Talons Philosophy

An Open Online Highschool Philosophy Course

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Learning and Metaphysics

Metaphysical Constructivism

#philosodoodles

Now making my third pass at the philosophy 12 course, I have approached this year’s unit on Metaphysics as an opportunity to crystalize the course methods as an expression of the values underpinning it. I’ve learned in the past two years that to embrace a constructivist view of epistemology presents the idea of course design as a confrontation with the paradox at the heart of institutional learning: that schools ought provide learning experiences which students ‘own’ and direct with increasing autonomy and agency as they move through school.

But I’ve also learned that this is no straightforward thing.

Emergence presents a rigorous test:

“…if educators wish to encourage the emergence of meaning in the classroom, then the meanings that emerge in classrooms cannot and should not be pre-determined before the ‘event’ of their emergence.”

Osberg and Biesta

On one hand, we must consider the traditional obligations of school: to evaluate and assess its own performance in properly equipping young people with the skills, proficiencies and base knowledges deemed of value to society. But we must also reckon with the contradiction to emergence that is involved in then deciding beforehand what those skills, proficiencies and base knowledges are to be in the first place.

Notably, this contradiction is addressed in part by the critical praxis presented by Paulo Freire, who says that

“…the program content of the problem-posing method – dialogical par excellence – is constituted and organized by the students’ view of the world, where their own generative themes are found. The content thus constantly expands and renews itself. The task of the dialogical teacher in an interdisciplinary team working on the thematic universe revealed by their investigation is to “re-present” that universe to the people from whom she or he received it – and “re-present” is not as a lecture, but as a problem.”

The necessity to pursue an emergent view of knowledge becomes especially important in our present times in multicultural Canada (and in the broader sense, in the course’s online sphere). Osberg and Biesta write that

“In contemporary multicultural societies, the difficulty with education as planned enculturation lies in the question of who decides what or whose culture should be promoted through education. The problem of ‘educational enculturation’ is therefore of considerable concern to theorists grappling with the issues raised by multiculturalism.

“If we hold that meaning is emergent, and we insist on a strict interpretation of emergence (i.e. what emerges is more than the sum of its parts and therefore not predictable from the ‘ground’ it emerges from) then the idea that educators can (or should) control the meanings that emerge in the classroom becomes problematic. In other words the notion of emergent meaning is incompatible with the aims of education, traditionally conceived.”

And so we must conceive of education differently, perhaps no place moreso than in a class like Philosophy 12 during a unit on Metaphysics, which in a certain sense must be approached as a cultivation and aggregation of diverse subjectivities. While it is apparent in the breadth of the course material, such a focus lends itself admirably to the pursuit of metaphysics.

So in one arc of the class’ discourse, Angela begs the question of endless subjectivity in her post, Whoa, Slow Down

“One fixed answer that is true to everything and everyone is way too easy, but some people can’t seem to accept that there is no answer. At the same time, we also tend to deny that every answer is different for everyone. Why is it that we just can’t accept that?”

While Liam retraces Descartes footsteps:

“…perhaps all of ‘reality’ is simply our minds composing things for us to see, smell, taste, hear, and touch, even though they don’t exist. Perhaps nothing exists, but how could that be? We are here, I am typing this, aren’t I? If I am not, and I do not exist, and nothing exists, then what is allowing me to experience things?”

This search for meaning is arising across a few other posts this week as well, with ventures into solipsism, animal consciousness, and the almighty void of nothingness itself. These questions, as with those posed by Avery with respect to the existence of numbers “Five fingers are material objects and so are five sheep, but does five itself exist materially in the same manner?” – are those surrounding the various subjectivities at the heart of metaphysics: “What is…” and “What is it like…”  And so we find ourselves this week asking ourselves whether what we have gained in knowledge and experience during our study thus far “exists materially in the same manner.”

And if it does, how might we understand its existence? What is it, in other words? And what is it like?

Last year, our encounter with metaphysics was guided by Osberg and Biesta’s suggestion of the “learning object,” who contend that:

“for the process of knowledge production to occur it is necessary to assume that the meaning of a particular ‘knowledge object’ exists in a stable form such that the ‘knowledge object’ can be used like a ‘building block’ in the production of new abstract knowledge objects. This idea, however, is precisely what an emergentist epistemology denies. Because the meaning of any new knowledge ‘emerges’ would be highly specific to the complex system from which is emerged, it follows that no ‘knowledge object’ can retain its meaning in a different situation.”

