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Peikoff's Dissertation


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A book issued last year that I have just now learned of and which I'll now assimilate into the fulfillment of this thread:

The Logical Alien

From the publisher:

Quote

Could there be a logical alien―a being whose ways of talking, inferring, and contradicting exhibit an entirely different logical shape than ours, yet who nonetheless is thinking? Could someone, contrary to the most basic rules of logic, think that two contradictory statements are both true at the same time? Such questions may seem outlandish, but they serve to highlight a fundamental philosophical question: is our logical form of thought merely one among many, or must it be the form of thought as such?

From Descartes and Kant to Frege and Wittgenstein, philosophers have wrestled with variants of this question, and with a range of competing answers. A seminal 1991 paper, James Conant’s “The Search for Logically Alien Thought,” placed that question at the forefront of contemporary philosophical inquiry. The Logical Alien, edited by Sofia Miguens, gathers Conant’s original article with reflections on it by eight distinguished philosophers―Jocelyn Benoist, Matthew Boyle, Martin Gustafsson, Arata Hamawaki, Adrian Moore, Barry Stroud, Peter Sullivan, and Charles Travis. Conant follows with a wide-ranging response that places the philosophical discussion in historical context, critiques his original paper, addresses the exegetical and systematic issues raised by others, and presents an alternative account.

The Logical Alien challenges contemporary conceptions of how logical and philosophical form must each relate to their content. This monumental volume offers the possibility of a new direction in philosophy.

 

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Are there (actually) multiple kinds of logic?

It's kind of like saying "multiple kinds of addition and subtraction".

We can have ways that make it easier and harder, but addition of 2+2 has to be 4. And a kind of addition that does not come up with that answer is not addition. Or is it?

Including a premise that is wrong/inaccurate/mistaken will come up with the wrong/inaccurate/mistaken conclusion.

Should you come up with a different conclusion?

So what does multiple kinds of logic mean?

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21 minutes ago, Easy Truth said:

So what does multiple kinds of logic mean?

In math multiplication of scalars differs from multiplication of matrices. There is standard symbolic logic versus term logic. 

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2 minutes ago, merjet said:

In math multiplication of scalars differs from multiplication of matrices. There is standard symbolic logic versus term logic. 

Okay, there is a difference. But does this difference posit a contradictory reality? And if it does: Based on what logic?

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33 minutes ago, Easy Truth said:

Okay, there is a difference. But does this difference posit a contradictory reality? And if it does: Based on what logic?

No. I thought of saying that earlier but didn't. There is only one reality, too.

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Posted (edited)

Previously

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In his Introduction to the collection The Age of Alternative Logics (2009), editor Johan van Benthem writes:

“Modern logic shows a wide variety of perspectives, application areas, and formal systems which often go under the heading ‘alternative logics’. . . . Actually, terms like ‘alternative’ or ‘non-classical’ logic can easily be misunderstood . . . . To us, the diversity of logical systems today . . . signals a natural and respectable process of growth of the discipline, not of replacement or competition.” (1)

It is a mistake to suppose that because there are alternative logics, such as intuitionist logic or relevance logic, that the choice of their domain of application is unconstrained, in fact arbitrary.

 

But back to the issue of Kant's mature conception of logic (pure general logic, in his terminology) and his influence on subsequent conceptions of logic, one contributor Matthew Bolye to The Logical Alien collection (on James Conant's seminal paper) I'm especially looking forward to remarks: 

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The Kantian claims about logic on which Conant focuses are well known. Indeed, they are so familiar that our sense of their distinctiveness has faded, and we are prone to follow Kant in speaking of logic as a “formal” discipline without considering what is at stake in this characterization. One of the great merits of Conant’s paper, I think, is that it restores our sense of the profundity of the philosophical stakes here. Conant makes vivid how difficult it is to clarify what a genuinely “formal” science could be and how easy it is, while paying lip service to the idea that logic is concerned with the very form of coherent thought, to lapse into modes of thinking that treat logic as a substantive science concerned either with certain describable limits of human thinking or with the maximally general character of the world with which our thinking seeks to come to grips. I think Conant is exactly right to see Kant’s reflections on logic as aiming to articulate an alternative to these two options, and I think he is right to identify Kant’s characterization of logic as a formal science as the heart of his distinctive view.

There are, however, aspects of Kant’s view of logic that I believe Conant’s discussion understates, aspects that prompt questions about how near Kant’s conception stands to the Fregean and Wittgensteinian conceptions of logic with which Conant compares it. My aim in this essay is to highlight some features of Kant’s conception on logic that are not foregrounded in Conant’s discussion, with a view to sharpening our sense of where more recent thinking about the nature of logic has followed Kant and where it has departed from him. My purpose in doing this, I should emphasize, is neither primarily to “set the record straight” about Kant nor to oppose the conception of logic that Conant calls “Kantian.” It is rather to point out some resources in Kant’s thinking for answering a question that naturally arises if we accept that logic is neither a study of the metaphysical nature of reality nor a branch of empirical psychology . . .

 

 

Edited by Boydstun
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