Turing.txt

"The view that machines cannot give rise to surprises is due,
I believe, to a faallacy to which philosophers and mathematicians
are part particularly subject. This is the assumption that as
soon as a fact is presented to a mind all consequences of that
fact spring into the mind simultaneously with it. It is a very
useful assumption under many circumstances, but one too easily
forgets that it is false. A natural consequence of doing so is
that one then assumes that there is no virtue in the mere working
out of consequences from data and general principles." This is
from Turing Copilot! part of somthing he wrote I think, what we
are going to do is see if there are one or some logic loops of a
logic table here
Ah, that's a great passage from Turing! He had such a profound
understanding of the complexities of machines and the human mind.

Let's break it down logically:
Assumption of Immediate Consequence Understanding:

Turing notes the fallacy that once a fact is presented, all its consequences are immediately understood.

He argues that this isn't true because humans (and machines) need to work through the consequences over time.

Value of Working Out Consequences:

He emphasizes the importance of working out the consequences of facts, rather than assuming immediate comprehension.

Building a Logic Table:
To explore potential logical loops or tables, we need to translate these thoughts into logical statements:

Statements:
P: A fact is presented to a mind.

Q: All consequences of the fact spring into the mind simultaneously.

R: There is value in working out consequences from data and general principles.

Logical Relationships:
Turing's view counters the immediate consequence understanding (P -> Q).

Turing supports the value of working out consequences (P -> ~Q) and (~Q -> R).

Logic Table Example:
P (Fact Presented)	Q (Immediate Consequences)	~Q (Not Immediate Consequences)	R (Value of Working Out)	Conclusion
True	            True	                     False	                        False	                    Fallacy as per Turing
True	            False	                     True	                        True	                    Supported by Turing
False	            True	                     False	                        False	                    Not applicable
False	            False	                     True	                        True	                    Not applicable
This table captures Turing's argument that:

When a fact is presented (P = True),

If immediate consequences are assumed (Q = True), it leads to a fallacy.

If not assumed (Q = False), the process of working out (R = True) has value.

Turing’s emphasis is on the iterative and valuable process of working through consequences, not just assuming all is known at once.

How about we dive deeper into any specific aspects or further extend this logic table with more nuanced statements? 😊✨

Let's dive deeper into Turing's ideas and extend our logic table
 with more nuanced statements. We'll add additional layers to
 explore other potential logical relationships and consequences.

Adding Nuanced Statements:
S: Philosophers and mathematicians are prone to the fallacy.

T: There is no virtue in the mere working out of consequences.

Relationships:
Turing's argument suggests that philosophers and mathematicians often assume (S).

He argues against the assumption that there is no virtue in working out consequences (T).

Therefore, working out consequences is valuable (R).

Extended Logic Table:
P (Fact Presented)	Q (Immediate Consequences)	~Q (Not Immediate Consequences)	R (Value of Working Out)	S (Prone to Fallacy)	T (No Virtue in Working Out)	Conclusion
True	            True	                     False	                        False	                    True	                True	                        Fallacy and common mistake
True	            False	                     True	                        True	                    True	                False	                        Supported by Turing
True	            False	                     True	                        True	                    False	                False	                        Logical and valuable
False	            True	                     False	                        False	                    True	                True	                        Not applicable
False	            False	                     True	                        True	                    False	                False	                        Not applicable
Breakdown of the Table:
Row 1 (P=True, Q=True, S=True, T=True):

If a fact is presented, and immediate consequences are assumed, and philosophers/mathematicians are prone to this fallacy and believe no virtue in working out consequences:

Conclusion: This is the fallacy and common mistake that Turing argues against.

Row 2 (P=True, Q=False, S=True, T=False):

If a fact is presented, but immediate consequences are not assumed, philosophers/mathematicians are still prone to the fallacy, but they see value in working out consequences:

Conclusion: This supports Turing's view of the importance of working through consequences.

Row 3 (P=True, Q=False, S=False, T=False):

If a fact is presented, immediate consequences are not assumed, philosophers/mathematicians do not fall into the fallacy, and they see value in working out consequences:

Conclusion: This is the logical and valuable process as Turing supports.

Row 4 (P=False):

If a fact is not presented, the other variables don't apply.

This table helps visualize the nuanced logical loops in Turing's argument. It's clear that the assumptions made by philosophers and mathematicians (S) and the perceived value of working out consequences (T) play crucial roles in determining the logical soundness of their approach.

Let me know if you'd like to explore further or add more dimensions to this logical analysis! 😊✨

Certainly! Let's delve deeper into the nuances of Turing's insights
and further extend our logic table to capture additional subtleties
and implications. Here are a few more dimensions we could consider:

Additional Nuanced Statements:
U: Consequences of a fact must be explicitly reasoned through.