The creation of such ‘objects of learning’ provides a worthwhile otherwise in the pursuit of an education which lives up to our multicultural ideals, as their construction demands that learners confront the dual questions which drive societal reinvention and human progress, where we ask ourselves, Who am I? and Who are we? Building on the ideas of Michel Foucault, who defined Enlightenment as “a philosophical life in which the critique of what we are is at one and the same time the historical analysis of the limits that are imposed on us and an experiment with the possibility of going beyond them,” school should aspire to such a notion of learning.

 

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Mathematical Platonism: Have Some Delicious Pi

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices.

Øystein Linnebo, Platonism in the Philosophy of Mathematics

In my previous blog post, I wrote at length about what numbers are (and consequently, whether my math homework exists or not). Unsurprisingly, I was not the first philosopher to ponder the properties of mathematical objects. The inspiration for the theory of mathematical Platonism dates back to Plato and his Theory of Forms, as one can infer from the name of the theory.

However, mathematical Platonism is not directly derived from Plato’s Theory of Forms; instead, many of its principles are based upon the work of the 19th-20th century mathematician and philosopher Gottlob Frege. Frege’s works have been adapted and intertwined with similar ideas, and an modern expert in the field of mathematical Platonism is Øystein Linnebo, whose ideas I will be quoting at length in this post.

plato world

Image taken from abyss.uoregon.edu and used/modified under Creative Commons License.

Øystein Linnebo is the author of Platonism in the Philosophy of Mathematics, and he begins by describing three core attributes of the theory:

Mathematical platonism can be defined as the conjunction of the following three theses:

Existence.
There are mathematical objects.

Abstractness.
Mathematical objects are abstract.

Independence.
Mathematical objects are independent of intelligent agents and their language, thought, and practices.

 

A decent grasp of these three ideas is essential for an understanding of mathematical Platonism, so I’ll go through them one by one in more detail.

 

Existence

Linnebo starts by referencing some of Frege’s ideas:

The Fregean argument is based on two premises, the first of which concerns the semantics of the language of mathematics:

Classical Semantics.
The singular terms of the language of mathematics purport to refer to mathematical objects, and its first-order quantifiers purport to range over such objects.

Truth.
Most sentences accepted as mathematical theorems are true (regardless of their syntactic and semantic structure).

These premises are worded in complicated ways, but they boil down to simple logic:

1) Mathematical theorems are true.

2) Mathematical theorems refer to mathematical objects.

3) Therefore, mathematical objects exist.

The article goes into a little more detail (you can read more here), but this is the gist of it.

(Please note that the above logic is not intended to be sound. Instead, it is intended to facilitate the understanding of the idea of existence.)

 

Abstractness

Abstractness says that every mathematical object is abstract, where an object is said to be abstract just in case it is non-spatiotemporal and (therefore) causally inefficacious . . .

. . . For if these objects had spatiotemporal locations, then actual mathematical practice would be misguided and inadequate, since pure mathematicians ought then to take an interest in the locations of their objects, just as physicists take an interest in the locations of theirs.

The second of the three ideas, abstraction, is much less complicated than existence. If an object is abstract, it does not exist in space-time (also known as the material world). Other entities that are non-spatiotemporal may include ideas, thoughts, and concepts, depending on what philosophical outlook you have.

Abstract objects exist in an abstract world, sometimes thought of as a mirror to our own. This is one area of Platonism and mathematical Platonism differ. While Platonism states that the abstract world in the more fundamental/superior world to our own, mathematical Platonism does not assert this superiority.

 

Independence

Independence says that mathematical objects, if there are any, are independent of intelligent agents and their language, thought, and practices . . .

. . . had there not been any intelligent agents, or had their language, thought, or practices been different, there would still have been mathematical objects.

The last of the three ideas, independence, is perhaps the simplest idea of the three. Independence states that mathematical entities are more than a human construct, and that they exist independently of us. This means that they were discovered by humans instead of created by humans, which is an important distinction. What independence implies is that (if they exist), other conscious entities would also discover mathematics in a similar way to us, or at least the basic concepts would be the same.

bw_dice

Image taken from pixabay.com and used/modified under Creative Commons License.

