Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go. 

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      This week’s entry into the lexicon features yet another epistemological distinction: the difference between analytic and synthetic reasoning. These are common terms you will find in many works and texts books, but for clear and concise explanations of these terms, see Kant’s Groundwork for the Metaphysics of Morals, Nils Ch. Rauhut’s Ultimate Questions and A. C. Grayling’s An Introduction to Philosophical Logic. 

      Let’s jump right in.

      An analytic statement is one where the truth of the statement can be determined by the internal relationships between the words or symbols within the statement. Analytic reasoning looks to the internal consistency of a given set of symbols, statements, or ideas according to a particular theoretical system. Given certain rules, no outside information is needed – all of you have know is how words or symbols relate to each other. For example, take the statement: “A bachelor is an unmarried man.” You don’t have to have any knowledge of the world beyond the definition of the words involved to affirm that within the common sense of our grammar, this statement is true, and more fundamentally, because this statement is a definition, it can be used analytically regardless of whether this definition matches our typical use (though in this case, it does).

      Another example of a purely analytic statement comes from Augustine’s Soliloquies. In his attempt to ground an argument for the immortality of truth without the use of any empirical or worldly knowledge save the rules of grammar, he states (in rough paraphrase):

      If the world will last forever, then it is true that the world will last.

      This is an analytical tautology, or rather, an axiom, because it depends on no outside information to be proven true. It’s truth is self-evident. It doesn’t matter if it were known beyond the shadow of a doubt that the world were to end to tomorrow – this statement would still be true because of it’s conditional form. The relationship between the words in the proposition render it infallible. In fact, Augustine then goes on to claim:

      If the world will not last forever, then it is true that world will not last.

      From this, Augustine then deduces that whether or not the world lasts forever, truth itself will, meaning that Truth (now with a capital T) is an ontologically independent concept and not just an epistemological construct dependent on our evaluation of reality. It takes a few additional premises and extrapolations, and the validity and use-value of this argument are certainly debatable, but the main focus here is that the causal realities of the world are not relevant to the truth value of either of these statements. All that matters is the maintenance of internal consistency (and I’m deliberately leaving Tarski out of this in the name of simplicity, but feel free to take him up in the comments if you so desire).

      In contrast, synthetic reasoning requires that we have additional information from the world in order to determine the truth value of a given statement. Example: “Bill is a bachelor.” In this case, you have to know a little something about Bill himself in order to determine the truth of this statement – particularly, whether or not he is married. One thing to note is that a statement like this cannot be analytically false – while a synthetic need not be an analytical tautology, it cannot contain any logical contradictions either. If we were to say that “Bill is both married and a bachelor,” we would be saying something that could be neither analytically true, nor synthetically verified. since the terms “married” and “bachelor” (in their simplest colloquial interpretations) contradict each other.

      Similarly, questions about the long-term existence of the world require rather a grand mixture of analytic and synthetic reasoning. We would need a lot of empirical evidence – synthetically connected information – from the world, but since we would be engaging in a prediction, we would also need to analytic reasoning to help us organize this evidence and find patterns, while also keeping us from speculating too wildly.

      But this mixture needs a solid ground in one type of reasoning or the other, and it also requires a lot of awareness. Augustine’s first attempt to prove the immortality of truth in the Soliloquies makes liberal use of analytic statements and empirical observations, but because Augustine doesn’t recognize that he is mixing the two categories, he ends up in a contradiction, leading him to start over with a cleaner, more purely analytic slate. Of course, we can and do mix these types of reasoning successfully all the time, but typically only when we do so intentionally.

      As Godel proved, a system can either be axiomatically (internally) consistent, or it can be synthetically comprehensive, but it cannot be both. How we use and mix the analytic and synthetic modes of reasoning really does matter, whether we’re checking on Bill’s marital status or testing the limits of mathematical axioms – and it requires a great deal of self-awareness. Because of this, I would say that this bit of jargon is rather useful.