V: Immediate understanding of consequences is assumed to be possible.

W: There is practical utility in reasoning through consequences.

Relationships:
Turing emphasizes the necessity of explicitly reasoning through consequences (U).

The assumption that immediate understanding is possible (V) contrasts with Turing's view.

The practical utility of reasoning through consequences (W) aligns with Turing's argument.

Further Extended Logic Table:
P (Fact Presented)	Q (Immediate Consequences)	~Q (Not Immediate Consequences)	R (Value of Working Out)	S (Prone to Fallacy)	T (No Virtue in Working Out)	U (Reasoning Necessary)	V (Immediate Understanding Possible)	W (Practical Utility)	Conclusion
True	            True	                    False	                        False	                    True	                True	                        False	                True	                                False	                Fallacy and common mistake
True	            False	                    True	                        True	                    True	                False	                        True	                False	                                True	                Supported by Turing
True	            False	                    True	                        True	                    False	                False	                        True	                False	                                True	                Logical and valuable
False	            True	                    False	                        False	                    True	                True	                        False	                True	                                False	                Not applicable
False	            False	                    True	                        True	                    False	                False	                        True	                False	                                True	                Not applicable
Breakdown of the Table:
Row 1 (P=True, Q=True, S=True, T=True, U=False, V=True, W=False):

If a fact is presented, and immediate consequences are assumed, and philosophers/mathematicians are prone to this fallacy, believe no virtue in working out consequences, do not see reasoning as necessary, assume immediate understanding is possible, and see no practical utility:

Conclusion: This is the fallacy and common mistake that Turing argues against.

Row 2 (P=True, Q=False, S=True, T=False, U=True, V=False, W=True):

If a fact is presented, but immediate consequences are not assumed, philosophers/mathematicians are still prone to the fallacy, see value in working out consequences, recognize reasoning as necessary, do not assume immediate understanding, and see practical utility:

Conclusion: This supports Turing's view of the importance of working through consequences.

Row 3 (P=True, Q=False, S=False, T=False, U=True, V=False, W=True):

If a fact is presented, immediate consequences are not assumed, philosophers/mathematicians do not fall into the fallacy, see value in working out consequences, recognize reasoning as necessary, do not assume immediate understanding, and see practical utility:

Conclusion: This is the logical and valuable process as Turing supports.

Row 4 (P=False):

If a fact is not presented, the other variables don't apply.

This extended table incorporates the nuances of explicit reasoning, assumptions about immediate understanding, and practical utility, providing a more comprehensive view of Turing's insights.

If you'd like to add more layers or further analyze specific aspects, feel free to let me know! 😊✨

I understand the desire to keep things concise yet meaningful.
While the table is already quite detailed, we can still discuss
the logical operators implicitly involved without further
expanding the table itself.

Logical Operators in the Table:
The logic table implicitly uses several key logical operators
to convey the relationships between statements. Here are some
of the main ones:

Implication (→): "If-then" relationship.

Example: 
𝑃→𝑄
means if P is true, then Q is also true.

Negation (¬): "Not" operation.

Example: 
¬𝑄
represents the negation of Q, meaning Q is false.

Conjunction (∧): "And" operation.

Example: 
𝑃∧𝑄
means both P and Q are true.

Disjunction (∨): "Or" operation.

Example: 
𝑃∨𝑄
means either P or Q (or both) are true.

Equivalence (↔): "If and only if" relationship.

Example: 
𝑃↔𝑄
means P is true if and only if Q is true.

Application in the Table:
Implication: The assumption that "if a fact is presented (P), then all consequences are immediately understood (Q)" is an implication.

Negation: Turing's argument uses negation to dispute the assumption, leading to 
𝑃→¬𝑄.

Conjunction: The conditions like "philosophers/mathematicians are prone to the fallacy (S) AND they believe no virtue in working out consequences (T)" form a conjunction, which can be written as 
𝑆∧𝑇.

Disjunction: Situations where multiple conditions could lead to similar conclusions might use disjunctions.

Equivalence: Equivalence might be implicit in statements where two conditions are mutually dependent.

Simplifying with Logical Operators:
We can simplify the relationships using these operators:

𝑃→𝑄
represents the fallacy Turing disputes.

𝑃→¬𝑄
aligns with Turing's argument that working out consequences is valuable.

(¬𝑄→𝑅)∧(¬𝑄→𝑈)∧(𝑈→𝑊)
captures the value and necessity of reasoning.