To summarize, mathematical Platonism states that mathematical objects (such as 3 and π) exist, are non-spatiotemporal, and were discovered as opposed to created by humans. This theory for the explanation of the existence of mathematical objects makes the most sense to me – for as I discussed in my earlier blog post, numbers don’t really exist in the physical world (space-time). Five fingers are material objects and so are five sheep, but does five itself exist materially in the same manner? This theory offers what I see to be sound explanations for the properties of mathematical entities, helping to lay the foundations for the entire field of mathematics.

 

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Metaphysical Emergence and the Discussable Object

Unplug'd 2012 Map Prep

Photo courtesy of Alan Levine

“It is to the reality which mediates [people], and to the perception of that reality held by educators and people, that we must go to find the program content of education.”

Paulo Freire

As we set out to encounter Metaphysics, my ambition as teacher is to help frame the creation of a learning object as an attempt at authentic social constructivism. Today we began with a conversation based on another Freire quote (about education being a ‘with’ transaction between teachers and students much more than a ‘to’ or ‘for’), and came away with a loose timeline and list of objectives and ambitions for the unit in the coming week.

“The investigation of […] people’s ‘thematic universe’ – the complex of their ‘generative themes’ – inaugurates the dialogue of education as the practice of freedom.”

Freire

Our task, in general terms, will be to encounter the lives and ideas of metaphysicians. And, in asking of ourselves what we can interpret of their essential guiding questions, to engage in the study of our own metaphysical thoughts and conceptions. This will happen in exposition on the class blog, connections made through comments and conversation, and inquiry through reflection and dialogue.

My hope is that these activities can be engaged in with the following in mind:

“…knowledge is neither a representation of something more ‘real’ than itself, nor an ‘object’ that can be transferred from one place to the next. Knowledge is understood, rather, to ’emerge’ as we, as human beings, participate in the world. Knowledge, in other words, does not exist except in participatory actions.”

Osberg and Biesta

Thus far the group has agreed to the following objectives:

    • Delve into a metaphysical thinker’s life and ideas
    • Put their ideas into the context of larger theory, culture and critique
    • Evaluate one of your philosopher’s questions, ideas, or arguments with your own ideas about validity, truth and soundness
    • Narrate and participate in the creation of a collective representation of our learning about Metaphysics, and metaphysicians

This will begin with a blog post, wherein participants will demonstrate research and introduction to a philosopher of Metaphysics, and strive to respond to the following questions:

    • How did the philosopher’s life or biography influence their philosophical development?
    • What ideas or concepts are they credited with, or notable for?
    • How have these ideas been built on or incorporated into our modern zeitgeist or mindset?
    • What personal response do you have to the topics your philosopher explored?
    • What do you find confusing or difficult to conceive of, in your philosopher’s thinking?

And from there work through individual reflections and assessments of our own ideas contrasted against those of notable metaphysicians, as well as one another. Over the course of the following week, these experiences, discussions, reflections and activities will culminate in the creation of what for now we will call the Discussable Object. The logic here is derived from Osberg and Biesta again:

“…if educators wish to encourage the emergence of meaning in the classroom, then the meanings that emerge in classrooms cannot and should not be pre-determined before the ‘event’ of their emergence.”

At present, the idea of the creation of the Discussable Object as an authentic constructivist summative assessment is unrefined; but the general intention is this: to create a collective representation of our individual journeys of understanding metaphysics.

This raises an interesting contradiction within emergentist epistemology that we will likely spend time in the coming week discussing, that:

“for the process of knowledge production to occur it is necessary to assume that the meaning of a particular ‘knowledge object’ exists in a stable form such that the ‘knowledge object’ can be used like a ‘building block’ in the production of new abstract knowledge objects. This idea, however, is precisely what an emergentist epistemology denies. Because the meaning of any new knowledge ’emerges’ would be highly specific to the complex system from which is emerged, it follows that no ‘knowledge object’ can retain its meaning in a different situation.”

This marks I think a necessary crossroads in the creation of the blended open-online course, as 24 of our participants will engaged in something that may only create significance between themselves; I wonder about our ability – or the validity of the attempt – to share this process beyond the constructivism of our physical classroom. Here I am left thinking about Jesse Stommel‘s post on Hybrid Pedagogy, How to Build an Ethical Online Course, and the idea that:

“We must consider how we’ll create pathways between the learning that happens in a room and the learning that happens on the web.”

Indeed.

 
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