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Lecture

Feb 9 2011 Lecture Note

1 Page
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Department
Philosophy
Course Code
PHIL 1050
Professor
Mark Mc Cullagh

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February 9th Lecture
Pg. 115-125
Chapter 5: Frege’s New Logical World
- Both Aristotle & Descartes held that we know what is true, and hoow do we know the truths of geometry and
arithmetic and physics, because certain fundamental principle are known through institution & other truths are
validly deduced from these fundamental principles
- New science brought on in 17th century led to many philosophical problems
Why are the experimental & observational methods of modern science reliable?
If science depends on inferences made from observation & experiment what is the basis for our knowledge
of mathematics & for the special certainty that propositions in geometry & arithmetic seem to have?
- in 18th century, the new sciences of physics & chemistry seemed different from geometry & arithmetic
Unlike the new sciences, geometry & arithmetic did seem to depend on self-evident principles
- Descartes & Leibniz thought of physical objects as bundles of properties attached to a substance
- Descartes thought of mental objects as bundles of properties attached to a mental substance
Ideas are collection of properties attached to a mental substance… so an idea may be simple or complex
- Hume (18th century Scottish philosopher) used the IDEA
Thought some propositions are about matters of fact (eg. sky is blue,)
- Matters of fact can be discovered only from experience
- Other propositions are about (or true b/c of) relations among ideas
Hume’s proposal: True propositions that are about the relations among ideas can be known a priori, that is, in a
way not founded on any experience, essentially by a combination of what Descartes would have called
“natural light” and the method of analysis & synthesis. Propositions that aren’t about relations among our
ideas but instead are about the external world cant be known in this way
It doesn’t seem that mathematical truths can be obtained as relations among ideas
- Immanuel Kant (19th century philosopher) distinguished between propositions (or judgments as he would
have said) that are analytic & those that are synthetic”
in analytic judgments, but not in synthetic judgments the concept of the predicate contains the concept of
the subject
- Kant distinguished between priori & posteriori judgments
Priori judgements can be known by reason alone
A posteriori judgements cannot be known by reason alone but require the evidence provided by experience
- Kant suggests the world we experience and come to know is partly a world of our own creation
Frege, Logicism & Logic
- Freges alternative to Kant was: arithmetic & geometry are nothing but logic, & logic is certain & can be
known by reason alone

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Description
thFebruary 9 LecturePg 115125Chapter 5 Freges New Logical World Both AristotleDescartes held that we know what is true and hoow do we know the truths of geometry and arithmetic and physics because certain fundamental principle are known through institutionother truths are validly deduced from these fundamental principlesth New science brought on in 17 century led to many philosophical problems Why are the experimentalobservational methods of modern science reliable If science depends on inferences made from observationexperiment what is the basis for our knowledge of mathematicsfor the special certainty that propositions in geometryarithmetic seem to haveth in 18 century the new sciences of physicschemistry seemed different from geometryarithmeticUnlike the new sciences geometryarithmetic did seem to depend on selfevident principles DescartesLeibniz thought of physical objects as bundles of properties attached to a substance Descartes thought of mental objects as bundles of properties attached to a mental substance Ideas are collection of properties attached to a mental substance so an idea may be simple or complexth Hume18 century Scottish philosopher used the IDEAThought some propositions are about matters of facteg sky is blue
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