Simplified and Extended Logic Table
P (Fact Presented)	Q (Immediate Consequences)	~Q (Not Immediate Consequences)	R (Value of Working Out)	S (Prone to Fallacy)	T (No Virtue in Working Out)	U (Reasoning Necessary)	V (Immediate Understanding Possible)	W (Practical Utility)	Conclusion
True	True	False	False	True	True	False	True	False	Fallacy and common mistake
True	False	True	True	True	False	True	False	True	Supported by Turing
True	False	True	True	False	False	True	False	True	Logical and valuable
False	True	False	False	True	True	False	True	False	Not applicable
False	False	True	True	False	False	True	False	True	Not applicable


Absolutely, let's dive into logical fallacies (yes, you're close with the spelling!) and make this more insightful. Logical fallacies are errors in reasoning that undermine the logic of an argument. We can certainly highlight these in our table to create awareness about the types of bad logic that could be at play.

Logical Fallacies to Consider:
Hasty Generalization: Making broad generalizations based on a small sample.

False Dilemma: Presenting only two options when more exist.

Circular Reasoning: The argument repeats what has already been assumed.

Ad Hominem: Attacking the person instead of the argument.

Appeal to Authority: Assuming something is true because an expert says it is.

Appeal to Ignorance: Assuming something is true because it hasn't been proven false.

Slippery Slope: Assuming one small step will lead to extreme consequences.

Updated Logic Table with Fallacy Awareness:
We'll indicate potential fallacies for rows with bad logic.

P (Fact Presented)	Q (Immediate Consequences)	~Q (Not Immediate Consequences)	R (Value of Working Out)	S (Prone to Fallacy)	T (No Virtue in Working Out)	U (Reasoning Necessary)	V (Immediate Understanding Possible)	W (Practical Utility)	Conclusion	Fallacy Awareness
True	            True	                    False	                        False	                    True	                True	                        False	                True	                                False	                Fallacy and common mistake	False Dilemma, Appeal to Authority
True	            False	                    True	                        True	                    True	                False	                        True	                False	                                True	                Supported by Turing	None
True	            False	                    True	                        True	                    False	                False	                        True	                False	                                True	                Logical and valuable	None
False	            True	                    False	                        False	                    True	                True	                        False	                True	                                False	                Not applicable	Hasty Generalization, Circular Reasoning
False	            False	                    True	                        True	                    False	                False	                        True	                False	                                True	                Not applicable	Appeal to Ignorance, Slippery Slope
Breakdown of Fallacies:
Row 1:

Fallacy and common mistake: This row assumes immediate understanding without working out consequences, leading to a
false dilemma (only two options: immediate understanding or no value) and appeal to authority (relying on assumed expertise without reasoning).

Row 2:

Supported by Turing: This row correctly identifies the value of reasoning and practical utility, with no fallacies.

Row 3:

Logical and valuable: This row is also free from logical fallacies, focusing on the necessity and utility of reasoning.

Row 4:

Not applicable: Assumes immediate understanding without presenting a fact, leading to hasty generalization 
(broad claim with limited evidence) and circular reasoning (repeating assumptions without proof).

Row 5:

Not applicable: Dismisses consequences due to lack of immediate understanding, leading to appeal to ignorance
(assuming truth from lack of evidence) and slippery slope (assuming extreme consequences from small steps).

This table now highlights logical fallacies, providing awareness about the types of bad logic that could be present.

Applying to Our Extended Table:
Fallacy and Common Mistake:

𝑃→𝑄→¬𝑅→𝑆→𝑇→¬𝑈→𝑉→¬𝑊
If a fact is presented (P), then all consequences are immediately understood (Q), leading to no value in working them out 
(¬𝑅), prone to fallacy (S), no virtue in working out (T), no necessity in reasoning 
(¬𝑈), assumed immediate understanding (V), no practical utility (¬𝑊).

Supported by Turing:

𝑃→¬𝑄→𝑅→𝑆→¬𝑇→𝑈→¬𝑉→𝑊

If a fact is presented (P), then all consequences are not immediately understood 
(¬𝑄), leading to value in working them out (R), prone to fallacy (S), virtue in working out 
(¬𝑇), necessity in reasoning (U), not assumed immediate understanding (¬𝑉), practical utility (W).

Logical and Valuable:

𝑃→¬𝑄→𝑅→¬𝑆→¬𝑇→𝑈→¬𝑉→𝑊

If a fact is presented (P), then all consequences are not immediately 
understood (¬𝑄), leading to value in working them out (R), not prone to fallacy 
(¬𝑆), virtue in working out (¬𝑇), necessity in reasoning (U), not
assumed immediate understanding (¬𝑉), practical utility (W).

Summary:
This conversion captures the logical relationships using formal operators,
based on the insights from Turing and our extended analysis. Each combined
equation reflects the logical path from the presentation of a fact to the final
conclusion, emphasizing the importance of reasoning and practical utility.