      Posted in Series | 10 Comments | Tagged academia, analytic truth, definitions, epistemology, kant, knowledge, lexicon, logic, philosophy, reason, synthetic truth, truth claims, vocabulary, words
    • The Philosopher’s Lexicon: Ontology and Epistemology

      Posted at 1:00 pm by Michelle Joelle, on April 24, 2015

      Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go. 

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      One of the words for this week is “ontology”. Inspired by the post “Down With Reality” from the blog Blogging Is a Responsibility, I realized that no philosopher’s lexicon can be complete without this word. However, taken on its own, “ontology” is a tricky business, and so I will be pairing it with another philosophical concept: epistemology. Taken together, these terms are far easier to understand than they are in isolation.

      Ontology is, technically speaking, the study of being itself. What does it mean for something to exist? What does it mean for something to be “real”? You will often hear this term within the context of a debate over the “ontological status” of some proposed entity. What makes this a murky question is that the answer often comes in terms of degrees or sub-definitions.

      For example, when a philosopher raises questions about the ontological status of counting numbers, the question isn’t just asking whether or not counting numbers are real, but in what way they can be said to be real. Are they symbols which signify some conceptual reality that exists independently of themselves? Or is the concept of “number” bound up within the symbol itself? Are numbers actual objects of knowledge, or merely tools which aid our human knowledge, and not themselves objects of that knowledge?

      Epistemology is often posited as an alternative to ontology, as we see in the example above. Epistemology, strictly speaking, is the study of knowledge, and it too can often be found in the form of an adjective, treading in the murky waters of degree and sub-definition. When we ask about the epistemological status of numbers, we are primarily attempting to classify in what ways numbers can be known, and in what ways they aid in giving us knowledge of true things outside of our minds.

      To put it simply, ontology is about the nature of existence, and epistemology is about the way we know and understand things which can be said or thought to exist. These terms become most confusing when we mix them together, either intentionally or unintentionally.

      One example of an intentional collapse of the terms comes to us from Plato’s Republic. In the Republic, Socrates argues that all things which are ontologically real must be epistemologically knowable to a parallel degree, and then takes the converse to be equally true. Individual physical things are only knowable to individual people who have encountered those physical objects during their short lives, and are thus only real in a very limited way. However the idea behind a given physical object – its category, or the mathematical concepts that compose it – can be known with or without physical engagement with any particular object, and are thus real in a way that physical objects never can be. For instance, you may see many different individual chairs come and go, but the idea of the chair exists in your mind and in your knowledge regardless. Beyond that, your knowledge of the shapes made by those chairs can exist with or without any experience with any particular physical object at all. And beyond that, the pure ideas of “order” and “goodness” are independently knowable to anyone in any time, and are thus the most real of all. The union of the ontological and the epistemological here is the foundation of what people think of as Plato’s “theory of forms”, requiring an assumption of metaphysical ontology. Taken more empirically, such a union can lead to Berkley’s idealism, requiring an omniscient figure to explain away the threat of ontological solipsism.

      While the intentional collapse of ontology and epistemology is plenty objectionable to many philosophers and thinkers who would see these two qualifiers as explicitly separate, I think that the unintentional collapse of the two terms is far more dangerous. I think, however, that I’ve covered this as thoroughly as I am currently able in my posts on teaching, language, and the de dicto/de re distinction. However, keeping these two categories completely separate is not just itself a difficult task, but it raises a whole new set of difficulties about whether – and how – we can ever encounter and understand reality just as it is, or if we’ll only ever be able to develop our own mediated version of it.

      In other words, we might just be finding our way into an epistemological solipsism instead. And if the ontological and epistemological are truly separate, is there any way to know if we’ve ever known something real?

      Posted in Series | 14 Comments | Tagged academia, definitions, epistemology, knowledge, lexicon, ontology, philosophy, reality, vocabulary, words
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